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SOME ALTERNATIVE UNIFIED VIEWS FOR DARK ENERGY AND DARK MATTER G. J. MATHEWS∗ AND X. ZHAO Center for Astrophysics and JINA, University of Notre Dame, Notre Dame, IN 46656, USA ∗ E-mail:
[email protected] http://physics.nd.edu/Faculty/mathews.html K. ICHIKI Department of Physics and Astrophysics, Nagoya Univresity, Nagoya 464-8602, Japan E-mail:
[email protected] T. KAJINO National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan Department of Astronomy, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan E-mail:
[email protected] N. Q. LAN Physics Department, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam E-mail:
[email protected] The present closure contributions in dark energy and dark matter are nearly equal suggesting that they could be different aspects of the same physical phenomenon. We review constraints three postulates as to how such a unification might have been achieved. These include the possibility that: 1) the dark matter decays producing a bulk viscosity in the cosmic fluid; 2) the modification of the expansion rate by the inflow of dark matter from a bulk dimension in brane-world cosmology; and 3) relativistic corrections to the Friedmann equation from the presence of local inhomogeneities. Constraints on and observational tests of each of these cosmologies are described. Keywords: Dark Matter; Dark Energy; Unified dark matter; Brane-world cosmology; Bulk viscosity; Relativistic inhomogeneous cosmology
1. Introduction Understanding the nature and origin of both the dark energy and the cold dark matter constitutes a significant challenge to modern cosmology. However, the simple coincidence that both of these currently contribute comparable mass energy toward the closure of the universe begs the question as to whether they could be different manifestations of the same physical phenomenon. Here, we explore three possible mechanisms by which this unification of dark energy and dark matter could have arisen.
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2. Bulk Viscosity and Cosmic Acceleration from Decaying Dark Matter We have proposed1–3 a simple mechanism for the formation of such bulk viscosity and associated cosmic acceleration by the decay of a dark matter particle into relativistic products. Such decays heat the cosmic fluid and cause it to fall out of pressure and temperature equilibrium and can therefore be represented by a bulk viscosity. We have computed the magnitude-redshift relation for Type Ia supernovae in this cosmology and have shown that a single decay does not reproduce these data unless decays are delayed, e.g. by a cascade of particle decays, or a late decaying particle. We have adopted a form for the bulk viscosity coefficient based upon the formulation of Weinberg4 derived from a linearized radiation transport equation.5 We have shown,2,3 that an excellent fit can be obtained to the SNIa luminosity-redshift relation is possible. However, this requires three rather ad-hoc assumptions: 1) the dark matter decays only to non-detectable relativistic neutrinos; 2) The dark matter particle becomes unstable only at late times due to a time dependent mass crossing, a cosmic phase transition, or a particle cascade; and 3) The bulk viscosity coefficient is enhanced due to higher order terms in the radiation transport equation. Hence, we conclude that this is a viable, though somewhat contrived, possibility. 3. Dark Energy from Inflowing Dark Matter in Brane-World Cosmology We have also analyzed6 a mechanism by which the observed cosmic acceleration can be driven by the inflow of dark matter from a higher dimension (the bulk) into our three-space (the brane). We utilized the cosmological equations of motion6–8 with brane-bulk energy exchange to compare this modified expansion with the SNIa redshift-luminosity relation,9 the WMAP10 power spectrum and the matter power spectrum.11,12 Our best fit Λ = 0 growing cold dark matter (GCDM) models6 are nearly indistinguishable from the best fit Standard Λ+cold dark matter (SΛCDM) model. The only differences for the CMB and P (K) are on the very largest scales due to the ISW effect. An accelerating cosmology, however, requires that the sum of the dark matter and dark radiation terms remain nearly constant and that the EoS for matter in the brane be somewhat string-like. Hence, as bizarre as it sounds, we conclude that this brane-world cosmology represents a viable alternative model to the SΛCDM cosmology for an observer on the 3-brane. 4. Relativistic Corrections to the Friedmann Equation There has been considerable recent interest13 in the possibility that relativistic corrections to the Friedmann equation could lead to new terms which might account for the dark energy. This is a very subtle and controversial subject. The controversy13 is how to average the Ricci and extrinsic curvature tensors. To one school
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these must average to zero and recover a Friedmann cosmology. To the other school it does not. We have been attempting14 to numerically resolve this controversy in a detailed numerical large-scale structure simulation15 which includes relativistic corrections in the cosmic equations of motion. Our results in a conformally-flat16 weak-field Newtonian gauge are that this approach cannot account for the magnitude of the apparent dark energy. At best the inhomogeneities seem to contribute to the closure parameter an amount < 10−4 . Moreover, for the simulations at highest resolution the corrections enter with the wrong sign to be a dark energy. Hence, this does not appear to be a solution to the nature and origin of dark energy. We note however, that our simulations indicate that a better description of the formation of strong-field sources may significantly increase the inhomogeneous corrections. Work along this line is currently underway. References 1. J. R. Wilson, G. J. Mathews, and G. M. Fuller, PRD, 75, 043521 (2007); astroph/0609687. 2. G. J. Mathews, N. Q. Lan and C. Kolda, Phys. Rev. D78, 043525 (2008); astroph/08010853. 3. N. Q. Lan and G. J. Mathews, Communications in Physics, 19, 96-104 (2009) 4. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, (John Wiley & Sons, Inc. New York) (1972); Astrophys. J., 168, 175 (1971). 5. L. H. Thomas, Quart. J. Math. (Oxford), 1, 239 (1930). 6. K. Umezu, K. Ichiki, T. Kajino, G. J. Mathews, R. Nakamura, M. Yahiro, Phys. Rev. D 73, 063527 (2006). 7. K. Ichiki, P. M. Garnavich, T. Kajino, G. J. Mathews, and M. Yahiro, Phys. Rev. D 68, 083518 (2003). 8. E. Kiritsis, G. Kofinas, N. Tetradis, T. N. Tomaras and V. Zarikas, JHEP, 02, 035 (2003). 9. A. G. Riess, et al., Astrophys. J., 607, 665 (2004). 10. A. Kogut, et al., ApJ, 665, 355 (2007); D. Spergel, et al., ApJ, 665, 377 (2007); L. Page, et al., ApJ, 665, 335 (2007); G. Hinshaw, et al., ApJ, 665, 288 (2007); N. Jarosik, et al., ApJ, 665, 263 (2007). 11. S. Dodelson, et al. (SDSS Collaboration), Astrophys. J., 572, 140 (2002); M. Tegmark, A. J. S. Hamilton, and Y. Xu, MNRAS, 335, 887 (2002). 12. W. Percival, et al. (2dF Collaboration), MNRAS, 328, 1039 (2001). 13. T. Buchert, Gen. Relativ. Gravit. 40, 467 (2008). 14. X. Zhao, G. J. Mathews, Submitted to Phys. Rev. D (2009).astro-ph/0912.4750 15. V. Springel, Mon. Not. R. Astron. Soc., 364, 1105 (2005). 16. J. R. Wilson and G. J. Mathews, Relativistic Numerical Hydrodynamics, (Cambridge University Press; Cambridge, UK) (2003).
