# Nonstandard approach to gravity for the dark sector of the Universe

Stichel P, Zakrzewski WJ (2013)

Entropy 15(2): 559-605.

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Stichel, Peter

^{UniBi}; Zakrzewski, W. J.Abstract

We summarize the present state of research on the darkon fuid as a model forthe dark sector of the Universe. Nonrelativistic massless particles areintroduced as a realization of the Galilei group in an enlarged phase space.The additional degrees of freedom allow for a nonstandard, minimal coupling togravity respecting Einstein's equivalence principle. Extended to aself-gravitating fluid the Poisson equation for the gravitational potentialcontains a dynamically generated effective gravitational mass density of eithersign. The equations of motion (EOMs) contain no free parameters and areinvariant w.r.t. Milne gauge transformations. Fixing the gauge eliminates theunphysical degrees of freedom. The resulting Lagrangian possesses no freeparticle limit. The particles it describes, darkons, exist only as fluidparticles of a self-gravitating fluid. This darkon fluid realizes the zero-massGalilean algebra extended by dilations with dynamical exponent z = 5/3. Wereduce the EOMs to Friedmann-like equations, derive conserved quantities and aunique Hamiltonian dynamics by implementing dilation symmetry. By the Casimirof the Poisson-bracket (PB)-algebra we foliate the phase space and construct aLagrangian in reduced phase space. We solve the Friedmann-like equations withthe transition redshift and the value of the Casimir as integration constants.We obtain a deceleration phase for the early Universe and an acceleration phasefor the late Universe in agreement with observations. Steady state equations inthe spherically symmetric case may model a galactic halo. Numerical solutionsof a nonlinear diff?erential equation for the gravitational potential lead topredictions for the dark matter (DM) part of the rotation curves (RCs) ofgalaxies in qualitative agreement with observational data. We also present ageneral covariant generalization of the model.

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### Cite this

Stichel P, Zakrzewski WJ. Nonstandard approach to gravity for the dark sector of the Universe.

*Entropy*. 2013;15(2):559-605.Stichel, P., & Zakrzewski, W. J. (2013). Nonstandard approach to gravity for the dark sector of the Universe.

*Entropy*,*15*(2), 559-605. doi:10.3390/e15020559Stichel, P., and Zakrzewski, W. J. (2013). Nonstandard approach to gravity for the dark sector of the Universe.

*Entropy*15, 559-605.Stichel, P., & Zakrzewski, W.J., 2013. Nonstandard approach to gravity for the dark sector of the Universe.

*Entropy*, 15(2), p 559-605.P. Stichel and W.J. Zakrzewski, “Nonstandard approach to gravity for the dark sector of the Universe”,

*Entropy*, vol. 15, 2013, pp. 559-605.Stichel, P., Zakrzewski, W.J.: Nonstandard approach to gravity for the dark sector of the Universe. Entropy. 15, 559-605 (2013).

Stichel, Peter, and Zakrzewski, W. J. “Nonstandard approach to gravity for the dark sector of the Universe”.

*Entropy*15.2 (2013): 559-605.
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arXiv 1301.4486

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