Scalar-Tensor gravity with system-dependent potential and its relation with Renormalization Group extended General Relativity

We show that Renormalization Group extensions of the Einstein-Hilbert action for large scale physics are not, in general, a particular case of standard Scalar-Tensor (ST) gravity. We present a new class of ST actions, in which the potential is not necessarily fixed at the action level, and show that this extended ST theory formally contains the Renormalization Group case. We also propose here a Renormalization Group scale setting identification that is explicitly covariant and valid for arbitrary relativistic fluids.Comment: 29 pages, 2 figs. v2: small changes in text and ref's. v3: further details on the relation between this work and others on the Renormalization Group. Version to appear in JCA

Renormalization Group approach to Gravity: the running of G and L inside galaxies and additional details on the elliptical NGC 4494

We explore the phenomenology of nontrivial quantum effects on low-energy gravity. These effects come from the running of the gravitational coupling parameter G and the cosmological constant L in the Einstein-Hilbert action, as induced by the Renormalization Group (RG). The Renormalization Group corrected General Relativity (RGGR model) is used to parametrize these quantum effects, and it is assumed that the dominant dark matter-like effects inside galaxies is due to these nontrivial RG effects. Here we present additional details on the RGGR model application, in particular on the Poisson equation extension that defines the effective potential, also we re-analyse the ordinary elliptical galaxy NGC 4494 using a slightly different model for its baryonic contribution, and explicit solutions are presented for the running of G and L. The values of the NGC 4494 parameters as shown here have a better agreement with the general RGGR picture for galaxies, and suggest a larger radial anisotropy than the previously published result.Comment: 9 pages, 2 figs. Based on a talk presented at the VIII International Workshop on the Dark Side of the Universe, June 10-15, 2012, Buzios, RJ, Brazil. v2: typos removed, matches published versio

Evolution of the phase-space density and the Jeans scale for dark matter derived from the Vlasov-Einstein equation

We discuss solutions of Vlasov-Einstein equation for collisionless dark matter particles in the context of a flat Friedmann universe. We show that, after decoupling from the primordial plasma, the dark matter phase-space density indicator Q remains constant during the expansion of the universe, prior to structure formation. This well known result is valid for non-relativistic particles and is not "observer dependent" as in solutions derived from the Vlasov-Poisson system. In the linear regime, the inclusion of velocity dispersion effects permits to define a physical Jeans length for collisionless matter as function of the primordial phase-space density indicator: \lambda_J = (5\pi/G)^(1/2)Q^(-1/3)\rho_dm^(-1/6). The comoving Jeans wavenumber at matter-radiation equality is smaller by a factor of 2-3 than the comoving wavenumber due to free-streaming, contributing to the cut-off of the density fluctuation power spectrum at the lowest scales. We discuss the physical differences between these two scales. For dark matter particles of mass equal to 200 GeV, the derived Jeans mass is 4.3 x 10^(-6) solar masses.Comment: 18 pages, 2 figures. Accepted for publication in JCA

Rastall Cosmology and the \Lambda CDM Model

Rastall's theory is based on the non-conservation of the energy-momentum tensor. We show that, in this theory, if we introduce a two-fluid model, one component representing vacuum energy whereas the other pressureless matter (e.g. baryons plus cold dark matter), the cosmological scenario is the same as for the \Lambda CDM model, both at background and linear perturbative levels, except for one aspect: now dark energy may cluster. We speculate that this can lead to a possibility of distinguishing the models at the non-linear perturbative level.Comment: 9 pages, 1 figure. Accepted for publication in Physical Review

A detailed first-order post-Newtonian analysis of massive Brans-Dicke theories: numerical constraints and the β\beta parameter meaning

Massive Brans-Dicke (BD) theory is among the simplest general relativity extensions. It is commonly found as the weak-field limit of other gravitational theories. Here we do a detailed post-Newtonian analysis of massive BD theories. We start by expanding the massive BD field equations following the Will-Nodtvedt Parameterized-Post-Newtonian (PPN) formalism, without point-particle approximations. A single potential that is not present in the standard PPN formalism is found. This new potential hinders immediate PPN conclusions. To proceed, we do a complete first-order post-Newtonian analysis and explicitly derive all the conserved quantities. After demanding that there exists a Newtonian limit by requiring the BD mass to be sufficiently large, we find, as expected, that $\gamma = 1$; but there is no effective $\beta$ parameter that can have the same physical role of the standard $\beta$ in PPN formalism. All the others standard PPN parameters can be extended to the massive BD case without issues and are shown to have the same values of general relativity. At last, we consider numerical relations on the periastron advance and the BD mass in two different physical contexts, the orbit of Mercury about the Sun and the orbit of the star S2 about the supermassive black hole in the Milky Way.Comment: 12 pages, 5 figure