José Beltrán and A. L. Maroto Dpto. Física teórica I, Universidad Complutense de Madrid XXXI Reunión Bienal de Física Granada, 11 de Septiembre de 2007.

José Beltrán and A. L. Maroto

Dpto. Física teórica I, Universidad Complutense de Madrid

XXXI Reunión Bienal de FísicaGranada, 11 de Septiembre de 2007

J. Beltrán and A.L. Maroto, Phys.Rev.D76:023003,2007 astro-ph/0703483

Outline

• Standard Cosmology• Dark Energy• Why moving Dark Energy?• The model• Effects on the CMB temperature fluctuations• Some Dark Energy models

– Constant equation of state– Scaling models– Tracking models– Null Dark Energy

• Conclusions

Standard Cosmology

Cosmological Principle: General Relativity:

R¹ º ¡12Rg¹ º = 8¼GT¹ ºHomegeneity and

Isotropy

ds2 = dt2 ¡ a(t)2

·dr2

1¡ kr2+d

¸

FLRW metric:Friedmann equation:

Equation of the acceleration:

H 2 =8¼G

3½¡

ka2

Äaa = ¡

4¼G3

(½+3p)

Observational Data

Explaining the acceleration

Energy density associated to ½¤ » (10¡ 12GeV)4

½vac » k4max » M 4

P = (1018GeV)4Vacuum energy

Cosmological constant

Quintessence

K-essence

Phantom

Chaplygin gas

f(R) gravities

Braneworlds (RS)

DGP

R¹ º ¡12Rg¹ º = 8¼GT¹ º

Why moving dark energy?

Matter at rest with respect to CMB?

WEAKLY INTERACTING DARK ENERGY

What is Dark Energy rest frame?

S. Zaroubi, astro-ph/0206052

Total energy-momentum tensor

The model

B, R, DM, DE.

T ¹ º =X

®

[(½®+p®)u¹®uº

®¡ p®g¹ º]

®=

Perfect fluid

Null fluid u¹NuN¹ = 0

u¹®= °®(1;~v®)

Equation of state:p®= w®½®

Einstein Equations DENSITY OF INERTIAL MASS

Dark Energy

R, B, DM

g0i ´ Si =P

®°2®(½®+p®)gij vj

®P®°2

®(½®+p®)g0i ´ Si =

P®°2

®(½®+p®)gij vj®P

®°2®(½®+p®)

VELOCITY OF THE COSMIC CENTER OF MASS

h(a) = 6Z a

a¤

1~a4

"Z ~a

a¤

a2X

®

(½®+p®) sinh2µ®dap

½

#d~ap

½h(a) = 6

Z a

a¤

1~a4

"Z ~a

a¤

a2X

®

(½®+p®) sinh2µ®dap

½

#d~ap

½

a? = a(1+±? )ak = a(1+±k)a? = a(1+±? )ak = a(1+±k)

h = 2(±k ¡ ±? )h = 2(±k ¡ ±? )Degree of anisotropy

Axisymmetric Bianchi type I metric

ds2 = dt2 ¡ a2? (dx2 +dy2) ¡ a2

kdz2

Conservation Equations

Slow moving fluids

Fast moving fluidsVz® = V®0

½® = ½®0a¡ 3(w®+1)

Null Fluid

pN = pN 0

½N = ½N 0(aka? )¡ 2 ¡ pN 0 ½N > 0) pN 0 < 0

Vz® = V®0a3w®¡ 1

It behaves as radiation at high redshifts

It behaves as a cosmological constant at low redshifts

½® = ½®0a¡ 21+ w ®

1¡ w ®?

Effects on the CMB : the dipole

Velocity of the observer with respect to the cosmic center of mass

A. L. Maroto, JCAP 0605:015 (2006)

Sachs-Wolfe effect to first order

±Tdipole

T' ~n ¢(~S ¡ ~V)j0dec

Effects on the CMB: the quadrupole

68% C.L.

95% C.L.

WMAP G. Hinshaw et al.Astro-ph/0603451

Q2T = Q2

A + Q2I ¡ 2f (µ; Á;®i)QA QIQ2

T = Q2A + Q2

I ¡ 2f (µ; Á;®i)QA QI

68% C.L.

95% C.L.

54¹ K 2 · (±TA )2 · 3857¹ K 2

0¹ K 2 · (±TA )2 · 9256¹ K 2

(±T)2obs = 236+560

¡ 137 ¹ K 2

(±T)2obs = 236+3591

¡ 182 ¹ K 2

Allowed region Lowering the quadrupole

QT = QA (µ; Á) +QI (®1;®2;®3)QT = QA (µ; Á) +QI (®1;®2;®3)E. F. Bunn et al., Phys. Rev. Lett. 77, 2883 (1996).

(±T)2A · 1861¹ K 2

(±T)2A · 5909¹ K 2

±TI = ±¹Tobs (±T)2I ' 1252¹ K 2

QA =2

5p

3jh0 ¡ hdecj

Constant equation of state

RMDE

wDE ' ¡ 1wDE ' ¡ 1 wD E 6= ¡ 1wD E 6= ¡ 1but

RMDE

½D E ' const

VD E / a¡ 4

½D E ' const

VD E / a¡ 4

Scaling models

R M DE

R M DE

R M DE

wD E = 0

w0D E

13

z > zeq

zeq > z > zT

zT > z w0D E ' ¡ 0:97

Scaling modelsParameter space(²;V¤

D E ) ² ´ ½¤D E½¤

R

Tracking models

R M DE R M DE

P. J. Steindhardt et al, Phys. Rev. D59, 123504 (1999)

DE density becomes completely negligible

Unstable against velocity

perturbations

Null Dark Energy

² ´ ½N 0½R 0

R M DE

QA ' 2:58²

Allowed region

V® ¿ 1

1£ 10¡ 6 · ² · 8:8£ 10¡ 6

0· ² · 1:4£ 10¡ 5

² · 6:1£ 10¡ 6

² · 1:1£ 10¡ 568% C.L.

68% C.L.

95% C.L.

95% C.L.

Conclusions• Starting from an isotropic universe, a moving dark

energy fluid can generate large scale anisotropy.

• This motion mainly affects CMB dipole and quadrupole.

• Models with constant equation of state lead to a situation in which all fluids are very nearly at rest.

• Tracking models are unstable against velocity perturbations, giving rise to extremely low DE densities.

• Scaling models and null fluids produce a non-negligible quadrupole compatible with the measured one for reasonable values of the parameters.