Jeans instability in non-minimal matter-curvature coupling gravity
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Regular Article - Theoretical Physics
Jeans instability in non-minimal matter-curvature coupling gravity Cláudio Gomesa Centro de Física do Porto, Rua do Campo Alegre s/n, 4169-007 Porto, Portugal
Received: 26 February 2020 / Accepted: 28 June 2020 / Published online: 17 July 2020 © The Author(s) 2020
Abstract The weak field limit of the nonminimally coupled Boltzmann equation is studied, and relations between the invariant Bardeen scalar potentials are derived. The Jean’s criterion for instabilities is found through the modified dispersion relation. Special cases are scrutinised and considerations on the model parameters are discussed for Bok globules.
1 Introduction The Boltzmann equation is a fundamental description of the microscopic world and is derived from the Liouville equation in phase space considering collisions between particles. From the former, one can derive macroscopic equations, such as the Navier-Stokes equation for fluids and the virial theorem for gravitationally bound systems [1], the Maxwell-Vlasov equations which characterise plasmas [2], the quantum Bloch-Boltzmann equations for electrons [3], and the evolution of primordial elements’ abundances in a de Sitter Universe [4]. From the Boltzmann equation it is also possible to build physical quantities from its moments, such as the particle number flux, the energy-momentum tensor or the entropy vector flux. The Boltzmann equation is sensible to relativistic and quantum effects. In particular, it can be generalised in order to account for modified gravity models. In fact, despite its successful agreement with a vast plethora of observational data tests [5,6], General Relativity (GR) lacks a fully consistent quantum version of it and requires two dark components to match observations at astrophysical and cosmological scales, namely dark matter and dark energy, which have not been directly observed so far. Thus, several alternative theories of gravity have been proposed over the years in the literature. One of the simplest generalisations of GR is the so-called f(R) theories which replace the Ricci scalar by a generic function of it in the action functional (see Refs. [7,8] for review on this a e-mail:
and Ref. [9] for a review on basic principles a gravity theory must obey and some extended theories of gravity). In fact, one specific proposal of such theories was firstly advanced in order to tackle the initial conditions problems of the standard Hot Big Bang model, namely through a nonsingular isotropic homogeneous solution which accounted for inflation [10]. Moreover, this model is still in excellent agreement with the most recent data from Planck mission [11]. (We refer the reader to Ref. [12] for a review of some exotic inflationary models in light of Planck data). Furthermore, f(R) theories of gravity have been used to address the problems of dark matter and dark energy (see e.g. Refs. [13,14]). It has also been found that by requiring that f(R) models to be regular at R = 0 leads to a behaviour compatible with an effective cosmological
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