1. Unified Models for Dark Matter and Dark Energy G. J. Mathews - Univ. Notre Dame VI th Rencontres du Vietnam August 7-11, 2006 Hanoi

2. Premise of this talk: It is an amazing coincidence that the dark energy and dark matter contribute comparable amounts of mass energy This begs the question as to whether they could be different aspects of the same physical phenomenon

3. Alternative Views: Dark Matter produces Dark Energy Unified/Interacting Dark Matter Relativistic/Inhomogeneous Corrections to Friedmann Cosmology Chaplygin Gas p = -A   Viscous/ Decaying Dark Matter Appearing Dark Matter

4. Appearing Dark Matter in Brane Cosmology G. J. Mathews, Univ. Notre Dame K. Umezu, K. Ichiki, T. Kajino, Tokyo Univ./NAOJ M. Yahiro, Kyushu Univ. PRD 73, (2006) 063527; astro-ph/0507227 Bulk Dimensionz Standard-model particles are dynamically confined to the 3-brane The possibility exists for particles to reside in the bulk The universe is described as an effective 3- brane Embedded in a large 5 dimensional anti- deSitter space (AdS 5 ). m0m0

5. 5 Bulk Dimension m0m0 Z The flow of matter from the bulk into the 3-brane will appear as spontaneous matter creation  H constant  acceleration This mimics a cosmological constant even for  4 =0 The flow of particles from the bulk to the brane produces an accelerating cosmology m0m0 m0m0 Kiritsis et al., hep-th/0207060, Tetradis hep-th/0211200, Umezu et al. astro-ph/0507227

6. 6 Modified Cosmic Expansion E = “Dark Radiation” or Electric part of the bulk Weyl tensor ds 2 = -  2 dt 2 + a(t,y)  ij dx i dx j + dz 2 T A B =(  +P)U A U B +  A B P ; U 5 = -Hl T A B (bulk)=(  DM +P DM )U 5 ; T 0 5 =-Hl  T A B (brane)=(  (z)/b)diag(-  - , -  +p, -  +p, -  +p,0) T A B (vacuum)= diag( -  5, -  5, -  5, -  5, -  5 ) - Static Bulk/Expanding 3- space

7. 7 Modified Equation of state Parametrize EOS in Bulk Only works if: q < 3 T 0 5 = -(  H/2)(  /a q ) q = 3 Normal matter, q = 4 Relativistic matter q = 1 Strings q = 0 Dark energy Best fit:  = 7.6, q = 1.0,  DM +  E = 0.26  DM = 3.1,  =0

8. 8 Accelerating Cosmology E

9. 9 Umezu, et al. (2006) Equivalently fit with  =0 or  CDM Fit to SNIa Data

10. 10 CMB Power Spectrum Umezu, et al. (2006) Diminished power for the lowest multipoles

11. 11 Matter Power Spectrum Less power on the scales near the horizon Umezu, et al. (2006)

12. Bulk Viscosity and Decaying Dark Matter G. J. Mathews C. Kolda and N. Q. Lan, Univ. Notre Dame J. R. Wilson, LLNL G. M. Fuller, UC San Diego 1.Decaying dark matter leads to dissipative bulk viscosity in the cosmic fluid 2.This viscosity may account for some or all of the apparent cosmic acceleration

13. Viscous Dark Matter Weinberg (1971) Bulk Viscosity Negative pressure => Dark Energy

14. Bulk Viscosity can fit the SNIa redshift relation A = 8  G  /H 0 Fabris et al. 2005 astro- ph/0503362

15. Need a Physical Model for Bulk Viscosity If a gas is out of pressure equilibrium as it expands or contracts a bulk viscosity is generated

16. 16 Particle decay Pressureless DM  relativistic particles P =  /3  Out of temperature and pressure equilibrium  Dissipation & Bulk Viscosity

17. During decay matter and relativistic particles are out of pressure and temperature equilibrium  = 3  h  eq [(1/3) - (∂P/  ]  eq =  /(1 + 3  H) Need (∂P/  ) ~ P/   1/3 P = (  l +   ) /3  =  DM +  b +  h +   +  l Weinberg (1971)

18. Candidates for Decaying Dark Matter sneutrino  g  e Gauge mediated supersymmetry breaking   R + R Decaying massive sterile neutrino S  e ’s ~~ ~

19. Particle decay  CDM BV  = 10 SNIa  M = 1.0

20. Why this does not work  tot falls off too rapidly with time Need constant  tot

21. How to fix this? Late decays: Cascading decays: Sterile neutrinos 1  2  3  4  5  6  regular neutrinos Late decays due to time varying mass or a late phase transition

22. Late Decaying Particles Accelerating

23. 23 Late Decaying Particles SNIa

24. Cascading particle Decays 1  2  3  4  5  6   CDM Delayed BV  = 10 SNIa  M = 1.0

25. 25 Conclusions Appearing dark matter: Can fit CMB, SNIa, and matter power spectrum constraints if EOS (q  1) Can test by observations: CMB supression/P(k) DM decay Can produce a bulk viscosity but its effect is too small Can account for some dark energy if particle decay is delayed by a cascade or a late phase transition/time- dependent mass

26. Bulk Viscosity from Particle Decay Conservation Eq. => First Law Entropy from decay Entropy density

27. 27 Conclusions Growing dark matter can fit CMB, SNIa, and matter power spectrum constraints if: –Matter in the bulk has a different EOS (q  1) –Dark matter is offset by dark radiation Can test by observations: 1.There should be an excess density of the dark matter particles compared to a standard cosmology 2.There should be diminished power for the largest structures near the scale of the horizon

28. ISW effect suppresses low multipoles Potentials Slowly varying