arXiv subjects

F. C. Carvalho

Publications and source records attributed to F. C. Carvalho.

At least 19 recordsLinked to original sources

arXiv2026

Effective chemical potential and its phenomenological implications for the Hubble parameter

In cosmological models, the Hubble parameter is determined by the time evolution of the scale factor, and current observations reveal a persistent tension between its values inferred from different probes, such as Cepheid variable stars and the cosmic microwave background. Within Tsallis' statistical framework, we identify two distinct definitions of fugacity associated with relativistic and non-relativistic regimes. For the non-relativistic sector, we introduce an effective chemical potential and establish its connection with the Gibbs free energy. We then explore a phenomenological correspondence between this effective chemical potential and an Unruh-like temperature associated with accelerated trajectories in an expanding cosmological background. As an application, we derive an effective expression for the Hubble parameter that includes a statistics-dependent contribution arising from the non-relativistic matter sector. This contribution suggests that non-Gaussian statistical effects, when consistently incorporated in the non-relativistic matter sector, can enhance the sensitivity of the expansion rate to underlying thermostatistical assumptions, achieving a substantial increase in sensitivity by approximately ten orders of magnitude when compared with previous relativistic constructions that investigated, at a phenomenological level, the discrepancy observed in current determinations of the Hubble constant.

gr-qc↗

arXiv2026

Generalized junction conditions for discontinuous metrics

In this work, the Darmois-Israel junction formalism is extended to the case of discontinuous metrics within the framework of Colombeau algebras of generalized functions. This formulation provides a mathematically consistent treatment of nonlinear operations involving singular quantities, such as products and derivatives of distributions. By relaxing the usual continuity condition on the metric, the generalized junction conditions naturally include higher-order singular terms in the curvature and in the surface energy-momentum tensor. These additional contributions represent new geometric degrees of freedom associated with genuine discontinuities in the space-time geometry. The resulting formalism recovers the traditional Darmois-Israel conditions as a limiting case, while offering a coherent extension applicable to geometric boundaries and abrupt transitions in space-time.

gr-qc↗

arXiv2025

A possible correction of the Saha curve for non-equilibrium states

It is widely known that the Saha equation is not suitable for describing plasmas out of thermodynamic equilibrium. The primordial hydrogen recombination plasma is an example of this. In this work, we propose a theoretical modification to the standard Saha curve motivated by Tsallis statistics. In particular, we explore the possibility that a time-dependent $q$-parameter may serve as an effective proxy for the evolving thermodynamic conditions during recombination, especially considering that hydrogen recombination occurs from excited states. Within this framework, the $q$-parameter could be interpreted as encoding departures from equilibrium and could play the role of effective time-dependent temperature. This indicates that the time evolution of the $q$-parameter could provide a phenomenological mechanism for incorporating non-equilibrium effects into the recombination history. Our findings suggest that the Tsallis parameterization provides an alternative path to fit the distribution of free electrons by using an effective temperature. The implications of this approach might go beyond its immediate applications, as the Saha equation is widely used in various scientific fields like astrophysics, cosmology, plasma physics, and condensed matter physics.

astro-ph.CO↗

arXiv2024

Generalized inflation in the context of $κ$-deformed theories

A new inflationary scenario driven by a slowly-rolling homogeneous scalar field whose potential $V\left(φ\right)$ is given by a generalized exponential function is investigated. Within the {\it slow-roll} approximation we obtain the main predictions of the model and compare them with current data from cosmic microwave background and large-scale structure observations. We show that this single scalar field model admits a wider set of solutions than usual exponential scenarios and predicts acceptable values of the spectral index, running of the spectral index and tensor-to-scalar ratio for the remaining number of {\it e}-folds lying in the interval $N = 55 \pm 5$ and an energy scale on which $λ\geq \sqrt{2}$; in particular, we observe that the value of the model parameter $κ$ depends on the analysis. Finally, the primordial local non-Gaussianity is briefly discussed where we conclude that $k\gtrsim 0.02$ for $f_\text{NL}^\text{local} \ll 1$.

astro-ph.CO↗

arXiv2024

Non-Gaussian Saha's ionization in Rindler spacetime and the equivalence principle

We investigate the non-Gaussian effects of the Saha equation in Rindler space via Tsallis statistics. By considering a system with cylindrical geometry, we deduce the non-Gaussian Saha ionization equation for a partially ionized hydrogen plasma that expands with uniform acceleration. We demonstrate conditions for the validity of the equivalence principle within the realms of both Boltzmann-Gibbs and Tsallis statistics. In the non-Gaussian framework, our findings reveal that the effective binding energy exhibits a quadratic dependence on the frame acceleration, in contrast to the linear dependence predicted by Boltzmann-Gibbs statistics. We show that an accelerated observer shall notice a more pronounced effect on the effective binding energy for $a>0$ and a more attenuated one when $a<0$. We also ascertain that an accelerated observer will measure values of $q$ smaller than those measured in the rest frame. Besides, assuming the equivalence principle, we examine the effects of the gravitational field on the photoionization of hydrogen atoms and pair production. We show that both photoionization and pair production are more intensely suppressed in regions with a strong gravitational field in a non-Gaussian context than in the Boltzmann-Gibbs framework. Lastly, constraints on the gravitational field and the electron and positron chemical potentials are derived.

astro-ph.CO↗

arXiv2023

Constraint on the chemical potentials of hydrogen and proton in recombination

In this paper, we revisit the hydrogen recombination history from a novel perspective: the evolution of chemical potentials. We derive expressions for the chemical potentials, which depend on the thermal bath temperature and the ionization degree of the universe. Our main finding reveals a constraint between the chemical potentials of hydrogen and proton at $z\approx 1200$ when the free electron fraction is $X_e\approx 1/3$. Furthermore, we present important data on the chemical potentials during recombination, highlighting the differences between the predictions of the Peebles' and CosmoRec code solutions. Finally, we discuss a particular case related to the chemical potential of hydrogen.

astro-ph.CO↗

arXiv2022

Non-Gaussian Effects of the Saha's Ionization in the Early Universe

Tsallis' thermostatistical has received increasing attention due to its success in describing phenomena that manifest unusual thermodynamic properties. In this context, the generalized Saha equation must follow a condition of generalized thermal equilibrium of matter and radiation. The present work aims to explore the non-Gaussian effects on Saha's ionization via Tsallis statistics. To accomplish this, we generalized the number density taking into account a non-Gaussian Fermi-Dirac distribution, and then set out the Saha equation for the cosmological recombination. As a result, we highlight two new non-Gaussian effects: $i$) two generalized chemical equilibrium conditions, one for the relativistic regime and the other for the non-relativistic one; and $ii$) the hydrogen binding $q$-energy. We demonstrated that to yields smooth shifts in the binding energy, the $a$-parameter must be very small. We also showed that binding $q$-energy exhibits symmetrical behavior around the value of the standard binding energy. Besides, we used the $q$-energy in order to access other hydrogen energy levels, and we ascertained the values of the $a$-parameter that access those levels and their relationship to temperature. Finally, we employed these results to examine the non-Gaussian effects of the deuterium bottleneck, recombination and the particle anti-particle excess.

astro-ph.CO↗

arXiv2019

Reconstruction of energy conditions from observations and implications for extended theories of gravity

The attempt to describe the recent accelerated expansion of the Universe includes different propositions for dark energy models and modified gravity theories. Establish their features in order to discriminate and even rule out part of these models using observational data is a fundamental issue of cosmology. In the present work we consider a class of extended theories of gravity (ETG) that are minimally coupled to the ordinary matter fields. In this context, and assuming a homogeneous and isotropic spacetime, we derive the energy conditions for this ETG class. We then put constraints on these conditions using a model-independent approach to reconstruct the deceleration function along with the Joint Light-curve Analysis (JLA) supernova sample, 11 baryon acoustic oscillation and 22 cosmic-chronometer measurements. We also consider an additional condition imposing the strong energy condition only on the ordinary matter. This is to guarantee the presence of only attractive matter in the energy-momentum tensor, at least in the redshift range of the observations, i.e., the recent accelerated expansion of the Universe is due solely to the modifications in the gravity theory. The main result of this work is a general reconstruction of the energy conditions valid for every considered ETG.

astro-ph.CO↗

arXiv2017

Coupling dark-baryonic matter density profile for vacuum decay scenarios

The cosmological consequences of an interacting model in which vacuum decay law is deducted from the effect that vacuum decay has on the dark matter evolution are investigated. Here, the baryonic matter is also considered as a fluid gravitationally coupled with dark matter. It is made a careful analysis to constrain this model with the observational data of growth rate of cosmic structures. The theoretical growth rate is followed since the primordial recombination and the main physical processes on the baryonic component are considered. As a complementary constraint, this model is compared with the observed CMB-BAO ratio as well with the gas mass fraction of cluster of galaxies. We found the best fit values for dark matter $Ω_{d0} = 0.269 ^{+0.023}_{-0.023}$ and for the decay parameter $ε= 0.02 ^{+0.04}_{-0.05}$.

astro-ph.CO↗

arXiv2017

Cosmological constant constraints from observation-derived energy condition bounds and their application to bimetric massive gravity

Among the various possibilities to probe the theory behind the recent accelerated expansion of the universe, the energy conditions (ECs) are of particular interest, since it is possible to confront and constrain the many models, including different theories of gravity, with observational data. In this context, we use the ECs to probe any alternative theory whose extra term acts as a cosmological constant. For this purpose, we apply a model-independent approach to reconstruct the recent expansion of the universe. Using Type Ia supernova, baryon acoustic oscillations and cosmic-chronometer data, we perform a Markov Chain Monte Carlo analysis to put constraints on the effective cosmological constant $Ω^0_{\rm eff}$. By imposing that the cosmological constant is the only component that possibly violates the ECs, we derive lower and upper bounds for its value. For instance, we obtain that $0.59 < Ω^0_{\rm eff} < 0.91$ and $0.40 < Ω^0_{\rm eff} < 0.93$ within, respectively, $1σ$ and $3σ$ confidence levels. In addition, about 30\% of the posterior distribution is incompatible with a cosmological constant, showing that this method can potentially rule it out as a mechanism for the accelerated expansion. We also study the consequence of these constraints for two particular formulations of the bimetric massive gravity. Namely, we consider the Visser's theory and the Hassan and Roses's massive gravity by choosing a background metric such that both theories mimic General Relativity with a cosmological constant. Using the $Ω^0_{\rm eff}$ observational bounds along with the upper bounds on the graviton mass we obtain constraints on the parameter spaces of both theories.

gr-qc↗

arXiv2016

A Bayesian estimate of the CMB-large-scale structure cross-correlation

Evidences for late-time acceleration of the Universe are provided by multiple probes, such as Type Ia supernovae, the cosmic microwave background (CMB) and large-scale structure (LSS). In this work, we focus on the integrated Sachs--Wolfe (ISW) effect, i.e., secondary CMB fluctuations generated by evolving gravitational potentials due to the transition between, e.g., the matter and dark energy (DE) dominated phases. Therefore, assuming a flat universe, DE properties can be inferred from ISW detections. We present a Bayesian approach to compute the CMB--LSS cross-correlation signal. The method is based on the estimate of the likelihood for measuring a combined set consisting of a CMB temperature and a galaxy contrast maps, provided that we have some information on the statistical properties of the fluctuations affecting these maps. The likelihood is estimated by a sampling algorithm, therefore avoiding the computationally demanding techniques of direct evaluation in either pixel or harmonic space. As local tracers of the matter distribution at large scales, we used the Two Micron All Sky Survey (2MASS) galaxy catalog and, for the CMB temperature fluctuations, the ninth-year data release of the Wilkinson Microwave Anisotropy Probe (WMAP9). The results show a dominance of cosmic variance over the weak recovered signal, due mainly to the shallowness of the catalog used, with systematics associated with the sampling algorithm playing a secondary role as sources of uncertainty. When combined with other complementary probes, the method presented in this paper is expected to be a useful tool to late-time acceleration studies in cosmology.

astro-ph.CO↗

arXiv2008

Cosmological Constraints from Hubble Parameter on f(R) Cosmologies

Modified $f(R)$ gravity in the Palatini approach has been presently applied to Cosmology as a realistic alternative to dark energy. In this concern, a number of authors have searched for observational constraints on several $f(R)$ gravity functional forms using mainly data of type Ia supenovae (SNe Ia), Cosmic Microwave Background ({\rm CMB}) radiation and Large Scale Structure ({\rm LSS}). In this paper, by considering a homogeneous and isotropic flat universe, we use determinations of the Hubble function $H(z)$, which are based on differential age method, to place bounds on the free parameters of the $f(R) = R - β/R^{n}$ functional form. We also combine the $H(z)$ data with constraints from Baryon Acoustic Oscillations ({\rm BAO}) and {\rm CMB} measurements, obtaining ranges of values for $n$ and $β$ in agreement with other independent analyses. We find that, for some intervals of $n$ and $β$, models based on $f(R) = R - β/R^{n}$ gravity in the Palatini approach, unlike the metric formalism, can produce the sequence of radiation-dominated, matter-dominated, and accelerating periods without need of dark energy.

astro-ph↗

arXiv2008

Latest supernovae constraints on f(R) cosmologies

A class of modified gravity, known as $f(R)$-gravity, has presently been applied to Cosmology as a realistic alternative to dark energy. In this paper we use the most recent Type-Ia Supernova (SNe Ia) data, the so-called \emph{Union} sample of 307 SNe Ia, to place bounds on a theory of the form $f(R)=R - β/R^n$ within the Palatini approach. Given the complementarity of SNe Ia data with other cosmological observables, a joint analysis with measurements of baryon acoustic oscillation peak and estimates of the {\rm CMB} shift parameter is also performed. We show that, for the allowed intervals of $n$, $Ω_{mo}$, and $β$, models based on $f(R) = R - β/R^{n}$ gravity in the Palatini approach can produce the sequence of radiation-dominated, matter-dominated, and accelerating periods without need of dark energy.

astro-ph↗

arXiv2008

Hybrid dark energy

Extending previous results [Phys. Rev. Lett. 97, 081301 (2006)], we explore the cosmological implications of a new quintessence scenario driven by a slow rolling homogeneous scalar field whose equation of state behaved as freezing over the entire cosmic evolution, is approaching -1 today, but will become thawing in the near future, thereby driving the Universe to an eternal deceleration. We argue that such a mixed behavior, named \emph{hybrid}, may reconcile the slight preference of current observational data for freezing potentials with the impossibility of defining observables in the String/M-theory context due to the existence of a cosmological event horizon in asymptotically de Sitter universes as, e.g., pure freezing scenarios.

astro-ph↗

arXiv2007

Energy conditions in f(R)-gravity

In order to shed some light on the current discussion about f(R)-gravity theories we derive and discuss the bounds imposed by the energy conditions on a general f(R) functional form. The null and strong energy conditions in this framework are derived from the Raychaudhuri's equation along with the requirement that gravity is attractive, whereas the weak and dominant energy conditions are stated from a comparison with the energy conditions that can be obtained in a direct approach via an effective energy-momentum tensor for f(R)-gravity. As a concrete application of the energy conditions to locally homogeneous and isotropic f(R)-cosmology, the recent estimated values of the deceleration and jerk parameters are used to examine the bounds from the weak energy condition on the parameters of two families of f(R)-gravity theories.

astro-ph↗

arXiv2007

CMB and LSS constraints on a single-field model of inflation

A new inflationary scenario whose exponential potential $V(Φ)$ has a quadratic dependence on the field $Φ$ in addition to the standard linear term is confronted with the tree-year observations of the Wilkinson-Microwave Anisotropy Probe and the Sloan Digital Sky Survey data. The number of e-folds ($N$), the ratio of tensor-to-scalar perturbations ($r$), the spectral scalar index of the primordial power spectrum ($n_s$) and its running ($dn_s/d\ln k$) depend on the dimensionless parameter $α$ multiplying the quadratic term in the potential. In the limit $α\to 0$ all the results of the standard exponential potential are fully recovered. For values of $α\neq 0$, we find that the model predictions are in good agreement with the current observations of the Cosmic Microwave Background (CMB) anisotropies and Large-Scale Structure (LSS) in the Universe.

astro-ph↗

arXiv2006

$β$-exponential inflation

An inflationary scenario driven by a slow rolling homogeneous scalar field whose potential $V(Φ)$ is given by a generalized exponential function is discussed. Within the {\sl slow-roll} approximation we investigate some of the main predictions of the model and compare them with current data from Cosmic Microwave Background and Large-Scale Structure observations. In particular, we show that this single scalar field model admits a wider range of solutions than do conventional exponential scenarios and predicts acceptable values of the scalar spectral index and of the tensor-to-scalar ratio for the remaining number of {\sl e-folds} lying in the interval $N = 54 \pm 7$ and energy scales of the order of Planck scale. The running of the spectral index is briefly discussed to show that both negative and positive values are predicted by the model here proposed.

astro-ph↗

arXiv2006

Scalar-field-dominated cosmology with a transient accelerating phase

A new cosmological scenario driven by a slow rolling homogeneous scalar field whose exponential potential $V(Φ)$ has a quadratic dependence on the field $Φ$ in addition to the standard linear term is discussed. The derived equation of state for the field predicts a transient accelerating phase, in which the Universe was decelerated in the past, began to accelerate at redshift $z \sim 1$, is currently accelerated, but, finally, will return to a decelerating phase in the future. This overall dynamic behavior is profoundly different from the standard $Λ$CDM evolution, and may alliviate some conflicts in reconciling the idea of a dark energy-dominated universe with observables in String/M-theory. The theoretical predictions for the present transient scalar field plus dark matter dominated stage are confronted with cosmological observations in order to test the viability of the scenario.

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