Thermodynamics of f(R)f(R) Gravity: The Double Well Potential Case

In this work we further extend the analysis of $f(R)$ theories of gravity in the metric formalism under the approach of a Thermodynamics analogy, proposed in arXiv:1911.04830v3. Here we assume a double-well inflationary potential in the Einstein frame and obtain a parametric form of $f(R)$ in the corresponding Jordan frame. The whole Thermodynamics picture then follows: an equation of state, binodal and spinodal curves, phase transition, critical quantities (pressure, volume and temperature), entropy jumps, specific-heat divergence (and the corresponding critical exponent) and a butterfly catastrophe.Comment: 13 pages, 13 figures. arXiv admin note: substantial text overlap with arXiv:1911.0483

On Perturbations in Warm Inflation

Warm inflation is an interesting possibility of describing the early universe, whose basic feature is the absence, at least in principle, of a preheating or reheating phase. Here we analyze the dynamics of warm inflation generalizing the usual slow-roll parameters that are useful for characterizing the inflationary phase. We study the evolution of entropy and adiabatic perturbations, where the main result is that for a very small amount of dissipation the entropy perturbations can be neglected and the purely adiabatic perturbations will be responsible for the primordial spectrum of inhomogeneities. Taking into account the COBE-DMR data of the cosmic microwave background anisotropy as well as the fact that the interval of inflation for which the scales of astrophysical interest cross outside the Hubble radius is about 50 e-folds before the end of inflation, we could estimate the magnitude of the dissipation term. It was also possible to show that at the end of inflation the universe is hot enough to provide a smooth transition to the radiation era.Comment: 12 pages, no figures, requires revtex4. Further explanation on the origin of the entropy perturbation, reference added and minor notation change. Version accepted for publication in Phys. Rev.

Trans-Planckian Physics from a Nonlinear Dispersion Relation

We study a particular nonlinear dispersion relation $\omega_p(k_p)$ -- a series expansion in the physical wavenumber $k_p$ -- for modeling first-order corrections in the equation of motion of a test scalar field in a de Sitter spacetime from trans-Planckian physics in cosmology. Using both a numerical approach and a semianalytical one, we show that the WKB approximation previously adopted in the literature should be used with caution, since it holds only when the comoving wavenumber $k\gg aH$. We determine the amplitude and behavior of the corrections on the power spectrum for this test field. Furthermore, we consider also a more realistic model of inflation, the power-law model, using only a numerical approach to determine the corrections on the power spectrum.Comment: 11 pages, 10 figures. Some changes made, comments and references added, a figure added, typos corrected, conclusions unchanged, version accepted for pubblication in Phys. Rev.

Dark Interactions and Cosmological Fine-Tuning

Cosmological models involving an interaction between dark matter and dark energy have been proposed in order to solve the so-called coincidence problem. Different forms of coupling have been studied, but there have been claims that observational data seem to narrow (some of) them down to something annoyingly close to the $\Lambda$CDM model, thus greatly reducing their ability to deal with the problem in the first place. The smallness problem of the initial energy density of dark energy has also been a target of cosmological models in recent years. Making use of a moderately general coupling scheme, this paper aims to unite these different approaches and shed some light as to whether this class of models has any true perspective in suppressing the aforementioned issues that plague our current understanding of the universe, in a quantitative and unambiguous way.Comment: 13 pages, 9 figures, accepted for publication in JCAP. Minor corrections, one figure replaced, references adde

Type Ia supernova parameter estimation: a comparison of two approaches using current datasets

By using the Sloan Digital Sky Survey (SDSS) first year type Ia supernova (SN Ia) compilation, we compare two different approaches (traditional \chi^2 and complete likelihood) to determine parameter constraints when the magnitude dispersion is to be estimated as well. We consider cosmological constant + Cold Dark Matter (\Lambda CDM) and spatially flat, constant w Dark Energy + Cold Dark Matter (FwCDM) cosmological models and show that, for current data, there is a small difference in the best fit values and $\sim$ 30% difference in confidence contour areas in case the MLCS2k2 light-curve fitter is adopted. For the SALT2 light-curve fitter the differences are less significant ($\lesssim$ 13% difference in areas). In both cases the likelihood approach gives more restrictive constraints. We argue for the importance of using the complete likelihood instead of the \chi^2 approach when dealing with parameters in the expression for the variance.Comment: 16 pages, 5 figures. More complete analysis by including peculiar velocities and correlations among SALT2 parameters. Use of 2D contours instead of 1D intervals for comparison. There can be now a significant difference between the approaches, around 30% in contour area for MLCS2k2 and up to 13% for SALT2. Generic streamlining of text and suppression of section on model selectio