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.