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Based on 2003.05931 LM, Eiichiro Komatsu, Kaloian D. Lozanov and Yuki Watanabe Effects of the gravitational Chern-Simons term during axion-SU(2) inflation Max Planck Institute for Astrophysics, Garching Leila Mirzagholi Zooming in on Axions in the Early Universe, June 2020, CERN
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Mar 12, 2023

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Page 1: mirzagholi.pdf - CERN Indico

Based on 2003.05931LM, Eiichiro Komatsu, Kaloian D. Lozanov and Yuki Watanabe

Effects of the gravitational Chern-Simons term during axion-SU(2) inflation

Max Planck Institute for Astrophysics, Garching

Leila Mirzagholi

Zooming in on Axions in the Early Universe, June 2020, CERN

Page 2: mirzagholi.pdf - CERN Indico

The Basics of the ModelSpectator axion-SU(2) Gauge Field

L = LEH + L' � 1

2(@�)2 � U(�)� 1

4F a

µ⌫F aµ⌫ +

�1�

4fF a

µ⌫F̃ aµ⌫

<latexit sha1_base64="Ah71J78SRQP0hNED2VolGCMwnzM=">AAACsHicdVFda9swFJW9ry77yrbHvYiFQUaZsZI0TR4GZWOhD3vooF47Ysdcy3KjVf5AkgvB6P/teW/7N5PdFNKyXRAcnXvPle65SSW40r7/x3Hv3X/w8NHe496Tp8+ev+i/fPVdlbWkLKClKOV5AooJXrBAcy3YeSUZ5IlgZ8nl5zZ/dsWk4mVxqjcVi3K4KHjGKWhLxf1fYQ56TUE0Xw3+iHducfPl2OD921R4BbJac4M/4D CTQBtimpEZhhVIzUHgkK75+9XIpoNhh3cLJwYvVmCb5DUOi9osVg3gm8v+ti4U9vMpxKTrZUXZHVWouUhZszC76l4v7g98j0ymB+M59r0ROZxOZxaMyYwczDHx/C4GaBsncf93mJa0zlmhqQCllsSvdNS0g1DBTC+sFauAXsIFW1pYQM5U1HSOG/zOMinOSmlPoXHH7ioayJXa5ImtbO1Td3Mt+a/cstbZLGp4UdWaFfT6oawWWJe4XR9OuWRUi40FQCW3f8V0DdY4bZfcmnAzKf4/CEbe3CPfJoOjT1s39tAb9BYNEUGH6AgdoxMUIOp4zqkTOSt37P5wYxeuS11nq3mNboX78y9RDtL9</latexit><latexit sha1_base64="Ah71J78SRQP0hNED2VolGCMwnzM=">AAACsHicdVFda9swFJW9ry77yrbHvYiFQUaZsZI0TR4GZWOhD3vooF47Ysdcy3KjVf5AkgvB6P/teW/7N5PdFNKyXRAcnXvPle65SSW40r7/x3Hv3X/w8NHe496Tp8+ev+i/fPVdlbWkLKClKOV5AooJXrBAcy3YeSUZ5IlgZ8nl5zZ/dsWk4mVxqjcVi3K4KHjGKWhLxf1fYQ56TUE0Xw3+iHducfPl2OD921R4BbJac4M/4D CTQBtimpEZhhVIzUHgkK75+9XIpoNhh3cLJwYvVmCb5DUOi9osVg3gm8v+ti4U9vMpxKTrZUXZHVWouUhZszC76l4v7g98j0ymB+M59r0ROZxOZxaMyYwczDHx/C4GaBsncf93mJa0zlmhqQCllsSvdNS0g1DBTC+sFauAXsIFW1pYQM5U1HSOG/zOMinOSmlPoXHH7ioayJXa5ImtbO1Td3Mt+a/cstbZLGp4UdWaFfT6oawWWJe4XR9OuWRUi40FQCW3f8V0DdY4bZfcmnAzKf4/CEbe3CPfJoOjT1s39tAb9BYNEUGH6AgdoxMUIOp4zqkTOSt37P5wYxeuS11nq3mNboX78y9RDtL9</latexit><latexit sha1_base64="Ah71J78SRQP0hNED2VolGCMwnzM=">AAACsHicdVFda9swFJW9ry77yrbHvYiFQUaZsZI0TR4GZWOhD3vooF47Ysdcy3KjVf5AkgvB6P/teW/7N5PdFNKyXRAcnXvPle65SSW40r7/x3Hv3X/w8NHe496Tp8+ev+i/fPVdlbWkLKClKOV5AooJXrBAcy3YeSUZ5IlgZ8nl5zZ/dsWk4mVxqjcVi3K4KHjGKWhLxf1fYQ56TUE0Xw3+iHducfPl2OD921R4BbJac4M/4D CTQBtimpEZhhVIzUHgkK75+9XIpoNhh3cLJwYvVmCb5DUOi9osVg3gm8v+ti4U9vMpxKTrZUXZHVWouUhZszC76l4v7g98j0ymB+M59r0ROZxOZxaMyYwczDHx/C4GaBsncf93mJa0zlmhqQCllsSvdNS0g1DBTC+sFauAXsIFW1pYQM5U1HSOG/zOMinOSmlPoXHH7ioayJXa5ImtbO1Td3Mt+a/cstbZLGp4UdWaFfT6oawWWJe4XR9OuWRUi40FQCW3f8V0DdY4bZfcmnAzKf4/CEbe3CPfJoOjT1s39tAb9BYNEUGH6AgdoxMUIOp4zqkTOSt37P5wYxeuS11nq3mNboX78y9RDtL9</latexit><latexit sha1_base64="Ah71J78SRQP0hNED2VolGCMwnzM=">AAACsHicdVFda9swFJW9ry77yrbHvYiFQUaZsZI0TR4GZWOhD3vooF47Ysdcy3KjVf5AkgvB6P/teW/7N5PdFNKyXRAcnXvPle65SSW40r7/x3Hv3X/w8NHe496Tp8+ev+i/fPVdlbWkLKClKOV5AooJXrBAcy3YeSUZ5IlgZ8nl5zZ/dsWk4mVxqjcVi3K4KHjGKWhLxf1fYQ56TUE0Xw3+iHducfPl2OD921R4BbJac4M/4D CTQBtimpEZhhVIzUHgkK75+9XIpoNhh3cLJwYvVmCb5DUOi9osVg3gm8v+ti4U9vMpxKTrZUXZHVWouUhZszC76l4v7g98j0ymB+M59r0ROZxOZxaMyYwczDHx/C4GaBsncf93mJa0zlmhqQCllsSvdNS0g1DBTC+sFauAXsIFW1pYQM5U1HSOG/zOMinOSmlPoXHH7ioayJXa5ImtbO1Td3Mt+a/cstbZLGp4UdWaFfT6oawWWJe4XR9OuWRUi40FQCW3f8V0DdY4bZfcmnAzKf4/CEbe3CPfJoOjT1s39tAb9BYNEUGH6AgdoxMUIOp4zqkTOSt37P5wYxeuS11nq3mNboX78y9RDtL9</latexit>

inflation action Spectator sector

Aa0 = 0, Aa

i = a(t)Q(t)�ai<latexit sha1_base64="dlAudZXWRkjE92StSoihrhy/+0A=">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</latexit><latexit sha1_base64="dlAudZXWRkjE92StSoihrhy/+0A=">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</latexit><latexit sha1_base64="dlAudZXWRkjE92StSoihrhy/+0A=">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</latexit><latexit sha1_base64="dlAudZXWRkjE92StSoihrhy/+0A=">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</latexit>

Slow-roll background solution

See the talks by Emma Dimastrogiovanni and Tomo Fujita

�A1i = (t̃+, t̃⇥, 0)

<latexit sha1_base64="UnVfpWuWDMofvcd6cW4MPjWceek=">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</latexit><latexit sha1_base64="UnVfpWuWDMofvcd6cW4MPjWceek=">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</latexit><latexit sha1_base64="UnVfpWuWDMofvcd6cW4MPjWceek=">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</latexit><latexit sha1_base64="UnVfpWuWDMofvcd6cW4MPjWceek=">AAACG3icdVDLSiNBFK1Wx0d0NOrSTWEQlJGmyzxMFoKPjUuFiQpJpqmuvtHC6gdVt4XQ5EPc+CtuXKi4Elz4N1ZixJlBDxSce8693LonSJU06Hmvztj4xI/JqemZwuzcz/mF4uLSiUkyLaApEpXos4AbUDKGJkpUcJZq4FGg4DS4PBj4p1egjUzi39hLoRPx81h2peBoJb9YboegkNO9P8yXdIeut1GqEHLs+7826WeRWxqB6W9Sb8MvljyXVWrVcoN67hbbrtXqlpRZnVUblLneECUywpFffG6HicgiiFEobkyLeSl2cq5RCgX9QjszkHJxyc+hZWnM7aZOPjyuT9esEtJuou2LkQ7VvydyHhnTiwLbGXG8MP97A/Err5Vht97JZZxmCLF4X9TNFMWEDpKiodQgUPUs4UJL+1cqLrjmAm2eBRvCx6X0e9LcchsuO66UdvdHaUyTFbJK1gkj22SXHJIj0iSCXJNbck8enBvnznl0nt5bx5zRzDL5B87LG2xOoJk=</latexit>

�A2i = (t̃⇥,�t̃+, 0)

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t̃L,R ⌘ 1p2(t̃+ ± it̃⇥)

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Gauge tensor perturbations

Maleknejad - Sheikh-Jabbari 2011

Maleknejad - Sheikh-Jabbari 2011, Adshead - Wyman 2012, Dimastrogiovanni - Fasiello - Tolley 2012, Namba - Dimastrogiovanni - Peloso 2013, Maleknejad - Sheikh-Jabbari 2013, Maleknejad - Sheikh-Jabbari - Soda 2013, Dimastrogiovanni - Peloso 2013, Adshead - Martinec -Wyman 2013, Dimastrogiovanni - Fasiello - Fujita 2016, Agrawal - Fujita - Komatsu 2017, Caldwell - Devulder 2017, Lozanov - Maleknejad - Komatsu 2018, Domcke et al 2018, …

ds2 = a2(⌧)h� d⌧2 + (1 + h̃+(⌧, z))dx

2 + (1� h̃+(⌧, z))dy2 + 2h̃⇥(⌧, z)dxdy + dz2

i

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Page 3: mirzagholi.pdf - CERN Indico

E.O.M. of GWs

1. Homogeneous solutions : GWs from vacuum fluctuations

H ⌘ a0/a<latexit sha1_base64="afZwKjP5eez9JGwjSmt7BE3h+Fo=">AAACAHicdVDLSgNBEJyNrxhfUS+Cl8Egelp3884t6CXHCEYDSQi9k0kyZPbhzGwgLPHir3jxoOLVz/Dm3zibRFDRgoaiqpvuLifgTCrL+jASS8srq2vJ9dTG5tb2Tnp371r6oSC0QXzui6YDknLm0YZiitNmICi4Dqc3zugi9m/GVEjme1dqEtCOCwOP9RkBpaVu+qDtghoS4FFtitv0NmRjDCdnkOqmM5Zp54uFXAVbZtYuFYtlTXJ22S5UsG1aM2TQAvVu+r3d80noUk8RDlK2bCtQnQiEYoTTaaodShoAGcGAtjT1wKWyE80+mOJjrfRw3xe6PIVn6veJCFwpJ66jO+N75W8vFv/yWqHqlzsR84JQUY/MF/VDjpWP4zhwjwlKFJ9oAkQwfSsmQxBAlA4tDuHrU/w/aWTNimlf5jPV80UaSXSIjtApslEJVVEN1VEDEXSHHtATejbujUfjxXidtyaMxcw++gHj7RP10pYi</latexit><latexit sha1_base64="afZwKjP5eez9JGwjSmt7BE3h+Fo=">AAACAHicdVDLSgNBEJyNrxhfUS+Cl8Egelp3884t6CXHCEYDSQi9k0kyZPbhzGwgLPHir3jxoOLVz/Dm3zibRFDRgoaiqpvuLifgTCrL+jASS8srq2vJ9dTG5tb2Tnp371r6oSC0QXzui6YDknLm0YZiitNmICi4Dqc3zugi9m/GVEjme1dqEtCOCwOP9RkBpaVu+qDtghoS4FFtitv0NmRjDCdnkOqmM5Zp54uFXAVbZtYuFYtlTXJ22S5UsG1aM2TQAvVu+r3d80noUk8RDlK2bCtQnQiEYoTTaaodShoAGcGAtjT1wKWyE80+mOJjrfRw3xe6PIVn6veJCFwpJ66jO+N75W8vFv/yWqHqlzsR84JQUY/MF/VDjpWP4zhwjwlKFJ9oAkQwfSsmQxBAlA4tDuHrU/w/aWTNimlf5jPV80UaSXSIjtApslEJVVEN1VEDEXSHHtATejbujUfjxXidtyaMxcw++gHj7RP10pYi</latexit><latexit sha1_base64="afZwKjP5eez9JGwjSmt7BE3h+Fo=">AAACAHicdVDLSgNBEJyNrxhfUS+Cl8Egelp3884t6CXHCEYDSQi9k0kyZPbhzGwgLPHir3jxoOLVz/Dm3zibRFDRgoaiqpvuLifgTCrL+jASS8srq2vJ9dTG5tb2Tnp371r6oSC0QXzui6YDknLm0YZiitNmICi4Dqc3zugi9m/GVEjme1dqEtCOCwOP9RkBpaVu+qDtghoS4FFtitv0NmRjDCdnkOqmM5Zp54uFXAVbZtYuFYtlTXJ22S5UsG1aM2TQAvVu+r3d80noUk8RDlK2bCtQnQiEYoTTaaodShoAGcGAtjT1wKWyE80+mOJjrfRw3xe6PIVn6veJCFwpJ66jO+N75W8vFv/yWqHqlzsR84JQUY/MF/VDjpWP4zhwjwlKFJ9oAkQwfSsmQxBAlA4tDuHrU/w/aWTNimlf5jPV80UaSXSIjtApslEJVVEN1VEDEXSHHtATejbujUfjxXidtyaMxcw++gHj7RP10pYi</latexit><latexit sha1_base64="afZwKjP5eez9JGwjSmt7BE3h+Fo=">AAACAHicdVDLSgNBEJyNrxhfUS+Cl8Egelp3884t6CXHCEYDSQi9k0kyZPbhzGwgLPHir3jxoOLVz/Dm3zibRFDRgoaiqpvuLifgTCrL+jASS8srq2vJ9dTG5tb2Tnp371r6oSC0QXzui6YDknLm0YZiitNmICi4Dqc3zugi9m/GVEjme1dqEtCOCwOP9RkBpaVu+qDtghoS4FFtitv0NmRjDCdnkOqmM5Zp54uFXAVbZtYuFYtlTXJ22S5UsG1aM2TQAvVu+r3d80noUk8RDlK2bCtQnQiEYoTTaaodShoAGcGAtjT1wKWyE80+mOJjrfRw3xe6PIVn6veJCFwpJ66jO+N75W8vFv/yWqHqlzsR84JQUY/MF/VDjpWP4zhwjwlKFJ9oAkQwfSsmQxBAlA4tDuHrU/w/aWTNimlf5jPV80UaSXSIjtApslEJVVEN1VEDEXSHHtATejbujUfjxXidtyaMxcw++gHj7RP10pYi</latexit>

h̃00ij + 2Hh̃0

ij + k2h̃ij = 0<latexit sha1_base64="ZUiqKzyqdsdUEKLNJqgRMrAYVw4=">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</latexit><latexit sha1_base64="ZUiqKzyqdsdUEKLNJqgRMrAYVw4=">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</latexit><latexit sha1_base64="ZUiqKzyqdsdUEKLNJqgRMrAYVw4=">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</latexit><latexit sha1_base64="ZUiqKzyqdsdUEKLNJqgRMrAYVw4=">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</latexit>

2. Inhomogeneous solutions : GWs from sources, e.g. gauge fields

h̃00ij + 2Hh̃0

ij + k2h̃ij = 16⇡Ga2⇡ij<latexit sha1_base64="x/xLTedp091u7m2Zolp4AANjfHw=">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</latexit><latexit sha1_base64="x/xLTedp091u7m2Zolp4AANjfHw=">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</latexit><latexit sha1_base64="x/xLTedp091u7m2Zolp4AANjfHw=">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</latexit><latexit sha1_base64="x/xLTedp091u7m2Zolp4AANjfHw=">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</latexit>

Vacuum vs. sourced

Page 4: mirzagholi.pdf - CERN Indico

E.O.M. of Tensor ModesAxion-SU(2) Gauge Fields

s = �1, 1<latexit sha1_base64="9vQFH9pP7a+9VBMTsZY+z5++mPg=">AAAB8XicdVDLSgMxFM3UVx1fVZdugkVwocOk7y6EohuXFRxbmA4lk2ba0MyDJCOU0s9w40LFrX/jzr8x01ZQ0QMXDufcy733+AlnUtn2h5FbWV1b38hvmlvbO7t7hf2DOxmnglCHxDwWXR9LyllEHcUUp91EUBz6nHb88VXmd+6pkCyObtUkoV6IhxELGMFKS66EF/AcnSHTNPuFom2hSq1abkLbKqF6rdbQpIwaqNqEyLLnKIIl2v3Ce28QkzSkkSIcS+kiO1HeFAvFCKczs5dKmmAyxkPqahrhkEpvOj95Bk+0MoBBLHRFCs7V7xNTHEo5CX3dGWI1kr+9TPzLc1MVNLwpi5JU0YgsFgUphyqG2f9wwAQlik80wUQwfSskIywwUTqlLISvT+H/xClZTQvdVIqty2UaeXAEjsEpQKAOWuAatIEDCIjBA3gCz4YyHo0X43XRmjOWM4fgB4y3T0nPjto=</latexit><latexit sha1_base64="9vQFH9pP7a+9VBMTsZY+z5++mPg=">AAAB8XicdVDLSgMxFM3UVx1fVZdugkVwocOk7y6EohuXFRxbmA4lk2ba0MyDJCOU0s9w40LFrX/jzr8x01ZQ0QMXDufcy733+AlnUtn2h5FbWV1b38hvmlvbO7t7hf2DOxmnglCHxDwWXR9LyllEHcUUp91EUBz6nHb88VXmd+6pkCyObtUkoV6IhxELGMFKS66EF/AcnSHTNPuFom2hSq1abkLbKqF6rdbQpIwaqNqEyLLnKIIl2v3Ce28QkzSkkSIcS+kiO1HeFAvFCKczs5dKmmAyxkPqahrhkEpvOj95Bk+0MoBBLHRFCs7V7xNTHEo5CX3dGWI1kr+9TPzLc1MVNLwpi5JU0YgsFgUphyqG2f9wwAQlik80wUQwfSskIywwUTqlLISvT+H/xClZTQvdVIqty2UaeXAEjsEpQKAOWuAatIEDCIjBA3gCz4YyHo0X43XRmjOWM4fgB4y3T0nPjto=</latexit><latexit sha1_base64="9vQFH9pP7a+9VBMTsZY+z5++mPg=">AAAB8XicdVDLSgMxFM3UVx1fVZdugkVwocOk7y6EohuXFRxbmA4lk2ba0MyDJCOU0s9w40LFrX/jzr8x01ZQ0QMXDufcy733+AlnUtn2h5FbWV1b38hvmlvbO7t7hf2DOxmnglCHxDwWXR9LyllEHcUUp91EUBz6nHb88VXmd+6pkCyObtUkoV6IhxELGMFKS66EF/AcnSHTNPuFom2hSq1abkLbKqF6rdbQpIwaqNqEyLLnKIIl2v3Ce28QkzSkkSIcS+kiO1HeFAvFCKczs5dKmmAyxkPqahrhkEpvOj95Bk+0MoBBLHRFCs7V7xNTHEo5CX3dGWI1kr+9TPzLc1MVNLwpi5JU0YgsFgUphyqG2f9wwAQlik80wUQwfSskIywwUTqlLISvT+H/xClZTQvdVIqty2UaeXAEjsEpQKAOWuAatIEDCIjBA3gCz4YyHo0X43XRmjOWM4fgB4y3T0nPjto=</latexit><latexit sha1_base64="9vQFH9pP7a+9VBMTsZY+z5++mPg=">AAAB8XicdVDLSgMxFM3UVx1fVZdugkVwocOk7y6EohuXFRxbmA4lk2ba0MyDJCOU0s9w40LFrX/jzr8x01ZQ0QMXDufcy733+AlnUtn2h5FbWV1b38hvmlvbO7t7hf2DOxmnglCHxDwWXR9LyllEHcUUp91EUBz6nHb88VXmd+6pkCyObtUkoV6IhxELGMFKS66EF/AcnSHTNPuFom2hSq1abkLbKqF6rdbQpIwaqNqEyLLnKIIl2v3Ce28QkzSkkSIcS+kiO1HeFAvFCKczs5dKmmAyxkPqahrhkEpvOj95Bk+0MoBBLHRFCs7V7xNTHEo5CX3dGWI1kr+9TPzLc1MVNLwpi5JU0YgsFgUphyqG2f9wwAQlik80wUQwfSskIywwUTqlLISvT+H/xClZTQvdVIqty2UaeXAEjsEpQKAOWuAatIEDCIjBA3gCz4YyHo0X43XRmjOWM4fgB4y3T0nPjto=</latexit>

@2xtA +

h1 +

2

x2

�mQ⇠1 � sx(mQ + ⇠1)

�itA = O(hA)

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@2xhA + (1�

2

x2)hA = O(tA)

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Gauge tensors split and one is amplified.

mQ ⌘ gAQ

H, ⇠1 ⌘ �1�̇

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A = L,R<latexit sha1_base64="bM+Do1YJpFn+TQf+23z1QqaRHkI=">AAAB8nicdVDLSgMxFM3UVx1fVZdugkVwIcOk7y6EqhsXLqpYW2iHkkkzbWjmQZIRytDfcONCxa1f486/MdNWUNEDFw7n3Mu997gRZ1LZ9oeRWVpeWV3Lrpsbm1vbO7ndvTsZxoLQFgl5KDoulpSzgLYUU5x2IkGx73LadscXqd++p0KyMLhVk4g6Ph4GzGMEKy31zDN4Cq9O4A00zX4ub1uoVCkX69C2CqhaqdQ0KaIaKtchsuwZ8mCBZj/33huEJPZpoAjHUnaRHSknwUIxwunU7MWSRpiM8ZB2NQ2wT6WTzG6ewiOtDKAXCl2BgjP1+0SCfSknvqs7faxG8reXin953Vh5NSdhQRQrGpD5Ii/mUIUwDQAOmKBE8YkmmAimb4VkhAUmSseUhvD1KfyftApW3ULXpXzjfJFGFhyAQ3AMEKiCBrgETdACBETgATyBZyM2Ho0X43XemjEWM/vgB4y3T5oXjwE=</latexit><latexit sha1_base64="bM+Do1YJpFn+TQf+23z1QqaRHkI=">AAAB8nicdVDLSgMxFM3UVx1fVZdugkVwIcOk7y6EqhsXLqpYW2iHkkkzbWjmQZIRytDfcONCxa1f486/MdNWUNEDFw7n3Mu997gRZ1LZ9oeRWVpeWV3Lrpsbm1vbO7ndvTsZxoLQFgl5KDoulpSzgLYUU5x2IkGx73LadscXqd++p0KyMLhVk4g6Ph4GzGMEKy31zDN4Cq9O4A00zX4ub1uoVCkX69C2CqhaqdQ0KaIaKtchsuwZ8mCBZj/33huEJPZpoAjHUnaRHSknwUIxwunU7MWSRpiM8ZB2NQ2wT6WTzG6ewiOtDKAXCl2BgjP1+0SCfSknvqs7faxG8reXin953Vh5NSdhQRQrGpD5Ii/mUIUwDQAOmKBE8YkmmAimb4VkhAUmSseUhvD1KfyftApW3ULXpXzjfJFGFhyAQ3AMEKiCBrgETdACBETgATyBZyM2Ho0X43XemjEWM/vgB4y3T5oXjwE=</latexit><latexit sha1_base64="bM+Do1YJpFn+TQf+23z1QqaRHkI=">AAAB8nicdVDLSgMxFM3UVx1fVZdugkVwIcOk7y6EqhsXLqpYW2iHkkkzbWjmQZIRytDfcONCxa1f486/MdNWUNEDFw7n3Mu997gRZ1LZ9oeRWVpeWV3Lrpsbm1vbO7ndvTsZxoLQFgl5KDoulpSzgLYUU5x2IkGx73LadscXqd++p0KyMLhVk4g6Ph4GzGMEKy31zDN4Cq9O4A00zX4ub1uoVCkX69C2CqhaqdQ0KaIaKtchsuwZ8mCBZj/33huEJPZpoAjHUnaRHSknwUIxwunU7MWSRpiM8ZB2NQ2wT6WTzG6ewiOtDKAXCl2BgjP1+0SCfSknvqs7faxG8reXin953Vh5NSdhQRQrGpD5Ii/mUIUwDQAOmKBE8YkmmAimb4VkhAUmSseUhvD1KfyftApW3ULXpXzjfJFGFhyAQ3AMEKiCBrgETdACBETgATyBZyM2Ho0X43XemjEWM/vgB4y3T5oXjwE=</latexit><latexit sha1_base64="bM+Do1YJpFn+TQf+23z1QqaRHkI=">AAAB8nicdVDLSgMxFM3UVx1fVZdugkVwIcOk7y6EqhsXLqpYW2iHkkkzbWjmQZIRytDfcONCxa1f486/MdNWUNEDFw7n3Mu997gRZ1LZ9oeRWVpeWV3Lrpsbm1vbO7ndvTsZxoLQFgl5KDoulpSzgLYUU5x2IkGx73LadscXqd++p0KyMLhVk4g6Ph4GzGMEKy31zDN4Cq9O4A00zX4ub1uoVCkX69C2CqhaqdQ0KaIaKtchsuwZ8mCBZj/33huEJPZpoAjHUnaRHSknwUIxwunU7MWSRpiM8ZB2NQ2wT6WTzG6ewiOtDKAXCl2BgjP1+0SCfSknvqs7faxG8reXin953Vh5NSdhQRQrGpD5Ii/mUIUwDQAOmKBE8YkmmAimb4VkhAUmSseUhvD1KfyftApW3ULXpXzjfJFGFhyAQ3AMEKiCBrgETdACBETgATyBZyM2Ho0X43XemjEWM/vgB4y3T5oXjwE=</latexit>

x ⌘ �k⌧<latexit sha1_base64="fIZQq0ak9Dony++VzFJC9eROrf4=">AAAB+nicdVDLSsNAFJ3UV42vWJduBovgxpD03V3RjcsKxgpNKJPptB06eTgzKS2hv+LGhYpbv8Sdf+OkraCiBy4czrmXe+/xY0aFtKwPLbe2vrG5ld/Wd3b39g+Mw8KtiBKOiYMjFvE7HwnCaEgcSSUjdzEnKPAZ6fjjy8zvTAgXNApv5CwmXoCGIR1QjKSSekZhCl1yn9AJPB+7EiW6rveMomXalVq13ISWWbLrtVpDkbLdsKtNaJvWAkWwQrtnvLv9CCcBCSVmSIiubcXSSxGXFDMy191EkBjhMRqSrqIhCojw0sXtc3iqlD4cRFxVKOFC/T6RokCIWeCrzgDJkfjtZeJfXjeRg4aX0jBOJAnxctEgYVBGMAsC9iknWLKZIghzqm6FeIQ4wlLFlYXw9Sn8nzgls2na15Vi62KVRh4cgxNwBmxQBy1wBdrAARhMwQN4As/aXHvUXrTXZWtOW80cgR/Q3j4BtFuTIg==</latexit><latexit sha1_base64="fIZQq0ak9Dony++VzFJC9eROrf4=">AAAB+nicdVDLSsNAFJ3UV42vWJduBovgxpD03V3RjcsKxgpNKJPptB06eTgzKS2hv+LGhYpbv8Sdf+OkraCiBy4czrmXe+/xY0aFtKwPLbe2vrG5ld/Wd3b39g+Mw8KtiBKOiYMjFvE7HwnCaEgcSSUjdzEnKPAZ6fjjy8zvTAgXNApv5CwmXoCGIR1QjKSSekZhCl1yn9AJPB+7EiW6rveMomXalVq13ISWWbLrtVpDkbLdsKtNaJvWAkWwQrtnvLv9CCcBCSVmSIiubcXSSxGXFDMy191EkBjhMRqSrqIhCojw0sXtc3iqlD4cRFxVKOFC/T6RokCIWeCrzgDJkfjtZeJfXjeRg4aX0jBOJAnxctEgYVBGMAsC9iknWLKZIghzqm6FeIQ4wlLFlYXw9Sn8nzgls2na15Vi62KVRh4cgxNwBmxQBy1wBdrAARhMwQN4As/aXHvUXrTXZWtOW80cgR/Q3j4BtFuTIg==</latexit><latexit sha1_base64="fIZQq0ak9Dony++VzFJC9eROrf4=">AAAB+nicdVDLSsNAFJ3UV42vWJduBovgxpD03V3RjcsKxgpNKJPptB06eTgzKS2hv+LGhYpbv8Sdf+OkraCiBy4czrmXe+/xY0aFtKwPLbe2vrG5ld/Wd3b39g+Mw8KtiBKOiYMjFvE7HwnCaEgcSSUjdzEnKPAZ6fjjy8zvTAgXNApv5CwmXoCGIR1QjKSSekZhCl1yn9AJPB+7EiW6rveMomXalVq13ISWWbLrtVpDkbLdsKtNaJvWAkWwQrtnvLv9CCcBCSVmSIiubcXSSxGXFDMy191EkBjhMRqSrqIhCojw0sXtc3iqlD4cRFxVKOFC/T6RokCIWeCrzgDJkfjtZeJfXjeRg4aX0jBOJAnxctEgYVBGMAsC9iknWLKZIghzqm6FeIQ4wlLFlYXw9Sn8nzgls2na15Vi62KVRh4cgxNwBmxQBy1wBdrAARhMwQN4As/aXHvUXrTXZWtOW80cgR/Q3j4BtFuTIg==</latexit><latexit sha1_base64="fIZQq0ak9Dony++VzFJC9eROrf4=">AAAB+nicdVDLSsNAFJ3UV42vWJduBovgxpD03V3RjcsKxgpNKJPptB06eTgzKS2hv+LGhYpbv8Sdf+OkraCiBy4czrmXe+/xY0aFtKwPLbe2vrG5ld/Wd3b39g+Mw8KtiBKOiYMjFvE7HwnCaEgcSSUjdzEnKPAZ6fjjy8zvTAgXNApv5CwmXoCGIR1QjKSSekZhCl1yn9AJPB+7EiW6rveMomXalVq13ISWWbLrtVpDkbLdsKtNaJvWAkWwQrtnvLv9CCcBCSVmSIiubcXSSxGXFDMy191EkBjhMRqSrqIhCojw0sXtc3iqlD4cRFxVKOFC/T6RokCIWeCrzgDJkfjtZeJfXjeRg4aX0jBOJAnxctEgYVBGMAsC9iknWLKZIghzqm6FeIQ4wlLFlYXw9Sn8nzgls2na15Vi62KVRh4cgxNwBmxQBy1wBdrAARhMwQN4As/aXHvUXrTXZWtOW80cgR/Q3j4BtFuTIg==</latexit>

hij ⌘ aMplp

2h̃ij , tai =

p2at̃ai

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h̃L,R ⌘ 1p2(h̃+ ± ih̃⇥)

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Page 5: mirzagholi.pdf - CERN Indico

Chiral Gravitational WavesParity is spontaneously broken by the background!

2 k |k� hR |

2 k |k� hL |

2 k |k� tR |

2 k |k� tL |

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Page 6: mirzagholi.pdf - CERN Indico

Symmetry demands more!

We have to consider all of parity-violating terms that arise from the same physics!

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Witten 1984, Choi 1997, Lue - Wang - Kamionowski 1999, Choi - Hwang - Hwang 2000

Page 7: mirzagholi.pdf - CERN Indico

Symmetry demands more!Add the Gravitational Chern-Simons term

L = LEH + L' + LSPEC + LGCS<latexit sha1_base64="6LnE9klIKne/FQp5dVdFDwemPCk=">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</latexit><latexit sha1_base64="6LnE9klIKne/FQp5dVdFDwemPCk=">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</latexit><latexit sha1_base64="6LnE9klIKne/FQp5dVdFDwemPCk=">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</latexit><latexit sha1_base64="6LnE9klIKne/FQp5dVdFDwemPCk=">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</latexit>

LGCS =�2�

4fRR̃

<latexit sha1_base64="3QbkS6grR27RaZziF1LEtr0Gd1A=">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</latexit><latexit sha1_base64="3QbkS6grR27RaZziF1LEtr0Gd1A=">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</latexit><latexit sha1_base64="3QbkS6grR27RaZziF1LEtr0Gd1A=">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</latexit><latexit sha1_base64="3QbkS6grR27RaZziF1LEtr0Gd1A=">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</latexit>

Page 8: mirzagholi.pdf - CERN Indico

E.O.M of GWsVacuum, sourced and modified

1. Homogeneous solutions : GWs from vacuum fluctuations ̃h00ij + 2Hh̃0

ij + k2h̃ij = 0<latexit sha1_base64="ZUiqKzyqdsdUEKLNJqgRMrAYVw4=">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</latexit><latexit sha1_base64="ZUiqKzyqdsdUEKLNJqgRMrAYVw4=">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</latexit><latexit sha1_base64="ZUiqKzyqdsdUEKLNJqgRMrAYVw4=">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</latexit><latexit sha1_base64="ZUiqKzyqdsdUEKLNJqgRMrAYVw4=">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</latexit>

2. Inhomogeneous solutions : GWs from sources, e.g. gauge fields

h̃00ij + 2Hh̃0

ij + k2h̃ij = 16⇡Ga2⇡ij<latexit sha1_base64="x/xLTedp091u7m2Zolp4AANjfHw=">AAACRnicdZBNSyNBEIZrortq3I+oRy+FYVFYGKajxuQgiB70qGBWIRNDT6djetPzQXePEIb5d168evMvePGg4tWeJMJu2C1oeHmfKqrrDRIptPG8B6c0N//p88LiUnn5y9dv3ysrq790nCrGWyyWsboMqOZSRLxlhJH8MlGchoHkF8HwqOAXN1xpEUfnZpTwTkivI9EXjBprdStXvhGyx7NB3s3E73xzE39izQ+pGTAqs5McZ7jFw6vajIv7SOp+IvAYaQETMbHL5W6l6rlkp7673UTPrZG9er1hxTZpkN0mEtcbVxWmddqt3Pu9mKUhjwyTVOs28RLTyagygkmel/1U84SyIb3mbSsjGnLdycY55PjDOj3sx8q+yODY/XMio6HWozCwncWFepYV5r9YOzX9RicTUZIaHrHJon4q0cRYhIo9oTgzcmQFZUrYvyIbUEWZsdEXIXxciv8XrZrbdMnZTvXgcJrGIqzDBmwBgT04gBM4hRYwuIVHeIYX5855cl6dt0lryZnOrMFfVYJ3M1av2w==</latexit><latexit sha1_base64="x/xLTedp091u7m2Zolp4AANjfHw=">AAACRnicdZBNSyNBEIZrortq3I+oRy+FYVFYGKajxuQgiB70qGBWIRNDT6djetPzQXePEIb5d168evMvePGg4tWeJMJu2C1oeHmfKqrrDRIptPG8B6c0N//p88LiUnn5y9dv3ysrq790nCrGWyyWsboMqOZSRLxlhJH8MlGchoHkF8HwqOAXN1xpEUfnZpTwTkivI9EXjBprdStXvhGyx7NB3s3E73xzE39izQ+pGTAqs5McZ7jFw6vajIv7SOp+IvAYaQETMbHL5W6l6rlkp7673UTPrZG9er1hxTZpkN0mEtcbVxWmddqt3Pu9mKUhjwyTVOs28RLTyagygkmel/1U84SyIb3mbSsjGnLdycY55PjDOj3sx8q+yODY/XMio6HWozCwncWFepYV5r9YOzX9RicTUZIaHrHJon4q0cRYhIo9oTgzcmQFZUrYvyIbUEWZsdEXIXxciv8XrZrbdMnZTvXgcJrGIqzDBmwBgT04gBM4hRYwuIVHeIYX5855cl6dt0lryZnOrMFfVYJ3M1av2w==</latexit><latexit sha1_base64="x/xLTedp091u7m2Zolp4AANjfHw=">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</latexit><latexit sha1_base64="x/xLTedp091u7m2Zolp4AANjfHw=">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</latexit>

3. Inhomogeneous solutions + Gravitational Chern-Simons term�1� s

⇠2k

H

�h00A + 2Hh0

A +�1� s

⇠2k

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�k2hA = 16⇡Ga2⇡ij

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H ⌘ a0/a<latexit sha1_base64="afZwKjP5eez9JGwjSmt7BE3h+Fo=">AAACAHicdVDLSgNBEJyNrxhfUS+Cl8Egelp3884t6CXHCEYDSQi9k0kyZPbhzGwgLPHir3jxoOLVz/Dm3zibRFDRgoaiqpvuLifgTCrL+jASS8srq2vJ9dTG5tb2Tnp371r6oSC0QXzui6YDknLm0YZiitNmICi4Dqc3zugi9m/GVEjme1dqEtCOCwOP9RkBpaVu+qDtghoS4FFtitv0NmRjDCdnkOqmM5Zp54uFXAVbZtYuFYtlTXJ22S5UsG1aM2TQAvVu+r3d80noUk8RDlK2bCtQnQiEYoTTaaodShoAGcGAtjT1wKWyE80+mOJjrfRw3xe6PIVn6veJCFwpJ66jO+N75W8vFv/yWqHqlzsR84JQUY/MF/VDjpWP4zhwjwlKFJ9oAkQwfSsmQxBAlA4tDuHrU/w/aWTNimlf5jPV80UaSXSIjtApslEJVVEN1VEDEXSHHtATejbujUfjxXidtyaMxcw++gHj7RP10pYi</latexit><latexit sha1_base64="afZwKjP5eez9JGwjSmt7BE3h+Fo=">AAACAHicdVDLSgNBEJyNrxhfUS+Cl8Egelp3884t6CXHCEYDSQi9k0kyZPbhzGwgLPHir3jxoOLVz/Dm3zibRFDRgoaiqpvuLifgTCrL+jASS8srq2vJ9dTG5tb2Tnp371r6oSC0QXzui6YDknLm0YZiitNmICi4Dqc3zugi9m/GVEjme1dqEtCOCwOP9RkBpaVu+qDtghoS4FFtitv0NmRjDCdnkOqmM5Zp54uFXAVbZtYuFYtlTXJ22S5UsG1aM2TQAvVu+r3d80noUk8RDlK2bCtQnQiEYoTTaaodShoAGcGAtjT1wKWyE80+mOJjrfRw3xe6PIVn6veJCFwpJ66jO+N75W8vFv/yWqHqlzsR84JQUY/MF/VDjpWP4zhwjwlKFJ9oAkQwfSsmQxBAlA4tDuHrU/w/aWTNimlf5jPV80UaSXSIjtApslEJVVEN1VEDEXSHHtATejbujUfjxXidtyaMxcw++gHj7RP10pYi</latexit><latexit sha1_base64="afZwKjP5eez9JGwjSmt7BE3h+Fo=">AAACAHicdVDLSgNBEJyNrxhfUS+Cl8Egelp3884t6CXHCEYDSQi9k0kyZPbhzGwgLPHir3jxoOLVz/Dm3zibRFDRgoaiqpvuLifgTCrL+jASS8srq2vJ9dTG5tb2Tnp371r6oSC0QXzui6YDknLm0YZiitNmICi4Dqc3zugi9m/GVEjme1dqEtCOCwOP9RkBpaVu+qDtghoS4FFtitv0NmRjDCdnkOqmM5Zp54uFXAVbZtYuFYtlTXJ22S5UsG1aM2TQAvVu+r3d80noUk8RDlK2bCtQnQiEYoTTaaodShoAGcGAtjT1wKWyE80+mOJjrfRw3xe6PIVn6veJCFwpJ66jO+N75W8vFv/yWqHqlzsR84JQUY/MF/VDjpWP4zhwjwlKFJ9oAkQwfSsmQxBAlA4tDuHrU/w/aWTNimlf5jPV80UaSXSIjtApslEJVVEN1VEDEXSHHtATejbujUfjxXidtyaMxcw++gHj7RP10pYi</latexit><latexit sha1_base64="afZwKjP5eez9JGwjSmt7BE3h+Fo=">AAACAHicdVDLSgNBEJyNrxhfUS+Cl8Egelp3884t6CXHCEYDSQi9k0kyZPbhzGwgLPHir3jxoOLVz/Dm3zibRFDRgoaiqpvuLifgTCrL+jASS8srq2vJ9dTG5tb2Tnp371r6oSC0QXzui6YDknLm0YZiitNmICi4Dqc3zugi9m/GVEjme1dqEtCOCwOP9RkBpaVu+qDtghoS4FFtitv0NmRjDCdnkOqmM5Zp54uFXAVbZtYuFYtlTXJ22S5UsG1aM2TQAvVu+r3d80noUk8RDlK2bCtQnQiEYoTTaaodShoAGcGAtjT1wKWyE80+mOJjrfRw3xe6PIVn6veJCFwpJ66jO+N75W8vFv/yWqHqlzsR84JQUY/MF/VDjpWP4zhwjwlKFJ9oAkQwfSsmQxBAlA4tDuHrU/w/aWTNimlf5jPV80UaSXSIjtApslEJVVEN1VEDEXSHHtATejbujUfjxXidtyaMxcw++gHj7RP10pYi</latexit>

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A = L,R<latexit sha1_base64="bM+Do1YJpFn+TQf+23z1QqaRHkI=">AAAB8nicdVDLSgMxFM3UVx1fVZdugkVwIcOk7y6EqhsXLqpYW2iHkkkzbWjmQZIRytDfcONCxa1f486/MdNWUNEDFw7n3Mu997gRZ1LZ9oeRWVpeWV3Lrpsbm1vbO7ndvTsZxoLQFgl5KDoulpSzgLYUU5x2IkGx73LadscXqd++p0KyMLhVk4g6Ph4GzGMEKy31zDN4Cq9O4A00zX4ub1uoVCkX69C2CqhaqdQ0KaIaKtchsuwZ8mCBZj/33huEJPZpoAjHUnaRHSknwUIxwunU7MWSRpiM8ZB2NQ2wT6WTzG6ewiOtDKAXCl2BgjP1+0SCfSknvqs7faxG8reXin953Vh5NSdhQRQrGpD5Ii/mUIUwDQAOmKBE8YkmmAimb4VkhAUmSseUhvD1KfyftApW3ULXpXzjfJFGFhyAQ3AMEKiCBrgETdACBETgATyBZyM2Ho0X43XemjEWM/vgB4y3T5oXjwE=</latexit><latexit sha1_base64="bM+Do1YJpFn+TQf+23z1QqaRHkI=">AAAB8nicdVDLSgMxFM3UVx1fVZdugkVwIcOk7y6EqhsXLqpYW2iHkkkzbWjmQZIRytDfcONCxa1f486/MdNWUNEDFw7n3Mu997gRZ1LZ9oeRWVpeWV3Lrpsbm1vbO7ndvTsZxoLQFgl5KDoulpSzgLYUU5x2IkGx73LadscXqd++p0KyMLhVk4g6Ph4GzGMEKy31zDN4Cq9O4A00zX4ub1uoVCkX69C2CqhaqdQ0KaIaKtchsuwZ8mCBZj/33huEJPZpoAjHUnaRHSknwUIxwunU7MWSRpiM8ZB2NQ2wT6WTzG6ewiOtDKAXCl2BgjP1+0SCfSknvqs7faxG8reXin953Vh5NSdhQRQrGpD5Ii/mUIUwDQAOmKBE8YkmmAimb4VkhAUmSseUhvD1KfyftApW3ULXpXzjfJFGFhyAQ3AMEKiCBrgETdACBETgATyBZyM2Ho0X43XemjEWM/vgB4y3T5oXjwE=</latexit><latexit sha1_base64="bM+Do1YJpFn+TQf+23z1QqaRHkI=">AAAB8nicdVDLSgMxFM3UVx1fVZdugkVwIcOk7y6EqhsXLqpYW2iHkkkzbWjmQZIRytDfcONCxa1f486/MdNWUNEDFw7n3Mu997gRZ1LZ9oeRWVpeWV3Lrpsbm1vbO7ndvTsZxoLQFgl5KDoulpSzgLYUU5x2IkGx73LadscXqd++p0KyMLhVk4g6Ph4GzGMEKy31zDN4Cq9O4A00zX4ub1uoVCkX69C2CqhaqdQ0KaIaKtchsuwZ8mCBZj/33huEJPZpoAjHUnaRHSknwUIxwunU7MWSRpiM8ZB2NQ2wT6WTzG6ewiOtDKAXCl2BgjP1+0SCfSknvqs7faxG8reXin953Vh5NSdhQRQrGpD5Ii/mUIUwDQAOmKBE8YkmmAimb4VkhAUmSseUhvD1KfyftApW3ULXpXzjfJFGFhyAQ3AMEKiCBrgETdACBETgATyBZyM2Ho0X43XemjEWM/vgB4y3T5oXjwE=</latexit><latexit sha1_base64="bM+Do1YJpFn+TQf+23z1QqaRHkI=">AAAB8nicdVDLSgMxFM3UVx1fVZdugkVwIcOk7y6EqhsXLqpYW2iHkkkzbWjmQZIRytDfcONCxa1f486/MdNWUNEDFw7n3Mu997gRZ1LZ9oeRWVpeWV3Lrpsbm1vbO7ndvTsZxoLQFgl5KDoulpSzgLYUU5x2IkGx73LadscXqd++p0KyMLhVk4g6Ph4GzGMEKy31zDN4Cq9O4A00zX4ub1uoVCkX69C2CqhaqdQ0KaIaKtchsuwZ8mCBZj/33huEJPZpoAjHUnaRHSknwUIxwunU7MWSRpiM8ZB2NQ2wT6WTzG6ewiOtDKAXCl2BgjP1+0SCfSknvqs7faxG8reXin953Vh5NSdhQRQrGpD5Ii/mUIUwDQAOmKBE8YkmmAimb4VkhAUmSseUhvD1KfyftApW3ULXpXzjfJFGFhyAQ3AMEKiCBrgETdACBETgATyBZyM2Ho0X43XemjEWM/vgB4y3T5oXjwE=</latexit>

Page 9: mirzagholi.pdf - CERN Indico

Axion-SU(2) Gauge fields + Gravitational Chern-Simons

@2xtA +

h1 +

2

x2

�mQ⇠1 � sx(mQ + ⇠1)

�itA = O(hA)

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⇣1� s⇠2x

⌘h@2xhA + (1�

2

x2)hA

i� 2s⇠2@xhA = O(tA)

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E.O.M of Tensor Modes

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A = L,R<latexit sha1_base64="bM+Do1YJpFn+TQf+23z1QqaRHkI=">AAAB8nicdVDLSgMxFM3UVx1fVZdugkVwIcOk7y6EqhsXLqpYW2iHkkkzbWjmQZIRytDfcONCxa1f486/MdNWUNEDFw7n3Mu997gRZ1LZ9oeRWVpeWV3Lrpsbm1vbO7ndvTsZxoLQFgl5KDoulpSzgLYUU5x2IkGx73LadscXqd++p0KyMLhVk4g6Ph4GzGMEKy31zDN4Cq9O4A00zX4ub1uoVCkX69C2CqhaqdQ0KaIaKtchsuwZ8mCBZj/33huEJPZpoAjHUnaRHSknwUIxwunU7MWSRpiM8ZB2NQ2wT6WTzG6ewiOtDKAXCl2BgjP1+0SCfSknvqs7faxG8reXin953Vh5NSdhQRQrGpD5Ii/mUIUwDQAOmKBE8YkmmAimb4VkhAUmSseUhvD1KfyftApW3ULXpXzjfJFGFhyAQ3AMEKiCBrgETdACBETgATyBZyM2Ho0X43XemjEWM/vgB4y3T5oXjwE=</latexit><latexit sha1_base64="bM+Do1YJpFn+TQf+23z1QqaRHkI=">AAAB8nicdVDLSgMxFM3UVx1fVZdugkVwIcOk7y6EqhsXLqpYW2iHkkkzbWjmQZIRytDfcONCxa1f486/MdNWUNEDFw7n3Mu997gRZ1LZ9oeRWVpeWV3Lrpsbm1vbO7ndvTsZxoLQFgl5KDoulpSzgLYUU5x2IkGx73LadscXqd++p0KyMLhVk4g6Ph4GzGMEKy31zDN4Cq9O4A00zX4ub1uoVCkX69C2CqhaqdQ0KaIaKtchsuwZ8mCBZj/33huEJPZpoAjHUnaRHSknwUIxwunU7MWSRpiM8ZB2NQ2wT6WTzG6ewiOtDKAXCl2BgjP1+0SCfSknvqs7faxG8reXin953Vh5NSdhQRQrGpD5Ii/mUIUwDQAOmKBE8YkmmAimb4VkhAUmSseUhvD1KfyftApW3ULXpXzjfJFGFhyAQ3AMEKiCBrgETdACBETgATyBZyM2Ho0X43XemjEWM/vgB4y3T5oXjwE=</latexit><latexit sha1_base64="bM+Do1YJpFn+TQf+23z1QqaRHkI=">AAAB8nicdVDLSgMxFM3UVx1fVZdugkVwIcOk7y6EqhsXLqpYW2iHkkkzbWjmQZIRytDfcONCxa1f486/MdNWUNEDFw7n3Mu997gRZ1LZ9oeRWVpeWV3Lrpsbm1vbO7ndvTsZxoLQFgl5KDoulpSzgLYUU5x2IkGx73LadscXqd++p0KyMLhVk4g6Ph4GzGMEKy31zDN4Cq9O4A00zX4ub1uoVCkX69C2CqhaqdQ0KaIaKtchsuwZ8mCBZj/33huEJPZpoAjHUnaRHSknwUIxwunU7MWSRpiM8ZB2NQ2wT6WTzG6ewiOtDKAXCl2BgjP1+0SCfSknvqs7faxG8reXin953Vh5NSdhQRQrGpD5Ii/mUIUwDQAOmKBE8YkmmAimb4VkhAUmSseUhvD1KfyftApW3ULXpXzjfJFGFhyAQ3AMEKiCBrgETdACBETgATyBZyM2Ho0X43XemjEWM/vgB4y3T5oXjwE=</latexit><latexit sha1_base64="bM+Do1YJpFn+TQf+23z1QqaRHkI=">AAAB8nicdVDLSgMxFM3UVx1fVZdugkVwIcOk7y6EqhsXLqpYW2iHkkkzbWjmQZIRytDfcONCxa1f486/MdNWUNEDFw7n3Mu997gRZ1LZ9oeRWVpeWV3Lrpsbm1vbO7ndvTsZxoLQFgl5KDoulpSzgLYUU5x2IkGx73LadscXqd++p0KyMLhVk4g6Ph4GzGMEKy31zDN4Cq9O4A00zX4ub1uoVCkX69C2CqhaqdQ0KaIaKtchsuwZ8mCBZj/33huEJPZpoAjHUnaRHSknwUIxwunU7MWSRpiM8ZB2NQ2wT6WTzG6ewiOtDKAXCl2BgjP1+0SCfSknvqs7faxG8reXin953Vh5NSdhQRQrGpD5Ii/mUIUwDQAOmKBE8YkmmAimb4VkhAUmSseUhvD1KfyftApW3ULXpXzjfJFGFhyAQ3AMEKiCBrgETdACBETgATyBZyM2Ho0X43XemjEWM/vgB4y3T5oXjwE=</latexit>

x ⌘ �k⌧<latexit sha1_base64="fIZQq0ak9Dony++VzFJC9eROrf4=">AAAB+nicdVDLSsNAFJ3UV42vWJduBovgxpD03V3RjcsKxgpNKJPptB06eTgzKS2hv+LGhYpbv8Sdf+OkraCiBy4czrmXe+/xY0aFtKwPLbe2vrG5ld/Wd3b39g+Mw8KtiBKOiYMjFvE7HwnCaEgcSSUjdzEnKPAZ6fjjy8zvTAgXNApv5CwmXoCGIR1QjKSSekZhCl1yn9AJPB+7EiW6rveMomXalVq13ISWWbLrtVpDkbLdsKtNaJvWAkWwQrtnvLv9CCcBCSVmSIiubcXSSxGXFDMy191EkBjhMRqSrqIhCojw0sXtc3iqlD4cRFxVKOFC/T6RokCIWeCrzgDJkfjtZeJfXjeRg4aX0jBOJAnxctEgYVBGMAsC9iknWLKZIghzqm6FeIQ4wlLFlYXw9Sn8nzgls2na15Vi62KVRh4cgxNwBmxQBy1wBdrAARhMwQN4As/aXHvUXrTXZWtOW80cgR/Q3j4BtFuTIg==</latexit><latexit sha1_base64="fIZQq0ak9Dony++VzFJC9eROrf4=">AAAB+nicdVDLSsNAFJ3UV42vWJduBovgxpD03V3RjcsKxgpNKJPptB06eTgzKS2hv+LGhYpbv8Sdf+OkraCiBy4czrmXe+/xY0aFtKwPLbe2vrG5ld/Wd3b39g+Mw8KtiBKOiYMjFvE7HwnCaEgcSSUjdzEnKPAZ6fjjy8zvTAgXNApv5CwmXoCGIR1QjKSSekZhCl1yn9AJPB+7EiW6rveMomXalVq13ISWWbLrtVpDkbLdsKtNaJvWAkWwQrtnvLv9CCcBCSVmSIiubcXSSxGXFDMy191EkBjhMRqSrqIhCojw0sXtc3iqlD4cRFxVKOFC/T6RokCIWeCrzgDJkfjtZeJfXjeRg4aX0jBOJAnxctEgYVBGMAsC9iknWLKZIghzqm6FeIQ4wlLFlYXw9Sn8nzgls2na15Vi62KVRh4cgxNwBmxQBy1wBdrAARhMwQN4As/aXHvUXrTXZWtOW80cgR/Q3j4BtFuTIg==</latexit><latexit sha1_base64="fIZQq0ak9Dony++VzFJC9eROrf4=">AAAB+nicdVDLSsNAFJ3UV42vWJduBovgxpD03V3RjcsKxgpNKJPptB06eTgzKS2hv+LGhYpbv8Sdf+OkraCiBy4czrmXe+/xY0aFtKwPLbe2vrG5ld/Wd3b39g+Mw8KtiBKOiYMjFvE7HwnCaEgcSSUjdzEnKPAZ6fjjy8zvTAgXNApv5CwmXoCGIR1QjKSSekZhCl1yn9AJPB+7EiW6rveMomXalVq13ISWWbLrtVpDkbLdsKtNaJvWAkWwQrtnvLv9CCcBCSVmSIiubcXSSxGXFDMy191EkBjhMRqSrqIhCojw0sXtc3iqlD4cRFxVKOFC/T6RokCIWeCrzgDJkfjtZeJfXjeRg4aX0jBOJAnxctEgYVBGMAsC9iknWLKZIghzqm6FeIQ4wlLFlYXw9Sn8nzgls2na15Vi62KVRh4cgxNwBmxQBy1wBdrAARhMwQN4As/aXHvUXrTXZWtOW80cgR/Q3j4BtFuTIg==</latexit><latexit sha1_base64="fIZQq0ak9Dony++VzFJC9eROrf4=">AAAB+nicdVDLSsNAFJ3UV42vWJduBovgxpD03V3RjcsKxgpNKJPptB06eTgzKS2hv+LGhYpbv8Sdf+OkraCiBy4czrmXe+/xY0aFtKwPLbe2vrG5ld/Wd3b39g+Mw8KtiBKOiYMjFvE7HwnCaEgcSSUjdzEnKPAZ6fjjy8zvTAgXNApv5CwmXoCGIR1QjKSSekZhCl1yn9AJPB+7EiW6rveMomXalVq13ISWWbLrtVpDkbLdsKtNaJvWAkWwQrtnvLv9CCcBCSVmSIiubcXSSxGXFDMy191EkBjhMRqSrqIhCojw0sXtc3iqlD4cRFxVKOFC/T6RokCIWeCrzgDJkfjtZeJfXjeRg4aX0jBOJAnxctEgYVBGMAsC9iknWLKZIghzqm6FeIQ4wlLFlYXw9Sn8nzgls2na15Vi62KVRh4cgxNwBmxQBy1wBdrAARhMwQN4As/aXHvUXrTXZWtOW80cgR/Q3j4BtFuTIg==</latexit>

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Page 10: mirzagholi.pdf - CERN Indico

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Page 12: mirzagholi.pdf - CERN Indico

With FF̃<latexit sha1_base64="h+k4v6XnV9rNE9CdF+26JurgO64=">AAAB+nicdVDLSsNAFJ34rPUV69LNYBFchaTv7opCcVnB2EITymQybYdOHsxMxBLyK25cqLj1S9z5N07aCip64MLhnHu59x4vZlRI0/zQ1tY3Nre2CzvF3b39g0P9qHQrooRjYuOIRXzgIUEYDYktqWRkEHOCAo+Rvje7zP3+HeGCRuGNnMfEDdAkpGOKkVTSSC85XsT8tOtIynySdrOsONLLpmHVGvVqG5pGxWo2Gi1FqlbLqrehZZgLlMEKvZH+7vgRTgISSsyQEEPLjKWbIi4pZiQrOokgMcIzNCFDRUMUEOGmi9szeKYUH44jriqUcKF+n0hRIMQ88FRngORU/PZy8S9vmMhxy01pGCeShHi5aJwwKCOYBwF9ygmWbK4IwpyqWyGeIo6wVHHlIXx9Cv8ndsVoG9Z1rdy5WKVRACfgFJwDCzRBB1yBHrABBvfgATyBZy3THrUX7XXZuqatZo7BD2hvn8HPlHk=</latexit><latexit sha1_base64="h+k4v6XnV9rNE9CdF+26JurgO64=">AAAB+nicdVDLSsNAFJ34rPUV69LNYBFchaTv7opCcVnB2EITymQybYdOHsxMxBLyK25cqLj1S9z5N07aCip64MLhnHu59x4vZlRI0/zQ1tY3Nre2CzvF3b39g0P9qHQrooRjYuOIRXzgIUEYDYktqWRkEHOCAo+Rvje7zP3+HeGCRuGNnMfEDdAkpGOKkVTSSC85XsT8tOtIynySdrOsONLLpmHVGvVqG5pGxWo2Gi1FqlbLqrehZZgLlMEKvZH+7vgRTgISSsyQEEPLjKWbIi4pZiQrOokgMcIzNCFDRUMUEOGmi9szeKYUH44jriqUcKF+n0hRIMQ88FRngORU/PZy8S9vmMhxy01pGCeShHi5aJwwKCOYBwF9ygmWbK4IwpyqWyGeIo6wVHHlIXx9Cv8ndsVoG9Z1rdy5WKVRACfgFJwDCzRBB1yBHrABBvfgATyBZy3THrUX7XXZuqatZo7BD2hvn8HPlHk=</latexit><latexit sha1_base64="h+k4v6XnV9rNE9CdF+26JurgO64=">AAAB+nicdVDLSsNAFJ34rPUV69LNYBFchaTv7opCcVnB2EITymQybYdOHsxMxBLyK25cqLj1S9z5N07aCip64MLhnHu59x4vZlRI0/zQ1tY3Nre2CzvF3b39g0P9qHQrooRjYuOIRXzgIUEYDYktqWRkEHOCAo+Rvje7zP3+HeGCRuGNnMfEDdAkpGOKkVTSSC85XsT8tOtIynySdrOsONLLpmHVGvVqG5pGxWo2Gi1FqlbLqrehZZgLlMEKvZH+7vgRTgISSsyQEEPLjKWbIi4pZiQrOokgMcIzNCFDRUMUEOGmi9szeKYUH44jriqUcKF+n0hRIMQ88FRngORU/PZy8S9vmMhxy01pGCeShHi5aJwwKCOYBwF9ygmWbK4IwpyqWyGeIo6wVHHlIXx9Cv8ndsVoG9Z1rdy5WKVRACfgFJwDCzRBB1yBHrABBvfgATyBZy3THrUX7XXZuqatZo7BD2hvn8HPlHk=</latexit><latexit sha1_base64="h+k4v6XnV9rNE9CdF+26JurgO64=">AAAB+nicdVDLSsNAFJ34rPUV69LNYBFchaTv7opCcVnB2EITymQybYdOHsxMxBLyK25cqLj1S9z5N07aCip64MLhnHu59x4vZlRI0/zQ1tY3Nre2CzvF3b39g0P9qHQrooRjYuOIRXzgIUEYDYktqWRkEHOCAo+Rvje7zP3+HeGCRuGNnMfEDdAkpGOKkVTSSC85XsT8tOtIynySdrOsONLLpmHVGvVqG5pGxWo2Gi1FqlbLqrehZZgLlMEKvZH+7vgRTgISSsyQEEPLjKWbIi4pZiQrOokgMcIzNCFDRUMUEOGmi9szeKYUH44jriqUcKF+n0hRIMQ88FRngORU/PZy8S9vmMhxy01pGCeShHi5aJwwKCOYBwF9ygmWbK4IwpyqWyGeIo6wVHHlIXx9Cv8ndsVoG9Z1rdy5WKVRACfgFJwDCzRBB1yBHrABBvfgATyBZy3THrUX7XXZuqatZo7BD2hvn8HPlHk=</latexit>

FF*

RR*

FF*+RR*

�1=�2=0

10-4 0.001 0.010 0.100 1 10 100

1

5

10

50

100

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2k|k�hL|

�2=4.5*10-6

10-4 0.001 0.010 0.100 1 10 100

1

5

10

50

100

-k�

2k|k�hR|

�2=4.5*10-6

Page 13: mirzagholi.pdf - CERN Indico

With FF*

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�1=�2=0

10-4 0.001 0.010 0.100 1 10

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�2=4.5*10-2

10-4 0.001 0.010 0.100 1 100.5

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�2=4.5*10-2

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Page 14: mirzagholi.pdf - CERN Indico

Right

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Page 15: mirzagholi.pdf - CERN Indico

⇣1� s⇠2x

⌘h@2xhA + (1�

2

x2)hA

i� 2s⇠2@xhA = O(tA)

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(1� ⇠2

Hkphy)

<latexit sha1_base64="wnxqlG6aTkcg1A8Y+kINrxe8i3c=">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</latexit><latexit sha1_base64="wnxqlG6aTkcg1A8Y+kINrxe8i3c=">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</latexit><latexit sha1_base64="wnxqlG6aTkcg1A8Y+kINrxe8i3c=">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</latexit><latexit sha1_base64="wnxqlG6aTkcg1A8Y+kINrxe8i3c=">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</latexit>

For s = 1 in physical coordinates:

The sign of the kinetic term in the equation of motion for the right-handed helicity becomes negative!

What About Ghosts?

Page 16: mirzagholi.pdf - CERN Indico

Instability Analysis

⇠2

H⇤ < 1

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This is an effective description so we can put a cut-off for our theory to prevent these instabilities.

⇤<latexit sha1_base64="Sfe8eRLMnIC8TeY3PQoRuGrpvgA=">AAAB73icdVDLSsNAFJ34rPFVdelmsAiuQtJ3d0U3LlxUMLbShjKZTNqhk0mYmQgl9CvcuFBx6++482+ctBVU9MDA4ZxzmXuPnzAqlW1/GCura+sbm4Utc3tnd2+/eHB4K+NUYOLimMWi5yNJGOXEVVQx0ksEQZHPSNefXOR+954ISWN+o6YJ8SI04jSkGCkt3Q2udDRApjkslmzLqdZrlRa0rbLTqNebmlScplNrQcey5yiBJTrD4vsgiHEaEa4wQ1L2HTtRXoaEopiRmTlIJUkQnqAR6WvKUUSkl80XnsFTrQQwjIV+XMG5+n0iQ5GU08jXyQipsfzt5eJfXj9VYdPLKE9SRThefBSmDKoY5tfDgAqCFZtqgrCgeleIx0ggrHRHeQlfl8L/iVu2WpZzXS21z5dtFMAxOAFnwAEN0AaXoANcgEEEHsATeDaE8Wi8GK+L6IqxnDkCP2C8fQJfv4+u</latexit><latexit sha1_base64="Sfe8eRLMnIC8TeY3PQoRuGrpvgA=">AAAB73icdVDLSsNAFJ34rPFVdelmsAiuQtJ3d0U3LlxUMLbShjKZTNqhk0mYmQgl9CvcuFBx6++482+ctBVU9MDA4ZxzmXuPnzAqlW1/GCura+sbm4Utc3tnd2+/eHB4K+NUYOLimMWi5yNJGOXEVVQx0ksEQZHPSNefXOR+954ISWN+o6YJ8SI04jSkGCkt3Q2udDRApjkslmzLqdZrlRa0rbLTqNebmlScplNrQcey5yiBJTrD4vsgiHEaEa4wQ1L2HTtRXoaEopiRmTlIJUkQnqAR6WvKUUSkl80XnsFTrQQwjIV+XMG5+n0iQ5GU08jXyQipsfzt5eJfXj9VYdPLKE9SRThefBSmDKoY5tfDgAqCFZtqgrCgeleIx0ggrHRHeQlfl8L/iVu2WpZzXS21z5dtFMAxOAFnwAEN0AaXoANcgEEEHsATeDaE8Wi8GK+L6IqxnDkCP2C8fQJfv4+u</latexit><latexit sha1_base64="Sfe8eRLMnIC8TeY3PQoRuGrpvgA=">AAAB73icdVDLSsNAFJ34rPFVdelmsAiuQtJ3d0U3LlxUMLbShjKZTNqhk0mYmQgl9CvcuFBx6++482+ctBVU9MDA4ZxzmXuPnzAqlW1/GCura+sbm4Utc3tnd2+/eHB4K+NUYOLimMWi5yNJGOXEVVQx0ksEQZHPSNefXOR+954ISWN+o6YJ8SI04jSkGCkt3Q2udDRApjkslmzLqdZrlRa0rbLTqNebmlScplNrQcey5yiBJTrD4vsgiHEaEa4wQ1L2HTtRXoaEopiRmTlIJUkQnqAR6WvKUUSkl80XnsFTrQQwjIV+XMG5+n0iQ5GU08jXyQipsfzt5eJfXj9VYdPLKE9SRThefBSmDKoY5tfDgAqCFZtqgrCgeleIx0ggrHRHeQlfl8L/iVu2WpZzXS21z5dtFMAxOAFnwAEN0AaXoANcgEEEHsATeDaE8Wi8GK+L6IqxnDkCP2C8fQJfv4+u</latexit><latexit sha1_base64="Sfe8eRLMnIC8TeY3PQoRuGrpvgA=">AAAB73icdVDLSsNAFJ34rPFVdelmsAiuQtJ3d0U3LlxUMLbShjKZTNqhk0mYmQgl9CvcuFBx6++482+ctBVU9MDA4ZxzmXuPnzAqlW1/GCura+sbm4Utc3tnd2+/eHB4K+NUYOLimMWi5yNJGOXEVVQx0ksEQZHPSNefXOR+954ISWN+o6YJ8SI04jSkGCkt3Q2udDRApjkslmzLqdZrlRa0rbLTqNebmlScplNrQcey5yiBJTrD4vsgiHEaEa4wQ1L2HTtRXoaEopiRmTlIJUkQnqAR6WvKUUSkl80XnsFTrQQwjIV+XMG5+n0iQ5GU08jXyQipsfzt5eJfXj9VYdPLKE9SRThefBSmDKoY5tfDgAqCFZtqgrCgeleIx0ggrHRHeQlfl8L/iVu2WpZzXS21z5dtFMAxOAFnwAEN0AaXoANcgEEEHsATeDaE8Wi8GK+L6IqxnDkCP2C8fQJfv4+u</latexit>

(1� ⇠2

Hkphy)

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Page 17: mirzagholi.pdf - CERN Indico

Constraints on Free Parameters

Conservative case: More radical case:

⇤ = Mpl<latexit sha1_base64="bdfr7ZOqQCUiJCm4kHzLdqgi9dA=">AAAB+nicdVDLSsNAFJ3UV62vWJduBovgKiR9dyEU3bhQqGBsoS1hMpm2QycPZiZiCfkVNy5U3Pol7vwbJ20FFT0wcDjnXO6d40aMCmmaH1puZXVtfSO/Wdja3tnd0/eLtyKMOSY2DlnIey4ShNGA2JJKRnoRJ8h3Gem60/PM794RLmgY3MhZRIY+Ggd0RDGSSnL04uBShT0ET+GVk0QsLRQcvWQaVrVeq7SgaZStRr3eVKRiNa1aC1qGOUcJLNFx9PeBF+LYJ4HEDAnRt8xIDhPEJcWMpIVBLEiE8BSNSV/RAPlEDJP57Sk8VooHRyFXL5Bwrn6fSJAvxMx3VdJHciJ+e5n4l9eP5ag5TGgQxZIEeLFoFDMoQ5gVAT3KCZZspgjCnKpbIZ4gjrBUdWUlfP0U/k/sstEyrOtqqX22bCMPDsEROAEWaIA2uAAdYAMM7sEDeALPWqo9ai/a6yKa05YzB+AHtLdPz/qTNg==</latexit><latexit sha1_base64="bdfr7ZOqQCUiJCm4kHzLdqgi9dA=">AAAB+nicdVDLSsNAFJ3UV62vWJduBovgKiR9dyEU3bhQqGBsoS1hMpm2QycPZiZiCfkVNy5U3Pol7vwbJ20FFT0wcDjnXO6d40aMCmmaH1puZXVtfSO/Wdja3tnd0/eLtyKMOSY2DlnIey4ShNGA2JJKRnoRJ8h3Gem60/PM794RLmgY3MhZRIY+Ggd0RDGSSnL04uBShT0ET+GVk0QsLRQcvWQaVrVeq7SgaZStRr3eVKRiNa1aC1qGOUcJLNFx9PeBF+LYJ4HEDAnRt8xIDhPEJcWMpIVBLEiE8BSNSV/RAPlEDJP57Sk8VooHRyFXL5Bwrn6fSJAvxMx3VdJHciJ+e5n4l9eP5ag5TGgQxZIEeLFoFDMoQ5gVAT3KCZZspgjCnKpbIZ4gjrBUdWUlfP0U/k/sstEyrOtqqX22bCMPDsEROAEWaIA2uAAdYAMM7sEDeALPWqo9ai/a6yKa05YzB+AHtLdPz/qTNg==</latexit><latexit sha1_base64="bdfr7ZOqQCUiJCm4kHzLdqgi9dA=">AAAB+nicdVDLSsNAFJ3UV62vWJduBovgKiR9dyEU3bhQqGBsoS1hMpm2QycPZiZiCfkVNy5U3Pol7vwbJ20FFT0wcDjnXO6d40aMCmmaH1puZXVtfSO/Wdja3tnd0/eLtyKMOSY2DlnIey4ShNGA2JJKRnoRJ8h3Gem60/PM794RLmgY3MhZRIY+Ggd0RDGSSnL04uBShT0ET+GVk0QsLRQcvWQaVrVeq7SgaZStRr3eVKRiNa1aC1qGOUcJLNFx9PeBF+LYJ4HEDAnRt8xIDhPEJcWMpIVBLEiE8BSNSV/RAPlEDJP57Sk8VooHRyFXL5Bwrn6fSJAvxMx3VdJHciJ+e5n4l9eP5ag5TGgQxZIEeLFoFDMoQ5gVAT3KCZZspgjCnKpbIZ4gjrBUdWUlfP0U/k/sstEyrOtqqX22bCMPDsEROAEWaIA2uAAdYAMM7sEDeALPWqo9ai/a6yKa05YzB+AHtLdPz/qTNg==</latexit><latexit sha1_base64="bdfr7ZOqQCUiJCm4kHzLdqgi9dA=">AAAB+nicdVDLSsNAFJ3UV62vWJduBovgKiR9dyEU3bhQqGBsoS1hMpm2QycPZiZiCfkVNy5U3Pol7vwbJ20FFT0wcDjnXO6d40aMCmmaH1puZXVtfSO/Wdja3tnd0/eLtyKMOSY2DlnIey4ShNGA2JJKRnoRJ8h3Gem60/PM794RLmgY3MhZRIY+Ggd0RDGSSnL04uBShT0ET+GVk0QsLRQcvWQaVrVeq7SgaZStRr3eVKRiNa1aC1qGOUcJLNFx9PeBF+LYJ4HEDAnRt8xIDhPEJcWMpIVBLEiE8BSNSV/RAPlEDJP57Sk8VooHRyFXL5Bwrn6fSJAvxMx3VdJHciJ+e5n4l9eP5ag5TGgQxZIEeLFoFDMoQ5gVAT3KCZZspgjCnKpbIZ4gjrBUdWUlfP0U/k/sstEyrOtqqX22bCMPDsEROAEWaIA2uAAdYAMM7sEDeALPWqo9ai/a6yKa05YzB+AHtLdPz/qTNg==</latexit>

⇤ = 20H<latexit sha1_base64="RW/rRpT6OdBDwWRFKXpNLsdzTFA=">AAAB+XicdVDLSsNAFJ3UV42vVJduBovgKiR9dyEU3XThooKxQhvKZDJth04ezEyUEvspblyouPVP3Pk3TtoKKnpg4HDOudw7x4sZFdKyPrTcyura+kZ+U9/a3tndMwr71yJKOCYOjljEbzwkCKMhcSSVjNzEnKDAY6TrTc4zv3tLuKBReCWnMXEDNArpkGIklTQwCv0LFfYRPIUlC7Z1XR8YRcu0K7VquQkts2TXa7WGImW7YVeb0DatOYpgic7AeO/7EU4CEkrMkBA924qlmyIuKWZkpvcTQWKEJ2hEeoqGKCDCTeenz+CxUnw4jLh6oYRz9ftEigIhpoGnkgGSY/Hby8S/vF4ihw03pWGcSBLixaJhwqCMYNYD9CknWLKpIghzqm6FeIw4wlK1lZXw9VP4P3FKZtO0LyvF1tmyjTw4BEfgBNigDlqgDTrAARjcgQfwBJ61e+1Re9FeF9Gctpw5AD+gvX0CGWqRgA==</latexit><latexit sha1_base64="RW/rRpT6OdBDwWRFKXpNLsdzTFA=">AAAB+XicdVDLSsNAFJ3UV42vVJduBovgKiR9dyEU3XThooKxQhvKZDJth04ezEyUEvspblyouPVP3Pk3TtoKKnpg4HDOudw7x4sZFdKyPrTcyura+kZ+U9/a3tndMwr71yJKOCYOjljEbzwkCKMhcSSVjNzEnKDAY6TrTc4zv3tLuKBReCWnMXEDNArpkGIklTQwCv0LFfYRPIUlC7Z1XR8YRcu0K7VquQkts2TXa7WGImW7YVeb0DatOYpgic7AeO/7EU4CEkrMkBA924qlmyIuKWZkpvcTQWKEJ2hEeoqGKCDCTeenz+CxUnw4jLh6oYRz9ftEigIhpoGnkgGSY/Hby8S/vF4ihw03pWGcSBLixaJhwqCMYNYD9CknWLKpIghzqm6FeIw4wlK1lZXw9VP4P3FKZtO0LyvF1tmyjTw4BEfgBNigDlqgDTrAARjcgQfwBJ61e+1Re9FeF9Gctpw5AD+gvX0CGWqRgA==</latexit><latexit sha1_base64="RW/rRpT6OdBDwWRFKXpNLsdzTFA=">AAAB+XicdVDLSsNAFJ3UV42vVJduBovgKiR9dyEU3XThooKxQhvKZDJth04ezEyUEvspblyouPVP3Pk3TtoKKnpg4HDOudw7x4sZFdKyPrTcyura+kZ+U9/a3tndMwr71yJKOCYOjljEbzwkCKMhcSSVjNzEnKDAY6TrTc4zv3tLuKBReCWnMXEDNArpkGIklTQwCv0LFfYRPIUlC7Z1XR8YRcu0K7VquQkts2TXa7WGImW7YVeb0DatOYpgic7AeO/7EU4CEkrMkBA924qlmyIuKWZkpvcTQWKEJ2hEeoqGKCDCTeenz+CxUnw4jLh6oYRz9ftEigIhpoGnkgGSY/Hby8S/vF4ihw03pWGcSBLixaJhwqCMYNYD9CknWLKpIghzqm6FeIw4wlK1lZXw9VP4P3FKZtO0LyvF1tmyjTw4BEfgBNigDlqgDTrAARjcgQfwBJ61e+1Re9FeF9Gctpw5AD+gvX0CGWqRgA==</latexit><latexit sha1_base64="RW/rRpT6OdBDwWRFKXpNLsdzTFA=">AAAB+XicdVDLSsNAFJ3UV42vVJduBovgKiR9dyEU3XThooKxQhvKZDJth04ezEyUEvspblyouPVP3Pk3TtoKKnpg4HDOudw7x4sZFdKyPrTcyura+kZ+U9/a3tndMwr71yJKOCYOjljEbzwkCKMhcSSVjNzEnKDAY6TrTc4zv3tLuKBReCWnMXEDNArpkGIklTQwCv0LFfYRPIUlC7Z1XR8YRcu0K7VquQkts2TXa7WGImW7YVeb0DatOYpgic7AeO/7EU4CEkrMkBA924qlmyIuKWZkpvcTQWKEJ2hEeoqGKCDCTeenz+CxUnw4jLh6oYRz9ftEigIhpoGnkgGSY/Hby8S/vF4ihw03pWGcSBLixaJhwqCMYNYD9CknWLKpIghzqm6FeIw4wlK1lZXw9VP4P3FKZtO0LyvF1tmyjTw4BEfgBNigDlqgDTrAARjcgQfwBJ61e+1Re9FeF9Gctpw5AD+gvX0CGWqRgA==</latexit>

⇠2 < H/Mpl<latexit sha1_base64="/nXBeI56vEOukGDBDXzZiIj1Us4=">AAAB/XicdVDLSsNAFJ3UV62vqLhyM1gEVzHpu+Ci6KYboYKxhTaEyXTaDp08mJmIJRT8FTcuVNz6H+78GydtBRU9cOFwzr3ce48XMSqkaX5omaXlldW17HpuY3Nre0ff3bsRYcwxsXHIQt7xkCCMBsSWVDLSiThBvsdI2xtfpH77lnBBw+BaTiLi+GgY0AHFSCrJ1Q96d9QtwDPYPL10k4hNYU7B1fOmYZUq5WIdmkbBqlYqNUWKVs0q16FlmDPkwQItV3/v9UMc+ySQmCEhupYZSSdBXFLMyDTXiwWJEB6jIekqGiCfCCeZnT+Fx0rpw0HIVQUSztTvEwnyhZj4nur0kRyJ314q/uV1YzmoOQkNoliSAM8XDWIGZQjTLGCfcoIlmyiCMKfqVohHiCMsVWJpCF+fwv+JXTDqhnVVyjfOF2lkwSE4AifAAlXQAE3QAjbAIAEP4Ak8a/fao/aivc5bM9piZh/8gPb2CRQZky8=</latexit><latexit sha1_base64="/nXBeI56vEOukGDBDXzZiIj1Us4=">AAAB/XicdVDLSsNAFJ3UV62vqLhyM1gEVzHpu+Ci6KYboYKxhTaEyXTaDp08mJmIJRT8FTcuVNz6H+78GydtBRU9cOFwzr3ce48XMSqkaX5omaXlldW17HpuY3Nre0ff3bsRYcwxsXHIQt7xkCCMBsSWVDLSiThBvsdI2xtfpH77lnBBw+BaTiLi+GgY0AHFSCrJ1Q96d9QtwDPYPL10k4hNYU7B1fOmYZUq5WIdmkbBqlYqNUWKVs0q16FlmDPkwQItV3/v9UMc+ySQmCEhupYZSSdBXFLMyDTXiwWJEB6jIekqGiCfCCeZnT+Fx0rpw0HIVQUSztTvEwnyhZj4nur0kRyJ314q/uV1YzmoOQkNoliSAM8XDWIGZQjTLGCfcoIlmyiCMKfqVohHiCMsVWJpCF+fwv+JXTDqhnVVyjfOF2lkwSE4AifAAlXQAE3QAjbAIAEP4Ak8a/fao/aivc5bM9piZh/8gPb2CRQZky8=</latexit><latexit sha1_base64="/nXBeI56vEOukGDBDXzZiIj1Us4=">AAAB/XicdVDLSsNAFJ3UV62vqLhyM1gEVzHpu+Ci6KYboYKxhTaEyXTaDp08mJmIJRT8FTcuVNz6H+78GydtBRU9cOFwzr3ce48XMSqkaX5omaXlldW17HpuY3Nre0ff3bsRYcwxsXHIQt7xkCCMBsSWVDLSiThBvsdI2xtfpH77lnBBw+BaTiLi+GgY0AHFSCrJ1Q96d9QtwDPYPL10k4hNYU7B1fOmYZUq5WIdmkbBqlYqNUWKVs0q16FlmDPkwQItV3/v9UMc+ySQmCEhupYZSSdBXFLMyDTXiwWJEB6jIekqGiCfCCeZnT+Fx0rpw0HIVQUSztTvEwnyhZj4nur0kRyJ314q/uV1YzmoOQkNoliSAM8XDWIGZQjTLGCfcoIlmyiCMKfqVohHiCMsVWJpCF+fwv+JXTDqhnVVyjfOF2lkwSE4AifAAlXQAE3QAjbAIAEP4Ak8a/fao/aivc5bM9piZh/8gPb2CRQZky8=</latexit><latexit sha1_base64="/nXBeI56vEOukGDBDXzZiIj1Us4=">AAAB/XicdVDLSsNAFJ3UV62vqLhyM1gEVzHpu+Ci6KYboYKxhTaEyXTaDp08mJmIJRT8FTcuVNz6H+78GydtBRU9cOFwzr3ce48XMSqkaX5omaXlldW17HpuY3Nre0ff3bsRYcwxsXHIQt7xkCCMBsSWVDLSiThBvsdI2xtfpH77lnBBw+BaTiLi+GgY0AHFSCrJ1Q96d9QtwDPYPL10k4hNYU7B1fOmYZUq5WIdmkbBqlYqNUWKVs0q16FlmDPkwQItV3/v9UMc+ySQmCEhupYZSSdBXFLMyDTXiwWJEB6jIekqGiCfCCeZnT+Fx0rpw0HIVQUSztTvEwnyhZj4nur0kRyJ314q/uV1YzmoOQkNoliSAM8XDWIGZQjTLGCfcoIlmyiCMKfqVohHiCMsVWJpCF+fwv+JXTDqhnVVyjfOF2lkwSE4AifAAlXQAE3QAjbAIAEP4Ak8a/fao/aivc5bM9piZh/8gPb2CRQZky8=</latexit>

⇠2 < 1/20<latexit sha1_base64="bKp6P02d8RxfKlBKaY6eJy6dmxE=">AAAB+XicdVDLSgMxFM34rPU11aWbYBFcjZO+Cy6KblxWsLbQDkMmzbShmQdJRi21n+LGhYpb/8Sdf2OmraCiBy4czrmXe+/xYs6ksu0PY2l5ZXVtPbOR3dza3tk1c3vXMkoEoS0S8Uh0PCwpZyFtKaY47cSC4sDjtO2NzlO/fUOFZFF4pcYxdQI8CJnPCFZacs1c7465BXgK0UnBzqZwzbxtoVKlXKxD2yqgaqVS06SIaqhch8iyZ8iDBZqu+d7rRyQJaKgIx1J2kR0rZ4KFYoTTabaXSBpjMsID2tU0xAGVzmR2+hQeaaUP/UjoChWcqd8nJjiQchx4ujPAaih/e6n4l9dNlF9zJiyME0VDMl/kJxyqCKY5wD4TlCg+1gQTwfStkAyxwETptNIQvj6F/5NWwapb6LKUb5wt0siAA3AIjgECVdAAF6AJWoCAW/AAnsCzcW88Gi/G67x1yVjM7IMfMN4+AeunkLw=</latexit><latexit sha1_base64="bKp6P02d8RxfKlBKaY6eJy6dmxE=">AAAB+XicdVDLSgMxFM34rPU11aWbYBFcjZO+Cy6KblxWsLbQDkMmzbShmQdJRi21n+LGhYpb/8Sdf2OmraCiBy4czrmXe+/xYs6ksu0PY2l5ZXVtPbOR3dza3tk1c3vXMkoEoS0S8Uh0PCwpZyFtKaY47cSC4sDjtO2NzlO/fUOFZFF4pcYxdQI8CJnPCFZacs1c7465BXgK0UnBzqZwzbxtoVKlXKxD2yqgaqVS06SIaqhch8iyZ8iDBZqu+d7rRyQJaKgIx1J2kR0rZ4KFYoTTabaXSBpjMsID2tU0xAGVzmR2+hQeaaUP/UjoChWcqd8nJjiQchx4ujPAaih/e6n4l9dNlF9zJiyME0VDMl/kJxyqCKY5wD4TlCg+1gQTwfStkAyxwETptNIQvj6F/5NWwapb6LKUb5wt0siAA3AIjgECVdAAF6AJWoCAW/AAnsCzcW88Gi/G67x1yVjM7IMfMN4+AeunkLw=</latexit><latexit sha1_base64="bKp6P02d8RxfKlBKaY6eJy6dmxE=">AAAB+XicdVDLSgMxFM34rPU11aWbYBFcjZO+Cy6KblxWsLbQDkMmzbShmQdJRi21n+LGhYpb/8Sdf2OmraCiBy4czrmXe+/xYs6ksu0PY2l5ZXVtPbOR3dza3tk1c3vXMkoEoS0S8Uh0PCwpZyFtKaY47cSC4sDjtO2NzlO/fUOFZFF4pcYxdQI8CJnPCFZacs1c7465BXgK0UnBzqZwzbxtoVKlXKxD2yqgaqVS06SIaqhch8iyZ8iDBZqu+d7rRyQJaKgIx1J2kR0rZ4KFYoTTabaXSBpjMsID2tU0xAGVzmR2+hQeaaUP/UjoChWcqd8nJjiQchx4ujPAaih/e6n4l9dNlF9zJiyME0VDMl/kJxyqCKY5wD4TlCg+1gQTwfStkAyxwETptNIQvj6F/5NWwapb6LKUb5wt0siAA3AIjgECVdAAF6AJWoCAW/AAnsCzcW88Gi/G67x1yVjM7IMfMN4+AeunkLw=</latexit><latexit sha1_base64="bKp6P02d8RxfKlBKaY6eJy6dmxE=">AAAB+XicdVDLSgMxFM34rPU11aWbYBFcjZO+Cy6KblxWsLbQDkMmzbShmQdJRi21n+LGhYpb/8Sdf2OmraCiBy4czrmXe+/xYs6ksu0PY2l5ZXVtPbOR3dza3tk1c3vXMkoEoS0S8Uh0PCwpZyFtKaY47cSC4sDjtO2NzlO/fUOFZFF4pcYxdQI8CJnPCFZacs1c7465BXgK0UnBzqZwzbxtoVKlXKxD2yqgaqVS06SIaqhch8iyZ8iDBZqu+d7rRyQJaKgIx1J2kR0rZ4KFYoTTabaXSBpjMsID2tU0xAGVzmR2+hQeaaUP/UjoChWcqd8nJjiQchx4ujPAaih/e6n4l9dNlF9zJiyME0VDMl/kJxyqCKY5wD4TlCg+1gQTwfStkAyxwETptNIQvj6F/5NWwapb6LKUb5wt0siAA3AIjgECVdAAF6AJWoCAW/AAnsCzcW88Gi/G67x1yVjM7IMfMN4+AeunkLw=</latexit>

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<latexit sha1_base64="5wmsVx3YwM/rzu+2PLI3O0arsQ4=">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</latexit><latexit sha1_base64="5wmsVx3YwM/rzu+2PLI3O0arsQ4=">AAACO3icdVBLSwMxGMzWV62vqkcvwSLUy7Kp2gd4KHrpRVC0ttAtSzbNtsHsgyQrlmV/mBd/hDdPXjyoePVuulZQ0YGQYWY+km/ciDOpLOvByM3Mzs0v5BcLS8srq2vF9Y1LGcaC0DYJeSi6LpaUs4C2FVOcdiNBse9y2nGvjid+55oKycLgQo0j2vfxMGAeI1hpySme21yHB9ipwENYgbbLhsOy7QlMki8HpYl9w/SVmbvfIydOEvE0TVpTr5DBKZYsE+1XD/Ya0DIrqFat1jXZQ3V00IDItDKUwBSnTvHeHoQk9mmgCMdS9pAVqX6ChWKE07Rgx5JGmFzhIe1pGmCfyn6SLZ/CHa0MoBcKfQIFM/X7RIJ9Kce+q5M+ViP525uIf3m9WHn1fsKCKFY0IJ8PeTGHKoSTJuGACUoUH2uCiWD6r5CMsK5F6b4nJXxtCv8n7YrZMNHZfql5NG0jD7bANigDBGqgCVrgFLQBAbfgETyDF+POeDJejbfPaM6YzmyCHzDePwBTGqyS</latexit><latexit sha1_base64="5wmsVx3YwM/rzu+2PLI3O0arsQ4=">AAACO3icdVBLSwMxGMzWV62vqkcvwSLUy7Kp2gd4KHrpRVC0ttAtSzbNtsHsgyQrlmV/mBd/hDdPXjyoePVuulZQ0YGQYWY+km/ciDOpLOvByM3Mzs0v5BcLS8srq2vF9Y1LGcaC0DYJeSi6LpaUs4C2FVOcdiNBse9y2nGvjid+55oKycLgQo0j2vfxMGAeI1hpySme21yHB9ipwENYgbbLhsOy7QlMki8HpYl9w/SVmbvfIydOEvE0TVpTr5DBKZYsE+1XD/Ya0DIrqFat1jXZQ3V00IDItDKUwBSnTvHeHoQk9mmgCMdS9pAVqX6ChWKE07Rgx5JGmFzhIe1pGmCfyn6SLZ/CHa0MoBcKfQIFM/X7RIJ9Kce+q5M+ViP525uIf3m9WHn1fsKCKFY0IJ8PeTGHKoSTJuGACUoUH2uCiWD6r5CMsK5F6b4nJXxtCv8n7YrZMNHZfql5NG0jD7bANigDBGqgCVrgFLQBAbfgETyDF+POeDJejbfPaM6YzmyCHzDePwBTGqyS</latexit><latexit sha1_base64="5wmsVx3YwM/rzu+2PLI3O0arsQ4=">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</latexit>

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◆2

<latexit sha1_base64="TiGoe7K0psDftx+amZjeceaL5sw=">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</latexit><latexit sha1_base64="TiGoe7K0psDftx+amZjeceaL5sw=">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</latexit><latexit sha1_base64="TiGoe7K0psDftx+amZjeceaL5sw=">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</latexit><latexit sha1_base64="TiGoe7K0psDftx+amZjeceaL5sw=">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</latexit>

�2 = 2⇠2�1

⇠1

✓Mpl

H

◆2

<latexit sha1_base64="vvaDDlmCpC93B20RD+H4fLcZk6I=">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</latexit><latexit sha1_base64="vvaDDlmCpC93B20RD+H4fLcZk6I=">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</latexit><latexit sha1_base64="vvaDDlmCpC93B20RD+H4fLcZk6I=">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</latexit><latexit sha1_base64="vvaDDlmCpC93B20RD+H4fLcZk6I=">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</latexit>

Page 18: mirzagholi.pdf - CERN Indico

Constraints on Free Parameters

No stringent constraints on �2<latexit sha1_base64="PQL7VrRMVNEc3uCQlA3oU8ZbKqE=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4GiZ9d1d047KCY4vtUDKZTBuayQxJRiilf+HGhYpbP8edf2OmraCiBwKHc84l9x4/4Uxpx/mwcmvrG5tb+e3Czu7e/kHx8OhWxakk1CUxj2XPx4pyJqirmea0l0iKI5/Trj+5zPzuPZWKxeJGTxPqRXgkWMgI1ka6G3ATDfCwXBgWS46NqvVapQUdu4wa9XrTkApqoloLIttZoARW6AyL74MgJmlEhSYcK9VHTqK9GZaaEU7nhUGqaILJBI9o31CBI6q82WLjOTwzSgDDWJonNFyo3ydmOFJqGvkmGWE9Vr+9TPzL66c6bHozJpJUU0GWH4UphzqG2fkwYJISzaeGYCKZ2RWSMZaYaFNSVsLXpfB/4pbtlo2uq6X2xaqNPDgBp+AcINAAbXAFOsAFBAjwAJ7As6WsR+vFel1Gc9Zq5hj8gPX2CYW5kF8=</latexit><latexit sha1_base64="PQL7VrRMVNEc3uCQlA3oU8ZbKqE=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4GiZ9d1d047KCY4vtUDKZTBuayQxJRiilf+HGhYpbP8edf2OmraCiBwKHc84l9x4/4Uxpx/mwcmvrG5tb+e3Czu7e/kHx8OhWxakk1CUxj2XPx4pyJqirmea0l0iKI5/Trj+5zPzuPZWKxeJGTxPqRXgkWMgI1ka6G3ATDfCwXBgWS46NqvVapQUdu4wa9XrTkApqoloLIttZoARW6AyL74MgJmlEhSYcK9VHTqK9GZaaEU7nhUGqaILJBI9o31CBI6q82WLjOTwzSgDDWJonNFyo3ydmOFJqGvkmGWE9Vr+9TPzL66c6bHozJpJUU0GWH4UphzqG2fkwYJISzaeGYCKZ2RWSMZaYaFNSVsLXpfB/4pbtlo2uq6X2xaqNPDgBp+AcINAAbXAFOsAFBAjwAJ7As6WsR+vFel1Gc9Zq5hj8gPX2CYW5kF8=</latexit><latexit sha1_base64="PQL7VrRMVNEc3uCQlA3oU8ZbKqE=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4GiZ9d1d047KCY4vtUDKZTBuayQxJRiilf+HGhYpbP8edf2OmraCiBwKHc84l9x4/4Uxpx/mwcmvrG5tb+e3Czu7e/kHx8OhWxakk1CUxj2XPx4pyJqirmea0l0iKI5/Trj+5zPzuPZWKxeJGTxPqRXgkWMgI1ka6G3ATDfCwXBgWS46NqvVapQUdu4wa9XrTkApqoloLIttZoARW6AyL74MgJmlEhSYcK9VHTqK9GZaaEU7nhUGqaILJBI9o31CBI6q82WLjOTwzSgDDWJonNFyo3ydmOFJqGvkmGWE9Vr+9TPzL66c6bHozJpJUU0GWH4UphzqG2fkwYJISzaeGYCKZ2RWSMZaYaFNSVsLXpfB/4pbtlo2uq6X2xaqNPDgBp+AcINAAbXAFOsAFBAjwAJ7As6WsR+vFel1Gc9Zq5hj8gPX2CYW5kF8=</latexit><latexit sha1_base64="PQL7VrRMVNEc3uCQlA3oU8ZbKqE=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4GiZ9d1d047KCY4vtUDKZTBuayQxJRiilf+HGhYpbP8edf2OmraCiBwKHc84l9x4/4Uxpx/mwcmvrG5tb+e3Czu7e/kHx8OhWxakk1CUxj2XPx4pyJqirmea0l0iKI5/Trj+5zPzuPZWKxeJGTxPqRXgkWMgI1ka6G3ATDfCwXBgWS46NqvVapQUdu4wa9XrTkApqoloLIttZoARW6AyL74MgJmlEhSYcK9VHTqK9GZaaEU7nhUGqaILJBI9o31CBI6q82WLjOTwzSgDDWJonNFyo3ydmOFJqGvkmGWE9Vr+9TPzL66c6bHozJpJUU0GWH4UphzqG2fkwYJISzaeGYCKZ2RWSMZaYaFNSVsLXpfB/4pbtlo2uq6X2xaqNPDgBp+AcINAAbXAFOsAFBAjwAJ7As6WsR+vFel1Gc9Zq5hj8gPX2CYW5kF8=</latexit>

Conservative case: More radical case:

⇤ = Mpl<latexit sha1_base64="bdfr7ZOqQCUiJCm4kHzLdqgi9dA=">AAAB+nicdVDLSsNAFJ3UV62vWJduBovgKiR9dyEU3bhQqGBsoS1hMpm2QycPZiZiCfkVNy5U3Pol7vwbJ20FFT0wcDjnXO6d40aMCmmaH1puZXVtfSO/Wdja3tnd0/eLtyKMOSY2DlnIey4ShNGA2JJKRnoRJ8h3Gem60/PM794RLmgY3MhZRIY+Ggd0RDGSSnL04uBShT0ET+GVk0QsLRQcvWQaVrVeq7SgaZStRr3eVKRiNa1aC1qGOUcJLNFx9PeBF+LYJ4HEDAnRt8xIDhPEJcWMpIVBLEiE8BSNSV/RAPlEDJP57Sk8VooHRyFXL5Bwrn6fSJAvxMx3VdJHciJ+e5n4l9eP5ag5TGgQxZIEeLFoFDMoQ5gVAT3KCZZspgjCnKpbIZ4gjrBUdWUlfP0U/k/sstEyrOtqqX22bCMPDsEROAEWaIA2uAAdYAMM7sEDeALPWqo9ai/a6yKa05YzB+AHtLdPz/qTNg==</latexit><latexit sha1_base64="bdfr7ZOqQCUiJCm4kHzLdqgi9dA=">AAAB+nicdVDLSsNAFJ3UV62vWJduBovgKiR9dyEU3bhQqGBsoS1hMpm2QycPZiZiCfkVNy5U3Pol7vwbJ20FFT0wcDjnXO6d40aMCmmaH1puZXVtfSO/Wdja3tnd0/eLtyKMOSY2DlnIey4ShNGA2JJKRnoRJ8h3Gem60/PM794RLmgY3MhZRIY+Ggd0RDGSSnL04uBShT0ET+GVk0QsLRQcvWQaVrVeq7SgaZStRr3eVKRiNa1aC1qGOUcJLNFx9PeBF+LYJ4HEDAnRt8xIDhPEJcWMpIVBLEiE8BSNSV/RAPlEDJP57Sk8VooHRyFXL5Bwrn6fSJAvxMx3VdJHciJ+e5n4l9eP5ag5TGgQxZIEeLFoFDMoQ5gVAT3KCZZspgjCnKpbIZ4gjrBUdWUlfP0U/k/sstEyrOtqqX22bCMPDsEROAEWaIA2uAAdYAMM7sEDeALPWqo9ai/a6yKa05YzB+AHtLdPz/qTNg==</latexit><latexit sha1_base64="bdfr7ZOqQCUiJCm4kHzLdqgi9dA=">AAAB+nicdVDLSsNAFJ3UV62vWJduBovgKiR9dyEU3bhQqGBsoS1hMpm2QycPZiZiCfkVNy5U3Pol7vwbJ20FFT0wcDjnXO6d40aMCmmaH1puZXVtfSO/Wdja3tnd0/eLtyKMOSY2DlnIey4ShNGA2JJKRnoRJ8h3Gem60/PM794RLmgY3MhZRIY+Ggd0RDGSSnL04uBShT0ET+GVk0QsLRQcvWQaVrVeq7SgaZStRr3eVKRiNa1aC1qGOUcJLNFx9PeBF+LYJ4HEDAnRt8xIDhPEJcWMpIVBLEiE8BSNSV/RAPlEDJP57Sk8VooHRyFXL5Bwrn6fSJAvxMx3VdJHciJ+e5n4l9eP5ag5TGgQxZIEeLFoFDMoQ5gVAT3KCZZspgjCnKpbIZ4gjrBUdWUlfP0U/k/sstEyrOtqqX22bCMPDsEROAEWaIA2uAAdYAMM7sEDeALPWqo9ai/a6yKa05YzB+AHtLdPz/qTNg==</latexit><latexit sha1_base64="bdfr7ZOqQCUiJCm4kHzLdqgi9dA=">AAAB+nicdVDLSsNAFJ3UV62vWJduBovgKiR9dyEU3bhQqGBsoS1hMpm2QycPZiZiCfkVNy5U3Pol7vwbJ20FFT0wcDjnXO6d40aMCmmaH1puZXVtfSO/Wdja3tnd0/eLtyKMOSY2DlnIey4ShNGA2JJKRnoRJ8h3Gem60/PM794RLmgY3MhZRIY+Ggd0RDGSSnL04uBShT0ET+GVk0QsLRQcvWQaVrVeq7SgaZStRr3eVKRiNa1aC1qGOUcJLNFx9PeBF+LYJ4HEDAnRt8xIDhPEJcWMpIVBLEiE8BSNSV/RAPlEDJP57Sk8VooHRyFXL5Bwrn6fSJAvxMx3VdJHciJ+e5n4l9eP5ag5TGgQxZIEeLFoFDMoQ5gVAT3KCZZspgjCnKpbIZ4gjrBUdWUlfP0U/k/sstEyrOtqqX22bCMPDsEROAEWaIA2uAAdYAMM7sEDeALPWqo9ai/a6yKa05YzB+AHtLdPz/qTNg==</latexit>

⇤ = 20H<latexit sha1_base64="RW/rRpT6OdBDwWRFKXpNLsdzTFA=">AAAB+XicdVDLSsNAFJ3UV42vVJduBovgKiR9dyEU3XThooKxQhvKZDJth04ezEyUEvspblyouPVP3Pk3TtoKKnpg4HDOudw7x4sZFdKyPrTcyura+kZ+U9/a3tndMwr71yJKOCYOjljEbzwkCKMhcSSVjNzEnKDAY6TrTc4zv3tLuKBReCWnMXEDNArpkGIklTQwCv0LFfYRPIUlC7Z1XR8YRcu0K7VquQkts2TXa7WGImW7YVeb0DatOYpgic7AeO/7EU4CEkrMkBA924qlmyIuKWZkpvcTQWKEJ2hEeoqGKCDCTeenz+CxUnw4jLh6oYRz9ftEigIhpoGnkgGSY/Hby8S/vF4ihw03pWGcSBLixaJhwqCMYNYD9CknWLKpIghzqm6FeIw4wlK1lZXw9VP4P3FKZtO0LyvF1tmyjTw4BEfgBNigDlqgDTrAARjcgQfwBJ61e+1Re9FeF9Gctpw5AD+gvX0CGWqRgA==</latexit><latexit sha1_base64="RW/rRpT6OdBDwWRFKXpNLsdzTFA=">AAAB+XicdVDLSsNAFJ3UV42vVJduBovgKiR9dyEU3XThooKxQhvKZDJth04ezEyUEvspblyouPVP3Pk3TtoKKnpg4HDOudw7x4sZFdKyPrTcyura+kZ+U9/a3tndMwr71yJKOCYOjljEbzwkCKMhcSSVjNzEnKDAY6TrTc4zv3tLuKBReCWnMXEDNArpkGIklTQwCv0LFfYRPIUlC7Z1XR8YRcu0K7VquQkts2TXa7WGImW7YVeb0DatOYpgic7AeO/7EU4CEkrMkBA924qlmyIuKWZkpvcTQWKEJ2hEeoqGKCDCTeenz+CxUnw4jLh6oYRz9ftEigIhpoGnkgGSY/Hby8S/vF4ihw03pWGcSBLixaJhwqCMYNYD9CknWLKpIghzqm6FeIw4wlK1lZXw9VP4P3FKZtO0LyvF1tmyjTw4BEfgBNigDlqgDTrAARjcgQfwBJ61e+1Re9FeF9Gctpw5AD+gvX0CGWqRgA==</latexit><latexit sha1_base64="RW/rRpT6OdBDwWRFKXpNLsdzTFA=">AAAB+XicdVDLSsNAFJ3UV42vVJduBovgKiR9dyEU3XThooKxQhvKZDJth04ezEyUEvspblyouPVP3Pk3TtoKKnpg4HDOudw7x4sZFdKyPrTcyura+kZ+U9/a3tndMwr71yJKOCYOjljEbzwkCKMhcSSVjNzEnKDAY6TrTc4zv3tLuKBReCWnMXEDNArpkGIklTQwCv0LFfYRPIUlC7Z1XR8YRcu0K7VquQkts2TXa7WGImW7YVeb0DatOYpgic7AeO/7EU4CEkrMkBA924qlmyIuKWZkpvcTQWKEJ2hEeoqGKCDCTeenz+CxUnw4jLh6oYRz9ftEigIhpoGnkgGSY/Hby8S/vF4ihw03pWGcSBLixaJhwqCMYNYD9CknWLKpIghzqm6FeIw4wlK1lZXw9VP4P3FKZtO0LyvF1tmyjTw4BEfgBNigDlqgDTrAARjcgQfwBJ61e+1Re9FeF9Gctpw5AD+gvX0CGWqRgA==</latexit><latexit sha1_base64="RW/rRpT6OdBDwWRFKXpNLsdzTFA=">AAAB+XicdVDLSsNAFJ3UV42vVJduBovgKiR9dyEU3XThooKxQhvKZDJth04ezEyUEvspblyouPVP3Pk3TtoKKnpg4HDOudw7x4sZFdKyPrTcyura+kZ+U9/a3tndMwr71yJKOCYOjljEbzwkCKMhcSSVjNzEnKDAY6TrTc4zv3tLuKBReCWnMXEDNArpkGIklTQwCv0LFfYRPIUlC7Z1XR8YRcu0K7VquQkts2TXa7WGImW7YVeb0DatOYpgic7AeO/7EU4CEkrMkBA924qlmyIuKWZkpvcTQWKEJ2hEeoqGKCDCTeenz+CxUnw4jLh6oYRz9ftEigIhpoGnkgGSY/Hby8S/vF4ihw03pWGcSBLixaJhwqCMYNYD9CknWLKpIghzqm6FeIw4wlK1lZXw9VP4P3FKZtO0LyvF1tmyjTw4BEfgBNigDlqgDTrAARjcgQfwBJ61e+1Re9FeF9Gctpw5AD+gvX0CGWqRgA==</latexit>

⇠2 < H/Mpl<latexit sha1_base64="/nXBeI56vEOukGDBDXzZiIj1Us4=">AAAB/XicdVDLSsNAFJ3UV62vqLhyM1gEVzHpu+Ci6KYboYKxhTaEyXTaDp08mJmIJRT8FTcuVNz6H+78GydtBRU9cOFwzr3ce48XMSqkaX5omaXlldW17HpuY3Nre0ff3bsRYcwxsXHIQt7xkCCMBsSWVDLSiThBvsdI2xtfpH77lnBBw+BaTiLi+GgY0AHFSCrJ1Q96d9QtwDPYPL10k4hNYU7B1fOmYZUq5WIdmkbBqlYqNUWKVs0q16FlmDPkwQItV3/v9UMc+ySQmCEhupYZSSdBXFLMyDTXiwWJEB6jIekqGiCfCCeZnT+Fx0rpw0HIVQUSztTvEwnyhZj4nur0kRyJ314q/uV1YzmoOQkNoliSAM8XDWIGZQjTLGCfcoIlmyiCMKfqVohHiCMsVWJpCF+fwv+JXTDqhnVVyjfOF2lkwSE4AifAAlXQAE3QAjbAIAEP4Ak8a/fao/aivc5bM9piZh/8gPb2CRQZky8=</latexit><latexit sha1_base64="/nXBeI56vEOukGDBDXzZiIj1Us4=">AAAB/XicdVDLSsNAFJ3UV62vqLhyM1gEVzHpu+Ci6KYboYKxhTaEyXTaDp08mJmIJRT8FTcuVNz6H+78GydtBRU9cOFwzr3ce48XMSqkaX5omaXlldW17HpuY3Nre0ff3bsRYcwxsXHIQt7xkCCMBsSWVDLSiThBvsdI2xtfpH77lnBBw+BaTiLi+GgY0AHFSCrJ1Q96d9QtwDPYPL10k4hNYU7B1fOmYZUq5WIdmkbBqlYqNUWKVs0q16FlmDPkwQItV3/v9UMc+ySQmCEhupYZSSdBXFLMyDTXiwWJEB6jIekqGiCfCCeZnT+Fx0rpw0HIVQUSztTvEwnyhZj4nur0kRyJ314q/uV1YzmoOQkNoliSAM8XDWIGZQjTLGCfcoIlmyiCMKfqVohHiCMsVWJpCF+fwv+JXTDqhnVVyjfOF2lkwSE4AifAAlXQAE3QAjbAIAEP4Ak8a/fao/aivc5bM9piZh/8gPb2CRQZky8=</latexit><latexit sha1_base64="/nXBeI56vEOukGDBDXzZiIj1Us4=">AAAB/XicdVDLSsNAFJ3UV62vqLhyM1gEVzHpu+Ci6KYboYKxhTaEyXTaDp08mJmIJRT8FTcuVNz6H+78GydtBRU9cOFwzr3ce48XMSqkaX5omaXlldW17HpuY3Nre0ff3bsRYcwxsXHIQt7xkCCMBsSWVDLSiThBvsdI2xtfpH77lnBBw+BaTiLi+GgY0AHFSCrJ1Q96d9QtwDPYPL10k4hNYU7B1fOmYZUq5WIdmkbBqlYqNUWKVs0q16FlmDPkwQItV3/v9UMc+ySQmCEhupYZSSdBXFLMyDTXiwWJEB6jIekqGiCfCCeZnT+Fx0rpw0HIVQUSztTvEwnyhZj4nur0kRyJ314q/uV1YzmoOQkNoliSAM8XDWIGZQjTLGCfcoIlmyiCMKfqVohHiCMsVWJpCF+fwv+JXTDqhnVVyjfOF2lkwSE4AifAAlXQAE3QAjbAIAEP4Ak8a/fao/aivc5bM9piZh/8gPb2CRQZky8=</latexit><latexit sha1_base64="/nXBeI56vEOukGDBDXzZiIj1Us4=">AAAB/XicdVDLSsNAFJ3UV62vqLhyM1gEVzHpu+Ci6KYboYKxhTaEyXTaDp08mJmIJRT8FTcuVNz6H+78GydtBRU9cOFwzr3ce48XMSqkaX5omaXlldW17HpuY3Nre0ff3bsRYcwxsXHIQt7xkCCMBsSWVDLSiThBvsdI2xtfpH77lnBBw+BaTiLi+GgY0AHFSCrJ1Q96d9QtwDPYPL10k4hNYU7B1fOmYZUq5WIdmkbBqlYqNUWKVs0q16FlmDPkwQItV3/v9UMc+ySQmCEhupYZSSdBXFLMyDTXiwWJEB6jIekqGiCfCCeZnT+Fx0rpw0HIVQUSztTvEwnyhZj4nur0kRyJ314q/uV1YzmoOQkNoliSAM8XDWIGZQjTLGCfcoIlmyiCMKfqVohHiCMsVWJpCF+fwv+JXTDqhnVVyjfOF2lkwSE4AifAAlXQAE3QAjbAIAEP4Ak8a/fao/aivc5bM9piZh/8gPb2CRQZky8=</latexit>

⇠2 < 1/20<latexit sha1_base64="bKp6P02d8RxfKlBKaY6eJy6dmxE=">AAAB+XicdVDLSgMxFM34rPU11aWbYBFcjZO+Cy6KblxWsLbQDkMmzbShmQdJRi21n+LGhYpb/8Sdf2OmraCiBy4czrmXe+/xYs6ksu0PY2l5ZXVtPbOR3dza3tk1c3vXMkoEoS0S8Uh0PCwpZyFtKaY47cSC4sDjtO2NzlO/fUOFZFF4pcYxdQI8CJnPCFZacs1c7465BXgK0UnBzqZwzbxtoVKlXKxD2yqgaqVS06SIaqhch8iyZ8iDBZqu+d7rRyQJaKgIx1J2kR0rZ4KFYoTTabaXSBpjMsID2tU0xAGVzmR2+hQeaaUP/UjoChWcqd8nJjiQchx4ujPAaih/e6n4l9dNlF9zJiyME0VDMl/kJxyqCKY5wD4TlCg+1gQTwfStkAyxwETptNIQvj6F/5NWwapb6LKUb5wt0siAA3AIjgECVdAAF6AJWoCAW/AAnsCzcW88Gi/G67x1yVjM7IMfMN4+AeunkLw=</latexit><latexit sha1_base64="bKp6P02d8RxfKlBKaY6eJy6dmxE=">AAAB+XicdVDLSgMxFM34rPU11aWbYBFcjZO+Cy6KblxWsLbQDkMmzbShmQdJRi21n+LGhYpb/8Sdf2OmraCiBy4czrmXe+/xYs6ksu0PY2l5ZXVtPbOR3dza3tk1c3vXMkoEoS0S8Uh0PCwpZyFtKaY47cSC4sDjtO2NzlO/fUOFZFF4pcYxdQI8CJnPCFZacs1c7465BXgK0UnBzqZwzbxtoVKlXKxD2yqgaqVS06SIaqhch8iyZ8iDBZqu+d7rRyQJaKgIx1J2kR0rZ4KFYoTTabaXSBpjMsID2tU0xAGVzmR2+hQeaaUP/UjoChWcqd8nJjiQchx4ujPAaih/e6n4l9dNlF9zJiyME0VDMl/kJxyqCKY5wD4TlCg+1gQTwfStkAyxwETptNIQvj6F/5NWwapb6LKUb5wt0siAA3AIjgECVdAAF6AJWoCAW/AAnsCzcW88Gi/G67x1yVjM7IMfMN4+AeunkLw=</latexit><latexit sha1_base64="bKp6P02d8RxfKlBKaY6eJy6dmxE=">AAAB+XicdVDLSgMxFM34rPU11aWbYBFcjZO+Cy6KblxWsLbQDkMmzbShmQdJRi21n+LGhYpb/8Sdf2OmraCiBy4czrmXe+/xYs6ksu0PY2l5ZXVtPbOR3dza3tk1c3vXMkoEoS0S8Uh0PCwpZyFtKaY47cSC4sDjtO2NzlO/fUOFZFF4pcYxdQI8CJnPCFZacs1c7465BXgK0UnBzqZwzbxtoVKlXKxD2yqgaqVS06SIaqhch8iyZ8iDBZqu+d7rRyQJaKgIx1J2kR0rZ4KFYoTTabaXSBpjMsID2tU0xAGVzmR2+hQeaaUP/UjoChWcqd8nJjiQchx4ujPAaih/e6n4l9dNlF9zJiyME0VDMl/kJxyqCKY5wD4TlCg+1gQTwfStkAyxwETptNIQvj6F/5NWwapb6LKUb5wt0siAA3AIjgECVdAAF6AJWoCAW/AAnsCzcW88Gi/G67x1yVjM7IMfMN4+AeunkLw=</latexit><latexit sha1_base64="bKp6P02d8RxfKlBKaY6eJy6dmxE=">AAAB+XicdVDLSgMxFM34rPU11aWbYBFcjZO+Cy6KblxWsLbQDkMmzbShmQdJRi21n+LGhYpb/8Sdf2OmraCiBy4czrmXe+/xYs6ksu0PY2l5ZXVtPbOR3dza3tk1c3vXMkoEoS0S8Uh0PCwpZyFtKaY47cSC4sDjtO2NzlO/fUOFZFF4pcYxdQI8CJnPCFZacs1c7465BXgK0UnBzqZwzbxtoVKlXKxD2yqgaqVS06SIaqhch8iyZ8iDBZqu+d7rRyQJaKgIx1J2kR0rZ4KFYoTTabaXSBpjMsID2tU0xAGVzmR2+hQeaaUP/UjoChWcqd8nJjiQchx4ujPAaih/e6n4l9dNlF9zJiyME0VDMl/kJxyqCKY5wD4TlCg+1gQTwfStkAyxwETptNIQvj6F/5NWwapb6LKUb5wt0siAA3AIjgECVdAAF6AJWoCAW/AAnsCzcW88Gi/G67x1yVjM7IMfMN4+AeunkLw=</latexit>

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<latexit sha1_base64="5wmsVx3YwM/rzu+2PLI3O0arsQ4=">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</latexit><latexit sha1_base64="5wmsVx3YwM/rzu+2PLI3O0arsQ4=">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</latexit><latexit sha1_base64="5wmsVx3YwM/rzu+2PLI3O0arsQ4=">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</latexit><latexit sha1_base64="5wmsVx3YwM/rzu+2PLI3O0arsQ4=">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</latexit>

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⇠ O(10)<latexit sha1_base64="1nP02caU9hprOpisrdXuedGtdtM=">AAAB/XicdVDLSgMxFM34rPU1Kq7cBItQN0NG6nTcFd24s4JjC52hZNK0Dc08SDJCGQr+ihsXKm79D3f+jZm2gooeCBzOuZd7csKUM6kQ+jAWFpeWV1ZLa+X1jc2tbXNn91YmmSDUIwlPRDvEknIWU08xxWk7FRRHIaetcHRR+K07KiRL4hs1TmkQ4UHM+oxgpaWuue9LFkE/wmpIMM+vJlUbHZe7ZgVZp45rOwgiC7mu47qa2LZTc+rQttAUFTBHs2u++72EZBGNFeFYyo6NUhXkWChGOJ2U/UzSFJMRHtCOpjGOqAzyafwJPNJKD/YToV+s4FT9vpHjSMpxFOrJIqf87RXiX14nU303yFmcZorGZHaon3GoElh0AXtMUKL4WBNMBNNZIRligYnSjRUlfP0U/k+8E+vMsq9rlcb5vI0SOACHoApsUAcNcAmawAME5OABPIFn4954NF6M19nogjHf2QM/YLx9AlyDlKg=</latexit><latexit sha1_base64="1nP02caU9hprOpisrdXuedGtdtM=">AAAB/XicdVDLSgMxFM34rPU1Kq7cBItQN0NG6nTcFd24s4JjC52hZNK0Dc08SDJCGQr+ihsXKm79D3f+jZm2gooeCBzOuZd7csKUM6kQ+jAWFpeWV1ZLa+X1jc2tbXNn91YmmSDUIwlPRDvEknIWU08xxWk7FRRHIaetcHRR+K07KiRL4hs1TmkQ4UHM+oxgpaWuue9LFkE/wmpIMM+vJlUbHZe7ZgVZp45rOwgiC7mu47qa2LZTc+rQttAUFTBHs2u++72EZBGNFeFYyo6NUhXkWChGOJ2U/UzSFJMRHtCOpjGOqAzyafwJPNJKD/YToV+s4FT9vpHjSMpxFOrJIqf87RXiX14nU303yFmcZorGZHaon3GoElh0AXtMUKL4WBNMBNNZIRligYnSjRUlfP0U/k+8E+vMsq9rlcb5vI0SOACHoApsUAcNcAmawAME5OABPIFn4954NF6M19nogjHf2QM/YLx9AlyDlKg=</latexit><latexit sha1_base64="1nP02caU9hprOpisrdXuedGtdtM=">AAAB/XicdVDLSgMxFM34rPU1Kq7cBItQN0NG6nTcFd24s4JjC52hZNK0Dc08SDJCGQr+ihsXKm79D3f+jZm2gooeCBzOuZd7csKUM6kQ+jAWFpeWV1ZLa+X1jc2tbXNn91YmmSDUIwlPRDvEknIWU08xxWk7FRRHIaetcHRR+K07KiRL4hs1TmkQ4UHM+oxgpaWuue9LFkE/wmpIMM+vJlUbHZe7ZgVZp45rOwgiC7mu47qa2LZTc+rQttAUFTBHs2u++72EZBGNFeFYyo6NUhXkWChGOJ2U/UzSFJMRHtCOpjGOqAzyafwJPNJKD/YToV+s4FT9vpHjSMpxFOrJIqf87RXiX14nU303yFmcZorGZHaon3GoElh0AXtMUKL4WBNMBNNZIRligYnSjRUlfP0U/k+8E+vMsq9rlcb5vI0SOACHoApsUAcNcAmawAME5OABPIFn4954NF6M19nogjHf2QM/YLx9AlyDlKg=</latexit><latexit sha1_base64="1nP02caU9hprOpisrdXuedGtdtM=">AAAB/XicdVDLSgMxFM34rPU1Kq7cBItQN0NG6nTcFd24s4JjC52hZNK0Dc08SDJCGQr+ihsXKm79D3f+jZm2gooeCBzOuZd7csKUM6kQ+jAWFpeWV1ZLa+X1jc2tbXNn91YmmSDUIwlPRDvEknIWU08xxWk7FRRHIaetcHRR+K07KiRL4hs1TmkQ4UHM+oxgpaWuue9LFkE/wmpIMM+vJlUbHZe7ZgVZp45rOwgiC7mu47qa2LZTc+rQttAUFTBHs2u++72EZBGNFeFYyo6NUhXkWChGOJ2U/UzSFJMRHtCOpjGOqAzyafwJPNJKD/YToV+s4FT9vpHjSMpxFOrJIqf87RXiX14nU303yFmcZorGZHaon3GoElh0AXtMUKL4WBNMBNNZIRligYnSjRUlfP0U/k+8E+vMsq9rlcb5vI0SOACHoApsUAcNcAmawAME5OABPIFn4954NF6M19nogjHf2QM/YLx9AlyDlKg=</latexit>

& 1.5⇥ 109<latexit sha1_base64="blHtENLH31a4dZ0kxG77Y+9tS9g=">AAACAXicdVDLSgMxFM3UV62vqitxEyyCqyEj7XS6K7pxWcHaQltLJk3b0MyD5I5QhuLGX3HjQsWtf+HOvzF9CCp6IHA451xu7vFjKTQQ8mFllpZXVtey67mNza3tnfzu3rWOEsV4nUUyUk2fai5FyOsgQPJmrDgNfMkb/uh86jduudIiCq9gHPNOQAeh6AtGwUjd/EF7AMYNsGOXcBtEwDV2yE1amXTzBWKXXM9xCSY28TzX8wxxHLfolk2czFBAC9S6+fd2L2JJwENgkmrdckgMnZQqEEzySa6daB5TNqID3jI0pGZXJ52dMMHHRunhfqTMCwHP1O8TKQ20Hge+SQYUhvq3NxX/8loJ9L1OKsI4AR6y+aJ+IjFEeNoH7gnFGcixIZQpYf6K2ZAqysC0ljMlfF2K/yf1U7tiO5fFQvVs0UYWHaIjdIIcVEZVdIFqqI4YukMP6Ak9W/fWo/Vivc6jGWsxs49+wHr7BA4mliY=</latexit><latexit sha1_base64="blHtENLH31a4dZ0kxG77Y+9tS9g=">AAACAXicdVDLSgMxFM3UV62vqitxEyyCqyEj7XS6K7pxWcHaQltLJk3b0MyD5I5QhuLGX3HjQsWtf+HOvzF9CCp6IHA451xu7vFjKTQQ8mFllpZXVtey67mNza3tnfzu3rWOEsV4nUUyUk2fai5FyOsgQPJmrDgNfMkb/uh86jduudIiCq9gHPNOQAeh6AtGwUjd/EF7AMYNsGOXcBtEwDV2yE1amXTzBWKXXM9xCSY28TzX8wxxHLfolk2czFBAC9S6+fd2L2JJwENgkmrdckgMnZQqEEzySa6daB5TNqID3jI0pGZXJ52dMMHHRunhfqTMCwHP1O8TKQ20Hge+SQYUhvq3NxX/8loJ9L1OKsI4AR6y+aJ+IjFEeNoH7gnFGcixIZQpYf6K2ZAqysC0ljMlfF2K/yf1U7tiO5fFQvVs0UYWHaIjdIIcVEZVdIFqqI4YukMP6Ak9W/fWo/Vivc6jGWsxs49+wHr7BA4mliY=</latexit><latexit sha1_base64="blHtENLH31a4dZ0kxG77Y+9tS9g=">AAACAXicdVDLSgMxFM3UV62vqitxEyyCqyEj7XS6K7pxWcHaQltLJk3b0MyD5I5QhuLGX3HjQsWtf+HOvzF9CCp6IHA451xu7vFjKTQQ8mFllpZXVtey67mNza3tnfzu3rWOEsV4nUUyUk2fai5FyOsgQPJmrDgNfMkb/uh86jduudIiCq9gHPNOQAeh6AtGwUjd/EF7AMYNsGOXcBtEwDV2yE1amXTzBWKXXM9xCSY28TzX8wxxHLfolk2czFBAC9S6+fd2L2JJwENgkmrdckgMnZQqEEzySa6daB5TNqID3jI0pGZXJ52dMMHHRunhfqTMCwHP1O8TKQ20Hge+SQYUhvq3NxX/8loJ9L1OKsI4AR6y+aJ+IjFEeNoH7gnFGcixIZQpYf6K2ZAqysC0ljMlfF2K/yf1U7tiO5fFQvVs0UYWHaIjdIIcVEZVdIFqqI4YukMP6Ak9W/fWo/Vivc6jGWsxs49+wHr7BA4mliY=</latexit><latexit sha1_base64="blHtENLH31a4dZ0kxG77Y+9tS9g=">AAACAXicdVDLSgMxFM3UV62vqitxEyyCqyEj7XS6K7pxWcHaQltLJk3b0MyD5I5QhuLGX3HjQsWtf+HOvzF9CCp6IHA451xu7vFjKTQQ8mFllpZXVtey67mNza3tnfzu3rWOEsV4nUUyUk2fai5FyOsgQPJmrDgNfMkb/uh86jduudIiCq9gHPNOQAeh6AtGwUjd/EF7AMYNsGOXcBtEwDV2yE1amXTzBWKXXM9xCSY28TzX8wxxHLfolk2czFBAC9S6+fd2L2JJwENgkmrdckgMnZQqEEzySa6daB5TNqID3jI0pGZXJ52dMMHHRunhfqTMCwHP1O8TKQ20Hge+SQYUhvq3NxX/8loJ9L1OKsI4AR6y+aJ+IjFEeNoH7gnFGcixIZQpYf6K2ZAqysC0ljMlfF2K/yf1U7tiO5fFQvVs0UYWHaIjdIIcVEZVdIFqqI4YukMP6Ak9W/fWo/Vivc6jGWsxs49+wHr7BA4mliY=</latexit>

Page 19: mirzagholi.pdf - CERN Indico

The inflation models with the spectator axion-SU(2) sector have unique signatures that are testable with the next generation of CMB experiments.

The inflation models with the spectator axion-SU(2) sector remain phenomenologically viable in the presence of the gravitational Chern-Simons term.

The effect of the gravitational Chern-Simons term on chiral gravitational waves can be as large as fifty percent amplification for the left-handed helicity mode functions.

Conclusion

Thank You!

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Right

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