1 General Relativistic Alternatives for Dark Matter and Dark Energy Grant J. Mathews Center for Astrophysics (CANDU) Department of Physics University of Notre Dame

Premise of this talk: Dark energy and dark matter contribute comparable amounts of mass energy This begs the question: Could they be different aspects of the same physical phenomenon? Appearing Dark Matter Viscous/Decaying Dark Matter Relativistic Corrections to Friedmann Cosmology

3 Bulk Dimension m0m0 Z The flow of matter back into the 3-brane will appear as spontaneous matter creation Fixed point solution => a constant energy density as the universe expands Dark Energy may be caused by t he inflow of dark matter from the bulk to our 3-space in 5 dimensional gravity m0m0 m0m0 Umezu, Ichiki, Kajino, Mathews, Yahiro PRD, (2006)

4 Transfer from/to the Bulk leads to Modified Cosmic Expansion E = “Dark Radiation” or Electric part of the bulk Weyl tensor

5 Accelerating Cosmology E

6 Growing Dark Matter Cosmology Umezu, et al. (2006) T 0 5 = (  DM + p) U 5 ; U 5 = -l H Supernovae are Fit with  =0 Supernovae

7 Growing Dark Matter Cosmology Umezu, et al. (2006) T 0 5 = (  DM + p) U 5 ; U 5 = -l H Explains the diminished power for the lowest multipoles in the CMB fluctuations CMB Power Spectrum

8 Growing Dark Matter Cosmology Umezu, et al. (2006) T 0 5 = (  DM + p) U 5 ; U 5 = -l H Matter Power Spectrum Less power on the scales near the horizon

Bulk Viscosity and Decaying Dark Matter G. J. Mathews, N. Q. Lan, C. Kolda - Univ. Notre Dame J. R. Wilson, LLNL G. M. Fuller, UC San Diego PRD in press/ astro-ph/ 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

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

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

During decay: matter and relativistic particles are out of pressure and temperature equilibrium  = 3  h  eq [(1/3) - (∂P/  ]  eq =  0   P(  )/  P(0)dt =  /(1 + 3  H) Need (∂P/  ) ~ P/   1/3 P = (  l +   ) /3  =  DM +  b +  h +   +  l Weinberg (1971)

Candidates for Decaying Dark Matter Late Cascading decays: Sterile neutrinos S  e 1  2  3  4  5  6  regular neutrinos Late decays due to time varying mass or a late phase transition: sneutrino  g  e Gauge mediated supersymmetry breaking   R + R ~~ ~ ~~~~~~

Late Decaying Particles Accelerating

15 Late Decaying Particles SNIa: Riess et al. 2004

16 Dark Energy Could be Correction for Non-Friedmannian Clumpy Cosmology Kolb et al. PRD, 71, , astro-ph/ In a clumpy universe the motion there are acceleration terms

17 Schools of Thought: This cannot produce Acceleration: (e.g.. Siegel & Fry 2005; Ishibashi & Wald 2006) Needs to be tested without recourse to perturbative schemes or special symmetry This can produce acceleration: Kolb 2005; 2006 This fits the luminosity-distance relation in special symmetric (e.g. Lemaitre-Tolman-Bondi ) models : Barausse et al. 2005; Celerier 2000; Menim et al. 2005a;b; Alnes, Amarzguioui, and Gron 2005; Enqvist & Mattsson 2006; Garfinkle 2006; Moffit 2006; Szydowski & Godowski 2006)

Modified Friedman Equation Zhao, Haywood Mathews (2006)

Large Scale Structure Zhao, Mathews, Haywood (2006) NN  Universe characterized by local regions with deepening potentials and large voids with diminishing gravity

20 Conclusions The challenge of accounting for dark matter and dark energy makes for an exciting time in relativity physics and cosmology

Is it vacuum energy? Is it Geometry?

Could Galaxy Rotation Curves be accounted for by relativistic corrections instead of dark matter? Cooperstock & Tieu astro-ph/ , Menzies & Mathews gr-qc/

Cooperstock & Tieu Model

25 Problem with this picture Implies DM is moved to outside galaxies, but is still there: M gal =  Menzies & Mathews (2006)

Parametrize EOS in Bulk Only works if: q < 3 Dark Matter is increasing 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

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

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

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

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

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