Davi C. Rodrigues

Rastall Cosmology and the \Lambda CDM Model

Rastalls 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.

Auxiliary fields representation for modified gravity models

We consider tensor-multiscalar representations for several types of modified gravity actions. The first example is the theory with the action representing an arbitrary smooth function of the scalar curvature R and {open_square}R, the integrand of the Gauss-Bonnet term and the square of the Weyl tensor. We present a simple procedure leading to an equivalent theory of a space-time metric and four auxiliary scalars and especially discuss the calibration of a cosmological constant and the condition of the existence of de Sitter-like solutions in the case of an empty universe. The condition for obtaining a smaller number of independent scalar fields is derived. The second example is the Eddington-like gravity action. In this case we show, in particular, the equivalence of the theory to general relativity with the cosmological constant term, with or without use of the first-order formalism, and also discuss some possible generalizations.

Modified gravity models and the central cusp of dark matter haloes in galaxies

The N-body dark matter (DM) simulations point that DM density profiles, e.g. the Navarro Frenk White (NFW) halo, should be cuspy in its centre, but observations disfavour this kind of DM profile. Here we consider whether the observed rotation curves close to the galactic centre can favour modified gravity models in comparison to the NFW halo, and how to quantify such difference. Two explicit modified gravity models are considered, Modified Newtonian Dynamics (MOND) and a more recent approach renormalization group effects in general relativity (RGGR). It is also the purpose of this work to significantly extend the sample on which RGGR has been tested in comparison to other approaches. By analysing 62 galaxies from five samples, we find that (i) there is a radius, given by half the disc scale length, below which RGGR and MOND can match the data about as well or better than NFW, albeit the formers have fewer free parameters; (ii) considering the complete rotation curve data, RGGR could achieve fits with better agreement than MOND, and almost as good as a NFW halo with two free parameters (NFW and RGGR have, respectively, two and one more free parameters than MOND).

Elliptical galaxies kinematics within general relativity with renormalization group effects

The renormalization group framework can be applied to Quantum Field Theory on curved space-time, but there is no proof whether the beta-function of the gravitational coupling indeed goes to zero in the far infrared or not. In a recent paper [1] we have shown that the amount of dark matter inside spiral galaxies may be negligible if a small running of the General Relativity coupling G is present (δG/G010−7 across a galaxy). Here we extend the proposed model to elliptical galaxies and present a detailed analysis on the modeling of NGC 4494 (an ordinary elliptical) and NGC 4374 (a giant elliptical). In order to compare our results to a well known alternative model to the standard dark matter picture, we also evaluate NGC 4374 with MOND. In this galaxy MOND leads to a significative discrepancy with the observed velocity dispersion curve and has a significative tendency towards tangential anisotropy. On the other hand, the approach based on the renormalization group and general relativity (RGGR) could be applied with good results to these elliptical galaxies and is compatible with lower mass-to-light ratios (of about the Kroupa IMF type).

Solar System constraints on Renormalization Group extended General Relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

General Relativity extensions based on Renormalization Group effects are motivated by a known physical principle and constitute a class of extended gravity theories that have some unexplored unique aspects. In this work we develop in detail the Newtonian and post Newtonian limits of a realisation called Renormalization Group extended General Relativity (RGGR). Special attention is taken to the external potential effect, which constitutes a type of screening mechanism typical of RGGR. In the Solar System, RGGR depends on a single dimensionless parameter

A method for evaluating models that use galaxy rotation curves to derive the density profiles

\bar \nu_\odot

Rastall’s cosmology and its observational constraints

, and this parameter is such that for

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

\bar \nu_\odot = 0

QUANTUM CORRECTIONS TO GRAVITY AND THEIR IMPLICATIONS FOR COSMOLOGY AND ASTROPHYSICS

one fully recovers GR in the Solar System. Previously this parameter was constrained to be

Scalar–tensor theories with an external scalar

|\bar \nu_\odot| \lesssim 10^{-21}