arXiv subjects

Marcelo H. Alvarenga

Publications and source records attributed to Marcelo H. Alvarenga.

7 recordsLinked to original sources

arXiv2026

Limits of the Rastall--Einstein Equivalence: Matter-Action Compatibility, FLRW Dynamics, and Exceptional Sectors

A regular Rastall metric equation can be written exactly as an Einstein equation with a conserved algebraic source. We examine whether this source redefinition also preserves a specified local matter-action class. For an isentropic barotropic fluid, keeping the particle-density variable and its conserved current fixed gives the compatibility condition $3nρ_{,nn}-ρ_{,n}=0$, whose non-Einstein solutions are $ρ(n)=ρ_Λ+C n^{4/3}$. For a minimally coupled first-derivative scalar field with the same field and kinetic variable, preservation of the local $\mathcal L_ϕ(X,ϕ)$ class gives $X\mathcal L_{ϕ,XX}-\mathcal L_{ϕ,X}=0$, and hence $\mathcal L_ϕ=\frac12\mathcal A(ϕ)X^2+\mathcal B(ϕ)$. These are off-shell functional compatibility tests within restricted continuum action classes; they do not by themselves establish equivalence of full solution spaces or observables. Throughout the analysis, $T_{μν}$ denotes the physical energy--momentum tensor of the specified matter model. Its Einstein-form algebraic image is $Θ_{μν}[T]=T_{μν}-αg_{μν}T$. We also complete the dictionary between two Ricci--trace parametrizations, including the coupling, and state a limited on-shell variational obstruction with its exceptions. The analysis includes Poisson-level weak-field matching for an operational rest-mass density, the singular FLRW branch $D(w)=0$, a classification of exceptional parameter sectors, and a comparison of Rastall gravity with standard unimodular gravity and nonconservative trace-free completions. The regular Rastall metric equation is therefore algebraically equivalent to an Einstein equation with a redefined source; equivalence of completed matter--gravity models is a separate, stronger requirement.

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arXiv2026

Wormhole Reconstruction in Non-Conservative Unimodular Gravity: Ricci Scalar as an Independently Prescribed Curvature Profile

The absence of an algebraic relation between the Ricci scalar and the trace of the energy-momentum tensor in Non-Conservative Unimodular Gravity ($\mathrm{NUG}$) opens new possibilities for constructing spacetime geometries from prescribed curvature profiles. Exploiting this property, we develop a curvature reconstruction framework in which traversable wormhole geometries are generated directly from a prescribed curvature profile rather than from the matter sector or the metric functions. The reconstruction procedure is implemented for a power-law Ricci scalar combined with three different redshift functions, leading to distinct classes of static and spherically symmetric wormhole solutions. We investigate their geometrical properties, asymptotic behavior and null energy condition. Although the radial null energy condition remains necessarily violated at the throat, we show that the dimensionless curvature parameter controls the intensity of the exotic matter supporting the wormhole, while the curvature exponent determines the global asymptotic structure of the reconstructed spacetime. In particular, the critical configuration separating asymptotically flat solutions from geometries with residual asymptotic deformation naturally emerges from the reconstruction scheme. These results establish curvature reconstruction from prescribed Ricci scalar profiles as a viable geometrical framework for generating compact-object spacetimes within non-conservative unimodular gravity.

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arXiv2025

Anisotropic Bianchi-I cosmological model in non-conservative unimodular gravity

In this article, we propose an anisotropic Bianchi-I type cosmological model in non-conservative Unimodular Gravity ($\mathrm{NUG}$). We show that simply using the Bianchi-I type metric does not resolve a striking characteristic of the field equations in $\mathrm{NUG}$: their underdetermination. This fact led us to implement extra conditions on the combination $\left(ρ+p\right)$ and, consequently, obtain a consistent background cosmological analysis. In the vacuum case, we obtain an analogy between the Kasner solutions and the equations in $\mathrm{NUG}$. We also propose a new analysis of a non-homogeneous equation of state, the combination $\left(ρ+p\right)=l$. We identify that the cosmological dynamics are strictly dependent on the value of the constant $l$. The physically interesting case is at the value $l<0$, which seems to indicate a super-accelerated, ghost-like universe. This case still requires a more detailed analysis, for example, from a thermodynamic point of view, keeping in mind that $\left(ρ+p\right)$ may be interpreted as enthalpy of the system. For the cases $\left(ρ+p\right)\propto a^{-3}$ and $\left(ρ+p\right) \propto a^{-4}$, we obtain a description consistent with the anisotropic cosmological model described by $\mathrm{GR}$. In all cases analyzed, a small value for the anisotropic parameter $Ω_{A}$ (on the order of $10^{-2}$) is required in order to have agreement, for example, with the age of the universe to be approximately $12-14\, \mathrm{Gyr}$, agreeing with the age of globular clusters. As the universe expands an isotropization is verified, with the anistropies going to zero asymptotically, similarly with what happens in an anistropic cosmological model based on $\mathrm{GR}$.

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arXiv2024

Holographic Ricci dark energy in Nonconservative Unimodular Gravity

The structure of unimodular gravity (UG) is invariant to a subclass of diffeomorphism, the transverse diffeomorphism, due to the unimodular condition ($\sqrt{-g}=ε=cte$). Consequently, there is a freedom to define how the conservation laws of the energy-momentum tensor in unimodular gravity in the cosmological context. One of the main characteristics of the complete system of equations that describe cosmological dynamics in UG is that they form an underdetermined system if the usual conservation law of the energy-momentum tensor is not used in your structure, that is, it is necessary to insert extra information into the system to solve the complete set of equations. In this article, we propose the construction of a background cosmological model based on the description of a holographic dark energy component with a cutoff of the order of Ricci scalar in non-conservative UG. Although this choice is indeed a new addition of information to the cosmological system, the complete set of equations remains underdetermined, however, the new feature of this cosmological model is the appearance of an interaction between matter and dark energy. Indeed, this is a well-known characteristic of cosmological models in which we have holographic dark energy density. Consequently, we propose an ansatz to the interaction term $Q=βH ρ_{m}$, and obtain the cosmological parameters of our model. We found a viable universe model with similar characteristics to the $Λ\mathrm{CDM}$ model. We performed statistical analysis of the background model using the "Cosmic Chronometer" (CC) data for $H(z)$, and obtain as a result using Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC) as model selection criteria that $Λ\mathrm{CDM}$ prevails as the best model. However, the proposed model is competitive when compared to the cosmological model $ω\mathrm{CDM}$.

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arXiv2023

Using cosmological perturbation theory to distinguish between General Relativity and Unimodular Gravity

Unimodular Gravity is one of the oldest geometric gravity theory alternative to General Relativity. Essentially, it is based on the Einstein-Hilbert Lagrangian with an additional constraint on the determinant of the metric. It can be explicitly shown that Unimodular Gravity can be recast as General Relativity in presence of a cosmological constant. This fact has led to many discussions on the equivalence of both theories at classical and quantum levels. Here we present an analysis focused on the classical scalar perturbations around a cosmological background. The discussion is extended for the case where a non-minimal coupled scalar field is introduced. Our results indicate that the equivalence is not verified completely at perturbative level.

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arXiv2021

Nonconservative unimodular gravity: Gravitational waves

Unimodular gravity is characterized by an extra condition with respect to General Relativity: the determinant of the metric is constant. This extra condition leads to a more restricted class of invariance by coordinate transformation. Even though, if the conservation of the energy-momentum tensor is imposed in unimodular gravity, the General Relativity theory is recovered with an additional integration constant which is associated to the cosmological term $Λ$. However, if the energy-momentum tensor does not conserve separately, a new geometric structure appears with potentially observational signatures. In this text, we consider the evolution of gravitational waves in the nonconservative unimodular gravity, showing how it differs from the usual signatures in the standard model.

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arXiv2021

Nonconservative unimodular gravity: a viable cosmological scenario

In this work we review the issue of imposing the conservation of the energy-momentum tensor as a necessary condition to recover the equivalence between the unimodular gravity and General Relativity (GR) equipped with a cosmological constant. This procedure is usually interpreted as an {\it ad hoc} imposition on the unimodular theory's structure. Whereas the consequences of avoiding the conservation of the total energy-momentum tensor has been already introduced in the literature, it has been not widely explored so far. We study an expanding universe sourced by a single effective perfect fluid such that the null divergence of its energy-momentum tensor is not imposed. As we shall show, in this scheme, the unimodular theory has its own conservation equation obtained from the Bianchi identities. We explore the evolution of the homogeneous and isotropic expanding background and show that a viable cosmological scenario exists. Also, we consider scalar perturbations with particular attention given to the gauge issue. We show that contrary to the traditional unimodular theory where the synchronous and longitudinal (newtonian) gauge for cosmological perturbations are not permitted, if the conservation of the energy-momentum is relaxed the scalar perturbations in the synchronous condition survive and present a growing mode behavior. We study therefore a new cosmological scenario in which the dynamics of the universe transits from the radiative phase directly to a accelerated one but allowing thus for structure formation.

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