Nonideal selfgravity and cosmology: Importance of correlations in the dynamics of the largescale structures of the Universe
Abstract
Aims: Inspired by the statistical mechanics of an ensemble of interacting particles (BBGKY hierarchy), we propose to account for smallscale inhomogeneities in selfgravitating astrophysical fluids by deriving a nonideal virial theorem and nonideal NavierStokes equations. These equations involve the pair radial distribution function (similar to the twopoint correlation function used to characterize the largescale structures of the Universe), similarly to the interaction energy and equation of state in liquids. Within this framework, smallscale correlations lead to a nonideal amplification of the gravitational interaction energy, whose omission leads to a missing mass problem, for instance, in galaxies and galaxy clusters.
Methods: We propose to use a decomposition of the gravitational potential into a near and farfield component in order to account for the gravitational force and correlations in the thermodynamics properties of the fluid. Based on the nonideal virial theorem, we also propose an extension of the Friedmann equations in the nonideal regime and use numerical simulations to constrain the contribution of these correlations to the expansion and acceleration of the Universe.
Results: We estimate that the nonideal amplification factor of the gravitational interaction energy of the baryons lies between 5 and 20, potentially explaining the observed value of the Hubble parameter (since the uncorrelated energy accounts for ∼5%). Within this framework, the acceleration of the expansion emerges naturally because the number of substructures induced by gravitational collapse increases, which in turn increases their contribution to the total gravitational energy. A simple estimate predicts a nonideal deceleration parameter q_{ni} ≃ −1; this is potentially the first determination of the observed value based on an intuitively physical argument. We also suggest that smallscale gravitational interactions in bound structures (spiral arms or local clustering) could yield a transition to a viscous regime that can lead to flat rotation curves. This transition could also explain the dichotomy between (Keplerian) low surface brightness elliptical galaxy and (nonkeplerian) spiral galaxy rotation profiles. Overall, our results demonstrate that nonideal effects induced by inhomogeneities must be taken into account, potentially with our formalism, in order to properly determine the gravitational dynamics of galaxies and the largescale Universe.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 March 2022
 DOI:
 10.1051/00046361/202142103
 arXiv:
 arXiv:2109.09087
 Bibcode:
 2022A&A...659A.108T
 Keywords:

 equation of state;
 gravitation;
 cosmology: theory;
 Astrophysics  Astrophysics of Galaxies;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Accepted in A&