The Layzer-Irvine equation in theories with non-minimal coupling between matter and curvature

Abstract

We derive the Layzer-Irvine equation for alternative gravitational theories with non-minimal coupling between curvature and matter for an homogeneous and isotropic Universe. As an application, we study the case of Abell 586, a relaxed and spherically symmetric galaxy cluster, assuming some matter density profiles.

Inflation in non-minimal matter-curvature coupling theories

“…This model has quite interesting implications for stellar stability [13], preheating after inflation [14], as well as in mimicking the dark matter in galaxies and clusters [15,16] or the late time accelerated expansion of the Universe [17]. This scenario has also a non-negligible impact in black hole physics [18], and on the generalisation of the Layzer-Irvine equation [19].…”

Jeans instability in non-minimal matter-curvature coupling gravity

“…Another successful alternative theory of gravity in shedding some light in the above mentioned problems relies in an extension of f(R) theories with a non-minimal coupling between matter and curvature [16]. In fact, it allows for a mimicking effect of dark matter effects at galaxies [17] and clusters of galaxies scales [18], it has some bearings on the late time acceleration [19], and is compatible with Planck's inflation data [20], gravitational waves measurements [21] and the modified virial theorem from the spherically relaxed Abell 586 cluster [22].…”

Pressureless stationary solutions in a Newton-Yukawa gravity model

“…Additional implications of the model have been extensively discussed in the literature and can be found in previously works of one of the authors [2,[33][34][35][36][37][38]. Considering the functions f i (R), i = 1, 2 to be analytical around R = 0, we can make use of a Taylor expansion and express…”