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

2. 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

3. Standard Cosmology Cosmological Principle: General Relativity: R ¹º ¡ 1 2 R g ¹º = 8 ¼ GT ¹º Homegeneity and Isotropy d s 2 = d t 2 ¡ a ( t ) 2 · d r 2 1 ¡ k r 2 + d ­ ¸ FLRW metric: Friedmann equation: Equation of the acceleration: H 2 = 8 ¼ G 3 ½ ¡ k a 2 Ä a a = ¡ 4 ¼ G 3 ( ½ + 3 p )

4. Observational Data

5. Explaining the acceleration Energy density associated to  ½ ¤ » ( 10 ¡ 12 G e V ) 4 ½ vac » k 4 max » M 4 P = ( 10 18 G e V ) 4 Vacuum energy Cosmological constant Quintessence K-essence Phantom Chaplygin gas f(R) gravities Braneworlds (RS) DGP R ¹º ¡ 1 2 R g ¹º = 8 ¼ GT ¹º

6. 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

7. Total energy-momentum tensor The model B, R, DM, DE. T ¹º = X ® [( ½ ® + p ® ) u ¹ ® u º ® ¡ p ® g ¹º ] ® = Perfect fluid Null fluid u ¹ N u N ¹ = 0 u ¹ ® = ° ® ( 1 ; ~ v ® ) Equation of state: p ® = w ® ½ ®

8. Einstein Equations DENSITY OF INERTIAL MASS Dark Energy R, B, DM VELOCITY OF THE COSMIC CENTER OF MASS Degree of anisotropy Axisymmetric Bianchi type I metric d s 2 = d t 2 ¡ a 2 ? ( d x 2 + d y 2 ) ¡ a 2 k d z 2

9. Conservation Equations Slow moving fluids Fast moving fluids V z® = V ® 0 ½ ® = ½ ® 0 a ¡ 3 ( w ® + 1 ) Null Fluid p N = p N 0 ½ N = ½ N 0 ( a k a ? ) ¡ 2 ¡ p N 0 ½ N > 0 ) p N 0 < 0 V z® = V ® 0 a 3 w ® ¡ 1 It behaves as radiation at high redshifts It behaves as a cosmological constant at low redshifts ½ ® = ½ ® 0 a ¡ 2 1 + w ® 1 ¡ w ® ?

10. 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 ± T d i po l e T ' ~ n ¢ ( ~ S ¡ ~ V )j 0 d ec

11. Effects on the CMB: the quadrupole 68% C.L. 95% C.L. WMAP G. Hinshaw et al. Astro-ph/0603451 68% C.L. 95% C.L. 54 ¹ K 2 · ( ± T A ) 2 · 3857 ¹ K 2 0 ¹ K 2 · ( ± T A ) 2 · 9256 ¹ K 2 ( ± T ) 2 o b s = 236 + 560 ¡ 137 ¹ K 2 ( ± T ) 2 o b s = 236 + 3591 ¡ 182 ¹ K 2 Allowed region Lowering the quadrupole E. F. Bunn et al., Phys. Rev. Lett. 77, 2883 (1996). ( ± T ) 2 A · 1861 ¹ K 2 ( ± T ) 2 A · 5909 ¹ K 2 ± T I = ± ¹ T o b s ( ± T ) 2 I ' 1252 ¹ K 2 Q A = 2 5 p 3 j h 0 ¡ h d ec j

12. Constant equation of state R M DE but R M DE

13. Scaling models R M DE w DE = 0 w 0 DE 1 3 z > z eq z eq > z > z T z T > z w 0 DE ' ¡ 0 : 97

14. Scaling models Parameter space ( ² ; V ¤ DE ) ² ´ ½ ¤ DE ½ ¤ R

15. Tracking models R M DE P. J. Steindhardt et al, Phys. Rev. D59, 123504 (1999) DE density becomes completely negligible Unstable against velocity perturbations

16. Null Dark Energy ² ´ ½ N 0 ½ R 0 R M DE Q A ' 2 : 58 ² 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 ¡ 5 68% C.L. 95% C.L.

17. 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.