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Unified Models of Dark Energy and Dark Matter using Two
Measures.
Eduardo Guendelman, Ben Gurion University,Israel.
What is beyond the SM,16 Conference Bled, 2013.
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We introduce 4 scalar fields in 4-D
Which will play an important geometrical
role, by the way, other authors have found
that 4 scalar fields in 4-D can be used to
define a generally covariant mass term for
the graviton . A much simpler use of four
scalars in 4D is to define a new MEASURE.
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The Basic Idea of the Two Measures Theory (TMT)
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simple example: Softly Broken Conformal Invariance,
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Now we will solve for the scalar
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Effective Potential for Exponential forms of U and V (scale invariance)
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Use of these ideas for unification of dark enegy and dark matter
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In a generally covariant form
We can write the energy momentum in a “fluid form”
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Indeed defining the four velocity
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The cosmic coincidence problem
Which is why the dark energy and the dark matter are of comparable magnitudes today?, do they balance?, but M, representing the DE is a constant!
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Some References
• Dynamical measure and field theory: Guendelman, A.B.Kaganovich Phys.Rev.D60:065004,1999. e-Print: gr-qc/9905029 .
• Model Constrained by S.I. : Scale invariance, new inflation and decaying lambda terms. E.I. Guendelman, Mod.Phys.Lett.A14:1043-1052,1999. e-Print: gr-qc/9901017
• Adding curvature Square and obtaining two flat regions : Inflation and transition to a slowly accelerating phase from SSB of scale invariance. E.I.Guendelman, O.Katz, Class.Quant.Grav.20:1715-1728,2003. e-Print: gr-qc/0211095
• Using this model plus CC in Einstein frame to get ………Emerging Universe from Scale Invariance. S. del Campo, E. I. Guendelman , R. Herrera , P.Labrana, JCAP 1006:026,2010. ePrint: arXiv:1006.5734 [astro-ph.CO]
• Expresing the results of the above in terms of the energy density of the flat region with lower energy density : Non Singular Origin of the Universe and its Present Vacuum Energy Density. E.I. Guendelman, Int.J.Mod.Phys.A26:2951-2972,2011. e-Print: arXiv:1103.1427 [gr-qc] See also Proceedings of What is beyond the Standard model for the year 2011.
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Dark Matter Dark Energy Unification
A two measure model of dark energy and dark matter.E. Guendelman, D. Singleton, N. Yongram: arXiv:1205.1056 [gr-qc], Published in JCAP 1211 (2012) 044; Unified DE/DM model with inverse Quintessence, S. Ansoldi and E. Guendelman, JCAP 1305 (2013) 036 e-Print: arXiv:1209.4758 [gr-qc]