arXiv subjects

R. R. Cuzinatto

Publications and source records attributed to R. R. Cuzinatto.

At least 19 recordsLinked to original sources

arXiv2026

Brans-Dicke-like field for co-varying $G$ and $c$: observational constraints

Ref. [Symmetry 15 (2023) 709] introduced a Brans-Dicke-like framework wherein the scalar field $ϕ$ is composed of both $G$ and $c$ which, for this reason, co-vary according to $c^{3}/G=\text{constant}$. In this paper, we use observational data to constrain the supposed co-varying $G$ and $c$, under the hypothesis of the validity of the standard Lemaitre formula $1+z\sim a^{-1}$. The datasets include SN Ia, BAO and the value of $θ$ extracted from CMB data. A proxy function is demanded for the varying $c$ since the framework does not provide a closed set of equations for computing the functional form of either $G$ or $c$ uniquely. Accordingly, we choose three separate parameterizations for $c\left(z\right)$ inspired both by desirable properties of the varying speed of light (VSL) and by successful phenomenological models from the literature -- including the one by Gupta (CCC framework in e.g. Ref. [Mon. Not. R. Astron. Soc., 498 (2020) 4481-4491]. When combined with DESI, Pantheon+ data strongly favor a variable speed of light with more than $3σ$ confidence level for all parameterizations considered in this paper, whereas Union2.1 suggests no variation of the speed of light. As we shall demonstrate, this apparent discrepancy is due to a strong correlation that emerges between $H_0$ and VSL.

astro-ph.CO↗

arXiv2025

Gravitational Waves Emission in Quadratic Gravity: longitudinal modes, angular momentum emission, and positivity of the radiated power

In this paper, the emission of gravitational waves in quadratic gravity theory is examined. The wave equations for massless and massive perturbations are derived, followed by the calculation of the energy and angular momentum radiated. In the quadrupole approximation, and taking into account only the transverse-traceless modes, it is shown that the theory avoids the issues generated by the Ostrogradsky instabilities and achieves positive energy and angular momentum emissions. As an example, a rotating ellipsoid with free precession is analyzed, and the effects of the massive perturbations on its rotation are highlighted.

gr-qc↗

arXiv2024

Aharonov-Bohm Effect in Generalized Electrodynamics

The Aharonov-Bohm (AB) effect is considered in the context of Generalized Electrodynamics (GE) by Podolsky and Bopp. GE is the only extension to Maxwell electrodynamics that is locally {\normalsize{}U(1)}-gauge invariant, admits linear field equations and contains higher-order derivatives of the vector potential. GE admits both massless and massive modes for the photon. We recover the ordinary quantum phase shift of the AB effect, derived in the context of Maxwell electrodynamics, for the massless mode of the photon in GE. The massive mode induces a correction factor to the AB phase shift depending on the photon mass. We study both the magnetic AB effect and its electric counterpart. In principle, accurate experimental observations of AB the phase shift could be used to constrain GE photon mass.

quant-ph↗

arXiv2024

Inflationary dynamics in modified gravity models

Higher-order theories of gravity are a branch of modified gravity wherein the geometrodynamics of the four-dimensional Riemannian manifold is determined by field equations involving derivatives of the metric tensor of order higher than two. This paper considers a general action built with the Einstein-Hilbert term plus additional curvature-based invariants, viz. the Starobinsky $R^{2}$-type term, a term scaling with $R^{3}$, and a correction of the type $R\square R$. The focus is on the background inflationary regime accommodated by these three models. For that, the higher-order field equations are built and specified for the FLRW line element. The dynanical analysis in the phase space is carried in each case. This analysis shows that the Starobinsky-plus-$R^{3}$ model keeps the good features exhibited by the pure Starobinsky inflationary model, although the set of initial conditions for the inflaton field $χ$ leading to a graceful exit scenario is more contrived; the coupling constant $α_{0}$ of the $R^{3}$ invariant is also constrained by the dynamical analysis. The Starobinsky-plus-$R\square R$ model turns out being a double-field inflation model; it consistently enables an almost-exponential primordial acceleration followed by a radiation dominated universe if its coupling $β_{0}$ takes values in the interval $0\leqβ_{0}\leq3/4$. The models introducing higher-order correction to Starobinsky inflation are interesting due to the possibility of a running spectral index $n_{s}$, something that is allowed by current CMB observations.

gr-qc↗

arXiv2023

Shadows of black holes at cosmological distances in the co-varying physical couplings framework

The co-varying physical couplings (CPC) framework states that physical parameters like the speed of light in vacuum $c$, the Newtonian constant $G$, and the cosmological constant $Λ$ could indeed vary with the spacetime coordinates $x^μ$. Here, we assume a temporal variation, that is, $c(t),G(t)$ and $Λ(t)$. We show that the McVittie spacetime, a black hole in an expanding universe, is a solution of the CPC framework providing naturally an important parameter of the model. Then, we calculate the shadow angular radius of this black hole at cosmological distances. A black hole shadow in the CPC context could be either larger or smaller than the same shadow in the standard cosmology. It depends on how the set $\{ c,G,Λ\}$ varies with time or with the cosmic expansion.

gr-qc↗

arXiv2022

Observational constraints on varying fundamental constants in a minimal CPC model

A minimal model based on the Co-varying Physical Couplings (CPC) framework for gravity is proposed. The CPC framework is based on the assumptions of a metric-compatible four-dimensional Riemannian manifold where a covariantly conserved stress-energy tensor acts as source of the field equations which are formally the same as Einstein field equations, but where the couplings $\{ G, c,Λ\}$ are allowed to vary simultaneously. The minimal CPC model takes $Λ$ as a genuine constant while $c$ and $G$ vary in an entangled way that is consistent with Bianchi identity and the aforementioned assumptions. The model is constrained using the most recent galaxy cluster gas mass fraction observational data. Our result indicates that the functions $c(z)$ and $G\left(z\right)=G_{0}\left(c/c_{0}\right)^{4}$ are compatible with constant couplings for the three different parameterizations of $c=c(z)$ adopted here.

gr-qc↗

arXiv2022

Gravitational waves in higher-order $R^{2}$ gravity

We perform a comprehensive study of gravitational waves in the context of the higher-order quadratic scalar curvature gravity, which encompasses the ordinary Einstein-Hilbert term in the action plus an $R^{2}$ contribution and a term of the type $R\square R$. The main focus is on gravitational waves emitted by binary systems such as binary black holes and binary pulsars in the approximation of circular orbits and nonrelativistic motion. The waveform of higher-order gravitational waves from binary black holes is constructed and compared with the waveform predicted by standard general relativity; we conclude that the merger occurs earlier in our model than what would be expected from GR. The decreasing rate of the orbital period in binary pulsars is used to constrain the coupling parameters of our higher-order $R^{2}$ gravity; this is done with Hulse-Taylor binary pulsar data leading to $κ_{0}^{-1}\lesssim1.1\times10^{16}\,\text{m}^{2}$, where $κ_{0}^{-1}$ is the coupling constant for the $R^{2}$ contribution.

gr-qc↗

arXiv2022

Testing a varying-$Λ$ model for dark energy within Co-varying Physical Couplings framework

The Co-varying Physical Couplings (CPC) framework is a modified gravity set up assuming Einstein Field Equations wherein the quantities $\{G,c,Λ\}$ are promoted to space-time functions. Bianchi identity and the requirement of stress-energy tensor conservation entangle the possible variations of the couplings $\{G,c,Λ\}$, which are forced to co-vary as dictated by the General Constraint (GC). In this paper we explore a cosmological model wherein $G$, $c$ and $Λ$ are functions of the redshift respecting the GC of the CPC framework. We assume a linear parametrization of $Λ$ in terms of the scale factor $a$. We use the ansatz $\dot{G}/G = σ\left( \dot{c}/c \right)$ with $σ=$ constant to deduce the functional forms of $c=c(z)$ and $G=G(z)$. We show that this varying-$\{G,c,Λ\}$ model fits SNe Ia data and $H(z)$ data with $σ= 3$. The model parameters can be constrained to describe dark energy at the background level.

gr-qc↗

arXiv2022

Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 1: Klein-Gordon oscillator

We analyse the Klein-Gordon oscillator in a cosmic string space-time and study the effects stemming from the rotating frame and non-commutativity in momentum space. We show that the latter mimics a constant magnetic field, imparting physical interpretation to the setup. The field equation for the scalar field is solved via separations of variables, and we obtain quantization of energy and angular momentum. The space-time metric is non-degenerate as long as the particle is confined within a hard-wall, whose position depends on the rotation frame velocity and the string mass parameter. We investigate the energy quantization both for a finite hard-wall (numerical evaluation) and in the limit of an infinite hard-wall (analytical treatment). We stress the effect of non-commutativity upon the energy quantization in each case.

gr-qc↗

arXiv2022

Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time. Part 2: Spin-zero Duffin-Kemmer-Petiau-like oscillator

We study the non-inertial effects of a rotating frame on a spin-zero, Duffin-Kemmer-Petiau (DKP)-like oscillator in a cosmic string space-time with non-commutative geometry in the momentum space. The spin-zero DKP-like oscillator is obtained from the Klein-Gordon Lagrangian with a non-standard prescription for the oscillator coupling. We find that the solutions of the time-independent radial equation with the non-zero non-commutativity parameter parallel to the string are related to the confluent hypergeometric function. We find the quantized energy eigenvalues of the non-commutative oscillator.

gr-qc↗

arXiv2021

LyST: a Scalar-Tensor Theory of Gravity on Lyra Manifold

We present a scalar-tensor theory of gravity on a torsion-free and metric compatible Lyra manifold. This is obtained by generalizing the concept of physical reference frame by considering a scale function defined over the manifold. The choice of a specific frame induces a local base, naturally non-holonomic, whose structure constants give rise to extra terms in the expression of the connection coefficients and in the expression for the covariant derivative. In the Lyra manifold, transformations between reference frames involving both coordinates and scale change the transformation law of tensor fields, when compared to those of the Riemann manifold. From a direct generalization of the Einstein-Hilbert minimal action coupled with a matter term, it was possible to build a Lyra invariant action, which gives rise to the associated Lyra Scalar-Tensor theory of gravity (LyST), with field equations for $g_{μν}$ and $ϕ$. These equations have a well-defined Newtonian limit, from which it can be seen that both metric and scale play a role in the description gravitational interaction. We present a spherically symmetric solution for the LyST gravity field equations. It dependent on two parameters $m$ and $r_{L}$, whose physical meaning is carefully investigated. We highlight the properties of LyST spherically symmetric line element and compare it to Schwarzchild solution.

gr-qc↗

arXiv2019

Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space-time

We examine the non-inertial effects of a rotating frame on a Dirac oscillator in a cosmic string space-time with non-commutative geometry in phase space. We observe that the approximate bound-state solutions are related to the biconfluent Heun polynomials. The related energies cannot be obtained in a closed form for all the bound states. We find the energy of the fundamental state analytically by taking into account the hard-wall confining condition. We describe how the ground-state energy scales with the new non-commutative term as well as with the other physical parameters of the system.

gr-qc↗

arXiv2019

$f\left(R,\nabla_{μ_{1}}R,\dots,\nabla_{μ_{1}}\dots\nabla_{μ_{n}}R\right)$ theories of gravity in Einstein frame: A higher order modified Starobinsky inflation model in the Palatini approach

In Cuzinatto et al. [Phys. Rev. D 93, 124034 (2016)], it has been demonstrated that theories of gravity in which the Lagrangian includes terms depending on the scalar curvature $R$ and its derivatives up to order $n$, i.e. $f\left(R,\nabla_μR,\nabla_{μ_{1}}\nabla_{μ_{2}}R,\dots,\nabla_{μ_{1}}\dots\nabla_{μ_{n}}R\right)$ theories of gravity, are equivalent to scalar-multitensorial theories in the Jordan frame. In particular, in the metric and Palatini formalisms, this scalar-multitensorial equivalent scenario shows a structure that resembles that of the Brans-Dicke theories with a kinetic term for the scalar field with $ω_{0}=0$ or $ω_{0}=-3/2$, respectively. In the present work, the aforementioned analysis is extended to the Einstein frame. The conformal transformation of the metric characterizing the transformation from Jordan's to Einstein's frame is responsible for decoupling the scalar field from the scalar curvature and also for introducing a usual kinetic term for the scalar field in the metric formalism. In the Palatini approach, this kinetic term is absent in the action. Concerning the other tensorial auxiliary fields, they appear in the theory through a generalized potential. As an example, the analysis of an extension of the Starobinsky model (with an extra term proportional to $\nabla_μR\nabla^μR$) is performed and the fluid representation for the energy-momentum tensor is considered. In the metric formalism, the presence of the extra term causes the fluid to be an imperfect fluid with a heat flux contribution; on the other hand, in the Palatini formalism the effective energy-momentum tensor for the extended Starobinsky gravity is that of a perfect fluid type. Finally, it is also shown that the extra term in the Palatini formalism represents a dynamical field which is able to generate an inflationary regime without a graceful exit.

gr-qc↗

arXiv2019

Introduction to Regge Calculus for Gravitation

With the theory of general relativity, Einstein abolished the interpretation of gravitation as a force and associated it to the curvature of spacetime. Tensorial calculus and differential geometry are the mathematical resources necessary to study the spacetime manifold in the context of Einstein's theory. In 1961, Tullio Regge published a work on which he uses the old idea of triangulation of surfaces aiming the description of curvature, and, therefore, gravitation, through the use of discrete calculus. In this paper, we approach Regge Calculus pedagogically, as well as the main results towards a discretized version of Einstein's theory of gravitation.

gr-qc↗

arXiv2019

Higher-order modified Starobinsky inflation

An extension of the Starobinsky model is proposed. Besides the usual Starobinsky Lagrangian, a term proportional to the derivative of the scalar curvature, $\nabla_μR\nabla^μR$, is considered. The analyzis is done in the Einstein frame with the introduction of a scalar field and a vector field. We show that inflation is attainable in our model, allowing for a graceful exit. We also build the cosmological perturbations and obtain the leading-order curvature power spectrum, scalar and tensor tilts and tensor-to-scalar ratio. The tensor and curvature power spectrums are compared to the most recent observations from BICEP2/Keck collaboration. We verify that the scalar-to-tensor rate $r$ can be expected to be up to three times the values predicted by Starobinsky model.

gr-qc↗

arXiv2018

Scalar-multi-tensorial equivalence for higher order $f\left( R,\nabla_μ R,\nabla_{μ_{1}}\nabla_{μ_{2}}R,...,\nabla_{μ_{1}}...\nabla_{μ_{n} }R\right)$ theories of gravity

The equivalence between theories depending on the derivatives of $R$, i.e. $f\left( R,\nabla R,...,\nabla^{n}R\right) $, and scalar-multi-tensorial theories is verified. The analysis is done in both metric and Palatini formalisms. It is shown that $f\left( R,\nabla R,...,\nabla^{n}R\right) $ theories are equivalent to scalar-multi-tensorial ones resembling Brans-Dicke theories with kinetic terms $ω_{0}=0$ and $ω_{0}= - \frac{3}{2}$ for metric and Palatini formalisms respectively. This result is analogous to what happens for $f(R)$ theories. It is worthy emphasizing that the scalar-multi-tensorial theories obtained here differ from Brans-Dicke ones due to the presence of multiple tensorial fields absent in the last. Furthermore, sufficient conditions are established for $f\left( R,\nabla R,...,\nabla^{n}R\right) $ theories to be written as scalar-multi-tensorial theories. Finally, some examples are studied and the comparison of $f\left( R,\nabla R,...,\nabla^{n}R\right) $ theories to $f\left( R,\Box R,...\Box^{n}R\right) $ theories is performed.

gr-qc↗

arXiv2018

Bopp-Podolsky black holes and the no-hair theorem

Bopp-Podolsky electrodynamics is generalized to curved space-times. The equations of motion are written for the case of static spherically symmetric black holes and their exterior solutions are analyzed using Bekenstein's method. It is shown the solutions split-up into two parts, namely a non-homogeneous (asymptotically massless) regime and a homogeneous (asymptotically massive) sector which is null outside the event horizon. In addition, in the simplest approach to Bopp-Podolsky black holes, the non-homogeneous solutions are found to be Maxwell's solutions leading to a Reissner-Nordström black hole. It is also demonstrated that the only exterior solution consistent with the weak and null energy conditions is the Maxwell's one. Thus, in light of energy conditions, it is concluded that only Maxwell modes propagate outside the horizon and, therefore, the no-hair theorem is satisfied in the case of Bopp-Podolsky fields in spherically symmetric space-times.

gr-qc↗

arXiv2017

de Broglie-Proca and Bopp-Podolsky massive photon gases in cosmology

We investigate the influence of massive photons on the evolution of the expanding universe. Two particular models for generalized electrodynamics are considered, namely de Broglie-Proca and Bopp-Podolsky electrodynamics. We obtain the equation of state (EOS) $P=P(\varepsilon)$ for each case using dispersion relations derived from both theories. The EOS are inputted into the Friedmann equations of a homogeneous and isotropic space-time to determine the cosmic scale factor $a(t)$. It is shown that the photon non-null mass does not significantly alter the result $a\propto t^{1/2}$ valid for a massless photon gas; this is true either in de Broglie-Proca's case (where the photon mass $m$ is extremely small) or in Bopp-Podolsky theory (for which $m$ is extremely large).

astro-ph.CO↗