Cosmo – Tahoe – September 2006 CMB constraints on inflation models with cosmic strings Mark Hindmarsh Neil Bevis (Sussex) Martin Kunz (Geneva) Jon Urrestilla.

Cosmo – Tahoe – September 2006

CMB constraints on inflation models with cosmic strings

Mark Hindmarsh

Neil Bevis (Sussex) Martin Kunz (Geneva)

Jon Urrestilla (Tufts, Sussex)

in preparation – MCMC WMAP3, polarisation astro-ph/0605018 – CMB TT calculations

astro-ph/0403029 – global textures



Introduction: inflation & strings

• Simplest model of the early Universe: inflationa

• General relativity + scalar field (quantum fluctuations)b

• String defectsc may be formed at end of hybrid inflationd

• Also at later thermal phase transitionse

• String/M-theory: strings from D + anti D-brane collisionsf

• Strings very important in SUSY F- & D-term inflationg

a) Starobinsky (1980); Sato (1981); Guth (1981); Hawking & Moss (1982); Linde (1982); Albrecht & Steinhardt (1982)

b) Mukhanov & Chibisov (1981); Hawking (1982); Starobinsky (1982); Guth & Pi (1982); Hawking & Moss (1983); Bardeen, Steinhardt, Turner (1983)

c) Hindmarsh & Kibble (1994); Vilenkin & Shellard(1994); Kibble (2004)d) Yokoyama (1989); Kofman,Linde,Starobinski (1996)e) Kibble (1976); Zurek (1996); Rajantie (2002)f) Jones, Stoica, Tye (2002); Dvali & Vilenkin (2003); Copeland, Myers, Polchinski (2003)g) Jeannerot (1995); Rocher & Sakellariadou (2006); Battye, Garbrecht, Pilaftsis (2006)


Strings in the early universe

• Form at t∼10−36 sec

• Observe at t0 ∼1017 sec.

• Scaling hypothesis: dimensional analysis based on physical

scales

• Once formed strings maintain a constant density parameter

Ωs

• With string tension μ, Ωs ∼ Gμ ∼10−6 for GUT scale strings


Observational signals of strings

Robust:

• Cosmic Microwave Background fluctuationsa

Uncertain (orders of magnitude):

• Gravitational radiationb

• Cosmic raysc

• Gravitational lensingd

• Baryon asymmetrye

a) Zel'dovich (1980); Vilenkin (1981); Kaiser & Stebbins (1984); Landriau & Shellard (2004); Wyman et al (2005); Bevis et al (2006)

b) Vachaspati & Vilenkin (1985); Hindmarsh (1990); Damour & Vilenkin (2000,2001,2005)c) Bhattarcharjee (1990); Sigl (1996); Protheroe (1996); Berezhinksi (1997); Vincent, M.H.,

Antunes (1998)d) Vilenkin (1984); Hindmarsh (1989); de Laix & Vachaspati (1996,1997)e) Bhattarcharjee, Kibble, Turok (1982); Brandenburger, Davis, M.H. (1991); Brandenburger,

Davis, Trodden (1994); Jeannerot (1996); Sahu, Bhattarcharjee, Yajnik (2004);Jeannerot & Postma (2005)


Uncertainty: energy loss

Scenario 1 (based on Nambu-Goto approximation & modelling)

• Long strings - loops - gravitational radiation

Scenario 2 (based on Classical Field Theory approximation)

• Long strings - tiny loops/massive radiation - high energy

particles

Need better understanding of coupling between large & small scales


Approximations

String/M-theory

(Energy << Mstring)

|

Quantum field theory(High occupation number)

|

Classical field theory(Low curvature string trajectory)

|

Ideal (Nambu-Goto) strings(Phenomenogical from simulations)

|

Moving segment model, VOS model

This work

Landriau & Shellard 2004

Wyman et al 2005


Strings in classical field theory

Standard Model of particle physics: spontaneous gauge symmetry-breaking

Simplest field theory with gauge SSB also has string-like classical solutions

Abelian Higgs model:

Energy-momentum tensor:

Gravitational perturbations proportional to:

CMB power spectrum proportional to:

μ: string tension

Ad: defect amplitude


Simulations: Lagrangian density

QuickTime™ and a decompressor

are needed to see this picture.


Simulations: energy density

QuickTime™ and a decompressor

are needed to see this picture.


Theory:

Lattice:

Times:

Final string curvature radius:

Simulations: the details

Visualisation runs:

Lattice:

Times:

Final string curvature radius:

Classical lattice field theory in parallel: www.latfield.org


Cut to the chase: TT spectrum

Normalisation at l=10:

This (astro-ph/0605018)

Wyman et al 2005

Landriau & Shellard 2004

Moving segment model

Nambu-Goto simulations


Bevis et al. 2004 - Global textures

Global O(4) textures - 3D classical field theory simulations

Unequal Time Correlator (UETC) methoda

CMBeasyb modified to accommodate sources of energy-momentum

Data: WMAP first year (and ACBAR, CBI, VSA)

MCMC fit – using modified CosmoMC - 7 parameters

Inflationary contribution uncorrelated with defects

a) Pen, Seljak, Turok (1997); Durrer, Kunz, Melchiorri (2001)b) Doran (2004)


Bevis et al. - defect degeneracy

WMAP 1yr + VSA + CBI + ACBAR data

Degeneracy involving Ad

2, As

2 (obviously) and bh2, h, ns allowing high defect fractions.

fd = fractional defect contribution at l=10

But large fd incompatible withKirkman et al. value of bh2

and Hubble Key Project value of hde

gene

racy


Defect degeneracy v. BBN & HKP

68%

95%

68%

95%

WMAP 1yr

WMAP 1yr+

BBN+

HKP

Detection of textures removed by BBN & HKP priorsfd,10 < 13% (95%)


String CMB from field theory

Cls for cosmic strings using field evolution simulations (astro-ph/0605018)c.f. Wyman et al. (2005, Err 2006) using moving segment modelc.f. global texturec.f. data: 3 year WMAP

Normalised to l=10

Cosmic strings (Wyman et al.)

Cosmic strings (Bevis et al.)

Global textures (Bevis et al.)


WMAP 3rd year (astro-ph/0603451)BOOMERanG (astro-ph/0507494)

CBI (astro-ph/0402359)VSA (astro-ph/0402498)

ACBAR (astro-ph/0212289)

MCMC: inflation + strings v. CMB


MCMC with “all” CMB data

Strings are favoured by the data - 2 sigma detection!

68%

95%


MCMC with WMAP3 data

Strings are favoured by the WMAP3 data, at between 1 and 2 sigma level

68%

95%


WMAP - why strings?


WMAP - why strings?


WMAP - why strings?


“All” CMB + BBN + HKP

WMAP 3rd year (astro-ph/0603451)BOOMERanG (astro-ph/0507494)

CBI (astro-ph/0402359)VSA (astro-ph/0402498)

ACBAR (astro-ph/0212289)+

BBN (astro-ph/0302006) HKP(astro-ph/0012376)


“All” CMB + BBN + HKP

“all” CMB

“all” CMB + BBN + HKP


WMAP normalization at l=10: 10 = 2.0 x 10-6 (astro-ph/0604018)

NB Moving segment model must be normalised from a simulation

“all” CMB

< 0.22

< 0.96 x 10-6

Constraints on string tension

“all” CMB + BBN + HKP

< 0.10

< 0.7 x 10-6

WMAP-3 only

< 0.19

< 0.9 x 10-6

Wyman et al. (2005,6): < 0.27 x 10-6 (astro-ph/0604141)

(moving segment model, WMAP-1 and SDSS, 10 = 1.1 x 10-6)

Fraisse 2006: < 0.26 x 10-6 (astro-ph/0603589)

(moving segment model, WMAP-3)


Polarization


Polarization

Tensors@ r=0.3

EE lensed


Conclusions

• First cosmic string CMB power spectra from classical field theory

• Normalisation to WMAP3 at l=10:

• First likelihood analysis for string CMB from classical field theory

• CMB data has a moderate preference (2-sigma) for strings

• Including of BBN and HKP priors reduces significance (1.5-sigma)

• Upper bound of 10% contribution to TT from strings at l=10

• Parallel N-dimensional field theory simulations: www.latfield.org

To do:• Fitting to SDSS data, inflation tensors• Low Higgs coupling (D-term inflation)• Other field theories (e.g. semilocal strings)

COSMO 2007COSMO 2007

University of Sussex, Brighton, U.K.

August 21-25 2007

University of Sussex, Brighton, U.K.

August 21-25 2007

Cosmo – Tahoe – September 2006 CMB constraints on inflation models with cosmic strings Mark Hindmarsh Neil Bevis (Sussex) Martin Kunz (Geneva) Jon Urrestilla.

Documents

gut scale strings slide

long strings loops

inflation models

vilenkin shellard1994

dvali vilenkin

damour vilenkin

end of hybrid inflation

bvachaspati vilenkin