Adiabatic regularization of the graviton stress-energy tensor in de Sitter space-time

We study the renormalized energy-momentum tensor of gravitons in a de Sitter space-time. After canonically quantizing only the physical degrees of freedom, we adopt the standard adiabatic subtraction used for massless minimally coupled scalar fields as a regularization procedure and find that the energy density of gravitons in the E(3) invariant vacuum is proportional to H^4, where H is the Hubble parameter, but with a positive sign. According to this result the scalar expansion rate, which is gauge invariant in de Sitter space-time, is increased by the fluctuations. This implies that gravitons may then add to conformally coupled matter in driving the Starobinsky model of inflation.Comment: 5 pages, revtex, final version accepted for publication in PR

An elusive radio halo in the merging cluster Abell 781?

Deep radio observations of the galaxy cluster Abell 781 have been carried out using the Giant Metrewave Radio Telescope at 325 MHz and have been compared to previous 610 MHz observations and to archival VLA 1.4 GHz data. The radio emission from the cluster is dominated by a diffuse source located at the outskirts of the X-ray emission, which we tentatively classify as a radio relic. We detected residual diffuse emission at the cluster centre at the level of S(325 MHz)~15-20 mJy. Our analysis disagrees with Govoni et al. (2011), and on the basis of simple spectral considerations we do not support their claim of a radio halo with flux density of 20-30 mJy at 1.4 GHz. Abell 781, a massive and merging cluster, is an intriguing case. Assuming that the residual emission is indicative of the presence of a radio halo barely detectable at our sensitivity level, it could be a very steep spectrum source.Comment: 5 pages, 4 figures, 1 table - Accepted for publication on Monthly Notices of the Royal Astronomical Society Letter

Stochastic growth of quantum fluctuations during slow-roll inflation

We compute the growth of the mean square of quantum fluctuations of test fields with small effective mass during a slowly changing, nearly de Sitter stage which took place in different inflationary models. We consider a minimally coupled scalar with a small mass, a modulus with an effective mass $\propto H^2$ (with $H$ as the Hubble parameter) and a massless non-minimally coupled scalar in the test field approximation and compare the growth of their relative mean square with the one of gauge-invariant inflaton fluctuations. We find that in most of the single field inflationary models the mean square gauge invariant inflaton fluctuation grows {\em faster} than any test field with a non-negative effective mass. Hybrid inflationary models can be an exception: the mean square of a test field can dominate over the gauge invariant inflaton fluctuation one on suitably choosing parameters. We also compute the stochastic growth of quantum fluctuation of a second field, relaxing the assumption of its zero homogeneous value, in a generic inflationary model; as a main result, we obtain that the equation of motion of a gauge invariant variable associated, order by order, with a generic quantum scalar fluctuation during inflation can be obtained only if we use the number of e-folds as the time variable in the corresponding Langevin and Fokker-Planck equations for the stochastic approach. We employ this approach to derive some bounds in the case of a model with two massive fields.Comment: 9 pages, 4 figures. Added references, minor changes, matches the version to be published in Phys. Rev.

Inflation and Reheating in Spontaneously Generated Gravity

Inflation is studied in the context of induced gravity (IG) $\gamma \sigma^2 R$, where $R$ is the Ricci scalar, $\sigma$ a scalar field and $\gamma$ a dimensionless constant, and diverse symmetry-breaking potentials $V(\sigma)$ are considered. In particular we compared the predictions for Landau-Ginzburg (LG) and Coleman-Weinberg (CW) type potentials and their possible generalizations with the most recent data. We find that large field inflation generally leads to fewer constraints on the parameters and the shape of the potential whereas small field inflation is more problematic and, if viable, implies more constraints, in particular on the parameter $\gamma$. We also examined the reheating phase and obtained an accurate analytical solution for the dynamics of inflaton and the Hubble parameter by using a multiple scale analysis (MSA). The solutions were then used to study the average expansion of the Universe, the average equation of state for the scalar field and both the perturbative and resonant decays of the inflaton field.Comment: 15 pages, 10 figures, to be published in Phys. Rev.

A note on the introduction of Hilbert’s Grundlagen der Geometrie

FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOWe present and discuss a change in the introduction of Hilbert’s Grundlagen der Geometrie between the fiirst and the subsequent editions: the disappearance of the reference to the independence of the axioms. We briefly outline the theoretical relevance of402517FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO2013/25095-42014/25342-

Reconstruction of Scalar Potentials in Modified Gravity Models

We employ the superpotential technique for the reconstruction of cosmological models with a non-minimally coupled scalar field evolving on a spatially flat Friedmann-Robertson-Walker background. The key point in this method is that the Hubble parameter is considered as a function of the scalar field and this allows one to reconstruct the scalar field potential and determine the dynamics of the field itself, without a priori fixing the Hubble parameter as a function of time or of the scale factor. The scalar field potentials that lead to de Sitter or asymptotic de Sitter solutions, and those that reproduce the cosmological evolution given by Einstein-Hilbert action plus a barotropic perfect fluid, have been obtained.Comment: 12 pages, 2 figures, accepted for publication in PR