Kinetic theory of Jean instability in Eddington-inspired Born–Infeld gravity

The European Physical Journal C, Oct 2017

We analyze the stability of self-gravitating systems which dynamics is investigated using the collisionless Boltzmann equation, and the modified Poisson equation of Eddington-inspired Born–Infield gravity. These equations provide a description of the Jeans paradigm used to determine the critical scale above which such systems collapse. At equilibrium, the systems are described using the time-independent Maxwell–Boltzmann distribution function \(f_0(v)\). Considering small perturbations to this equilibrium state, we obtain a modified dispersion relation, and we find a new characteristic scale length. Our results indicate that the dynamics of self-gravitating astrophysical systems can be fully addressed in the Eddington-inspired Born–Infeld gravity. The latter modifies the Jeans instability in high densities environments, while its effects become negligible in star formation regions.

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Kinetic theory of Jean instability in Eddington-inspired Born–Infeld gravity

The European Physical Journal C October 2017, 77:715 | Cite as Kinetic theory of Jean instability in Eddington-inspired Born–Infeld gravity AuthorsAuthors and affiliations Ivan De MartinoAntonio Capolupo Open Access Regular Article - Theoretical Physics First Online: 26 October 2017 340 Downloads 2 Citations Abstract We analyze the stability of self-gravitating systems which dynamics is investigated using the collisionless Boltzmann equation, and the modified Poisson equation of Eddington-inspired Born–Infield gravity. These equations provide a description of the Jeans paradigm used to determine the critical scale above which such systems collapse. At equilibrium, the systems are described using the time-independent Maxwell–Boltzmann distribution function \(f_0(v)\). Considering small perturbations to this equilibrium state, we obtain a modified dispersion relation, and we find a new characteristic scale length. Our results indicate that the dynamics of self-gravitating astrophysical systems can be fully addressed in the Eddington-inspired Born–Infeld gravity. The latter modifies the Jeans instability in high densities environments, while its effects become negligible in star formation regions. 1 Introduction In General Relativity (GR), matter is minimally coupled with the metric and the Einstein–Hilbert Lagrangian, which is linear in the Ricci scalar, gives rise to second order field equations. These are able to explain the dynamics of the particles up to a solar system scale, but they fail at scales of galaxies and beyond. The dynamics of self-gravitating systems and the current period of accelerated expansion of the Universe cannot be explained by just baryonic matter. Thus, GR needs to incorporate two unknown components to explain the dynamics at both galactic/extragalactic and cosmological scales. Specifically, almost \(\sim \)68% of the total amount of the matter and energy in the Universe should be in form of the cosmological constant, or more in general of dark energy, while \(\sim \)26% should be in the form of invisible and exotic particles, named dark matter. Nevertheless their fundamental nature is still unknown [1, 2, 3, 4]. The need to incorporate them has been interpreted as a breakdown of GR at astrophysical and cosmological scales, opening the door to alternative theories of gravity. Generalizations of the gravitational action have been extensively explored to overcome the need of these two exotic components. On th one hand these are motivated by their capability to explain the dynamics of self-gravitating systems and the accelerated expansion of the Universe without resorting to dark matter and/or dark energy [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. On the other hand, they are also motivated by the fact that GR is not the quantum theory of gravity needed to describe the space-time near the singularities, which, as is well known, seemingly cannot be avoided [15]. Although a quantum theory of gravity should be able to overcome such problems, there also exists the possibility to avoid singularities modifying the coupling between matter and gravity. In this context, Eddington-inspired Born–Infeld (EiBI) gravity has been recently proposed [16]. EiBI gravity is inspired by the Born–Infeld action for non-linear electrodynamics, with the Ricci tensor replacing the field tensor \(F_{\mu \nu }\). This structure was motived by some classes of string theories where the Born–Infeld electrodynamics arises as a low-energy effective theory [17, 18]. One of the most interesting features is that EiBI is equivalent to GR in the vacuum while it introduces modifications in dense matter environments, where GR is experimentally not well probed. EiBI is able to describe, with only a single extra parameter (\(\kappa \)), astrophysical objects such as the Sun [19] and the internal structure of compact objects [20, 21, 22, 23, 24, 25, 26], and the cosmological expansion of the Universe [22, 27, 28, 29, 30, 31] (for comprehensive reviews see [7, 12] and the references therein). Briefly, the gravitational action of EiBI gravity takes the following form: $$\begin{aligned} S=\frac{2}{\kappa }\int \mathrm{d}^4x\biggl (\sqrt{|g_{\mu \nu }+\kappa R_{\mu \nu }|}-\lambda \sqrt{-g}\biggr )+S_{\mathrm{matter}}[g,\phi _M], \end{aligned}$$ (1) where \(R_{\mu \nu }\) is the symmetric part of the Ricci tensor, \(\phi _M\) represents the matter field, and \(\lambda \) is a constant. The latter is linked to the cosmological constant in such a way that one obtains asymptotically flat solutions setting \(\lambda =1\). Finally, the field equations are built varying the action as in the Palatini approach. As in other modified theories of gravity, the Palatini approach is not equivalent to a pure metric one. However, the latter contains ghosts that can be eliminated only adding extra terms in the gravitational action [32, 33]. The higher order curvature terms account for both non-linear matter coupling an (...truncated)


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Ivan De Martino, Antonio Capolupo. Kinetic theory of Jean instability in Eddington-inspired Born–Infeld gravity, The European Physical Journal C, 2017, pp. 715, Volume 77, Issue 10, DOI: 10.1140/epjc/s10052-017-5300-0