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)
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
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.