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Nonstandard Approach to Gravity for the Dark Sector of the Universe
An der Krebskuhle 21, D-33619 Bielefeld, Germany
Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK
* Author to whom correspondence should be addressed.
Received: 6 December 2012; in revised form: 16 January 2013 / Accepted: 16 January 2013 / Published: 5 February 2013
Abstract: We summarize the present state of research on the darkon fluid as a model for the dark sector of the Universe. Nonrelativistic massless particles are introduced as a realization of the Galilei group in an enlarged phase space. The additional degrees of freedom allow for a nonstandard, minimal coupling to gravity respecting Einstein’s equivalence principle. Extended to a self-gravitating fluid the Poisson equation for the gravitational potential contains a dynamically generated effective gravitational mass density of either sign. The equations of motion (EOMs) contain no free parameters and are invariant w.r.t. Milne gauge transformations. Fixing the gauge eliminates the unphysical degrees of freedom. The resulting Lagrangian possesses no free particle limit. The particles it describes, darkons, exist only as fluid particles of a self-gravitating fluid. This darkon fluid realizes the zero-mass Galilean algebra extended by dilations with dynamical exponent z = 5/3 . We reduce the EOMs to Friedmann-like equations and derive conserved quantities and a unique Hamiltonian dynamics by implementing dilation symmetry. By the Casimir of the Poisson-bracket (PB)-algebra we foliate the phase space and construct a Lagrangian in reduced phase space. We solve the Friedmann-like equations with the transition redshift and the value of the Casimir as integration constants. We obtain a deceleration phase for the early Universe and an acceleration phase for the late Universe in agreement with observations. Steady state equations in the spherically symmetric case may model a galactic halo. Numerical solutions of a nonlinear differential equation for the gravitational potential lead to predictions for the dark matter (DM) part of the rotation curves (RCs) of galaxies in qualitative agreement with observational data. We also present a general covariant generalization of the model.
Keywords: nonrelativistic massless particles; nonstandard gravity; self-gravitating fluid; accelerated expansion; rotation curves; general covariance
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Stichel, P.C.; Zakrzewski, W.J. Nonstandard Approach to Gravity for the Dark Sector of the Universe. Entropy 2013, 15, 559-605.
Stichel PC, Zakrzewski WJ. Nonstandard Approach to Gravity for the Dark Sector of the Universe. Entropy. 2013; 15(2):559-605.
Stichel, Peter C.; Zakrzewski, Wojtek J. 2013. "Nonstandard Approach to Gravity for the Dark Sector of the Universe." Entropy 15, no. 2: 559-605.