1

General Relativistic Alternatives for Dark Matter and Dark Energy

Grant J. Mathews Center for Astrophysics (CANDU)Department of PhysicsUniversity of Notre Dame

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

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

m0

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 the inflow of dark matter from the bulk to our 3-space in 5 dimensional gravity

m0

m0

Umezu, Ichiki, Kajino, Mathews, Yahiro PRD, 73 063527 (2006)

4

Transfer from/to the Bulk leads to Modified Cosmic Expansion

• E = “Dark Radiation” or Electric part of the bulk Weyl tensor

€

ρ=ρM + ρ R + ρDM

€

H 2 =8πGN

3ρ −

ka2 +

Λ4

3+

κ 54

36ρ 2 + E

€

€

dEdt

+ 4HE =κ 5

4τ9

T05 =

κ 54τ9

Γρ DM

€

˙ ρ ρ

+ 3(1 + w) = −2T 05

5

Accelerating Cosmology

E

6

Growing Dark Matter CosmologyUmezu, et al. (2006)T0

5 = (ρDM + p) U5 ; U5 = -l H

Supernovae areFit with =0

Supernovae

7

Growing Dark Matter CosmologyUmezu, et al. (2006)T0

5 = (ρDM + p) U5 ; U5 = -l H

Explains the diminished power for the lowest multipoles in the CMBfluctuations

CMB Power Spectrum

8

Growing Dark Matter CosmologyUmezu, et al. (2006)T0

5 = (ρDM + p) U5 ; U5 = -l H

Matter Power Spectrum

Less power on the scales near the horizon

Bulk Viscosity and Decaying Dark MatterG. J. Mathews, N. Q. Lan, C. Kolda - Univ. Notre Dame

J. R. Wilson, LLNLG. M. Fuller, UC San Diego

PRD in press/ astro-ph/0609687

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

Viscous Dark MatterWeinberg (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 = ρ/3

Out of temperature and pressure equilibrium=> Dissipation & Bulk Viscosity

During decay: matter and relativistic particles are out of pressure and

temperature equilibrium = 3 ρ

heq[(1/3) - (∂P/ ρ]

eq = 0 P()/P(0)dt = /(1 + 3 H)

Need (∂P/ ρ) ~ P/ ρ 1/3

P = (ρl + ρ)/3

ρ = ρDM + ρb + ρh + ρ + ρl

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 ge

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, 023524 2006, astro-ph/0506534

In a clumpy universe the motion there are acceleration terms

€

H 2 =8πG

3ρeff

€

ρeff = ρD

−QD

16πG−

RD

16πG

€

QD =23

Θ2

D− Θ D

2− 2σ 2

( )

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 StructureZhao, Mathews, Haywood (2006)

Nρ

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/0507619, 0512048

Menzies & Mathews gr-qc/0604092

Cooperstock & Tieu Model

25

Problem with this picture• Implies DM is moved to outside galaxies,

but is still there: Mgal =

Menzies & Mathews (2006)

Particle decay

CDM

BV = 10

SNIa

M = 1.0

Why this does not work

ρtot falls off too rapidly with time

Need constant ρtot

Bulk Viscosity can fit the SNIa redshift relation

A = 8G /H0

Fabris et al. 2005 astro-ph/0503362

How to fix this?

Late decays:

Cascading decays: Sterile neutrinos1 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

BV = 10

SNIa

M = 1.0