arXiv subjects

Oliver F. Piattella

Publications and source records attributed to Oliver F. Piattella.

At least 19 recordsLinked to original sources

arXiv2026

A nonlinear Newtonian approximation to General Relativity

We investigate a nonrelativistic approximation to general relativity that does not require the metric coefficients to be weak perturbations of the Minkowski metric. Instead, we assume a differential hierarchy in which the contributions to the curvature containing second derivatives of the metric dominate over those quadratic in its first derivatives, while the metric-dependent coefficients multiplying the retained terms are kept fully nonlinear. Since this separation is not covariant, we formulate the approximation in harmonic coordinates, where it corresponds to retaining the principal part of the reduced Einstein equations. We show that the truncated Einstein tensor satisfies the contracted Bianchi identities up to the order neglected in the derivative hierarchy, ensuring compatibility with energy--momentum conservation at the retained order. The standard Newtonian equations are recovered in the weak-field regime, whereas outside it the dynamics retains a nonlinear dependence on the lapse and spatial metric. In particular, null geodesics probe the spatial geometry at leading order, suggesting gravitational lensing as a natural setting in which observable departures from the standard weak-field description may arise. We illustrate the construction with a static spatially isotropic configuration and discuss the scope and limitations of the approximation.

gr-qc↗

arXiv2026

Lensing in the McVittie metric

We investigate the effect of the cosmological expansion on the bending of light due to an isolated point-like mass. We adopt McVittie metric as the model for the geometry of the lens. Assuming a constant Hubble factor we find an analytic expression involving the bending angle, which turns out to be unaffected by the cosmological expansion at the leading order.

astro-ph.CO↗

arXiv2026

Lecture Notes in Cosmology

The first version of these lecture notes is based on the hand-written notes I prepared for the cosmology course taught to graduate students of PPGFis and PPGCosmo at the Federal University of Espírito Santo (UFES), starting in 2014. The course covers topics ranging from the evidence for the expanding universe to the anisotropies of the Cosmic Microwave Background. The notes are also available on my personal webpage (https://www.oliverfpiattella.eu) and have been published by Springer. The second version extends and updates the material presented in the first version, and typographical errors and mistakes have also been corrected.

astro-ph.CO↗

arXiv2025

More on the relativistic images produced in gravitational lensing

We investigate the gravitational lensing properties and the formation of relativistic images associated with black holes modeled by the Reissner-Nordström and Kerr space-time geometries. In particular, we perform numerical computations of the deflection angles, image angular positions, magnification factors (including demagnification), and time delays between distinct images, and we systematically quantify the dependence of these observables on the electric charge and spin parameters of the black hole.

gr-qc↗

arXiv2025

Tilt in quadratic gravity II

We investigate a tilted fluid component on a Bianchi V geometry in the theories of General Relativity (GR) and Quadratic Gravity (QG). The main objective of this work is the study of how the properties of matter can modify the future evolution of the attractors and their consequences on the regions of initial conditions of the solutions. As is well known, QG contains the Ruzmaikina-Ruzmaikin (RR) solution. This solution describes the slow-roll regime of Starobinsky's inflationary model, which is currently the best one due to the excellent agreement with Cosmic Microwave Background Radiation (CMBR) data. In QG, we found universes that can be attracted to the RR solution or recollapse toward the isotropic singularity attractor. If the Equation of State (EoS) parameter is ultra-radiative w>1/3, the tilt variable increases both in RR and Milne for QG or GR, respectively. In both cases, the fluid expansion and acceleration diverge, while the vorticity initially increases and then decreases to zero.

gr-qc↗

arXiv2025

Non zero Coriolis field in Ehlers' Frame Theory

Ehlers' Frame Theory is a class of geometric theories parameterized by $λ:= 1/c^2$ and identical to the General Theory of Relativity for $λ\neq 0$. The limit $λ\to 0$ does not recover Newtonian gravity, as one might expect, but yields the so-called Newton-Cartan theory of gravity, which is characterized by a second gravitational field $\boldsymbolω$, called the Coriolis field. Such a field encodes at a non-relativistic level the dragging feature of general spacetimes, as we show explicitly for the case of the $(η,H)$ geometries. Taking advantage of the Coriolis field, we apply Ehlers' theory to an axially symmetric distribution of matter, mimicking, for example, a disc galaxy, and show how its dynamics might reproduce a flattish rotation curve. In the same setting, we further exploit the formal simplicity of Ehlers' formalism in addressing non-stationary cases, which are remarkably difficult to be treated in the General Theory of Relativity. We show that the time derivative of the Coriolis field gives rise to a tangential acceleration which allows to study a possible formation in time of the rotation curve's flattish feature.

gr-qc↗

arXiv2024

Bayesian analysis of a Unified Dark Matter model with transition: can it alleviate the $H_{0}$ tension?

We consider cosmological models in which Dark Matter (DM) and Dark Energy (DE) are described by a single component, dubbed Unified Dark Matter (UDM) models, in which the DE-like part can have an equation state $<-1$ at late times without violating the null energy condition. In this paper, we investigate whether this feature can relieve the Hubble tension. We perform a Bayesian analysis of the model using SNIa data from Pantheon, the CMB distance prior from Planck, and the prior on the absolute magnitude $M$ of SNIa from SH0ES. Using the prior, the data suggests a smooth transition taking place at redshifts $z_{\rm t} \simeq 2.85$, which provides a value $H_0=69.64\pm 0.88$ for the Hubble constant, slightly alleviating the tension by $\sim 1.5 σ$. Without it, we obtain $H_0 = 67.6^{+1.3}_{-0.82}$ and a transition happening at $z_t=1.36$. We also discuss the importance of using the prior on $M$ for constraining this model.

astro-ph.CO↗

arXiv2023

On Rastall gravity formulation as a $f(R,\mathcal{L}_m)$ and a $f(R,T)$ theory

Rastall introduced a stress-energy tensor whose divergence is proportional to the gradient of the Ricci scalar. This proposal leads to a change in the form of the field equations of General Relativity, but it preserves the number of degrees of freedom. Rastall's field equations can be either interpreted as GR with a redefined SET, or it can imply different physical consequences inside the matter sector. We investigate limits under which the Rastall field equations can be directly derived from an action, in particular from two $f(R)$-gravity extensions: $f(R,\mathcal L_m)$ and $f(R,T)$. We show that there are similarities between these theories, but the Rastall SET cannot be fully recovered from them, apart from certain particular cases here discussed. It is remarkable that a simple, covariant and invertible redefinition of the SET, as the one proposed by Rastall, is hard to be directly implemented in the action.

gr-qc↗

arXiv2022

Gravitational lensing in a universe with matter and a cosmological constant

We extend the results obtained in \cite{Piattella_2016, mcvittie_2015} and \cite{Park_2008} for gravitational lensing in the McVittie metric by including the effect of the transition from the matter-dominated epoch of the Universe to the $Λ$-dominated era. We derive a formula that agrees with the previous results for the McVittie metric at lowest order, and compare the lensing angle predictions obtained from the Schwarzschild approximation, the McVittie model and higher order corrections to the McVittie model. In doing this, we test if, beyond the correction from the accelerated expansion of the Universe, there is a need for including the matter content of the Universe in modeling lens systems at the redshifts observed in lens systems. We investigate if there is a need for a modification of the lens equation from these corrections, and if so, to which order and whether it is measurable. We find that while the effect is of the same order as the one calculated previously, there is no significant contribution to the bending angle, as the 1st order effect is already of order $\mathcal{O}(θ_O^4)$ in the observed angle.

astro-ph.CO↗

arXiv2022

Inflation with sterile scalar coupled to massive fermions and to gravity

In the recent paper [3] it was shown that the consistency of the quantum theory of a sterile scalar coupled to massive fermions requires the inclusion of odd-power terms in the potential of scalar self-interaction. One of the most important examples of a sterile scalar is the inflaton, that is typically a real scalar field which does not belong to representations of particle physics gauge groups, such as $SU(2)$. Here we explore the effects of the odd-power terms in the inflaton potential on main observables, such as the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$, in the case of a strong, non-minimal coupling of the inflaton to gravity.

hep-th↗

arXiv2022

Bianchi IX gravitational collapse of matter inhomogeneities

We investigate a model of gravitational collapse of matter inhomogeneities where the latter are modelled as Bianchi type IX (BIX) spacetimes. We found that this model contains, as limiting cases, both the standard spherical collapse model and the Zeldovich solution for a 1-dimensional perturbation. We study how these models are affected by small anisotropic perturbations within the BIX potential. For the spherical collapse case, we found that the model is equivalent to a closed FLRW Universe filled with matter and two perfect fluids representing the anisotropic contributions. From the linear evolution up to the turnaround, the anisotropies effectively shift the value of the FLRW spatial curvature, because the fluids have effective Equation of State (EoS) parameters $w \approx -1/3$. Then we estimate the impact of such anisotropies on the number density of haloes using the Press-Schechter formalism. If a fluid description of the anisotropies is still valid after virialization, the averaged over time EoS parameters are $w\approx 1/3$. Using this and demanding hydrostatic equilibrium, we find a relation between the mass $M$, the average radius $R$ and the pressure $p$ of the virialized final structure. When we consider perturbations of the Zeldovich solution, our qualitative analysis suggests that the so called \textit{pancakes} exhibit oscillatory behavior, as would be expected in the case of a vacuum BIX spacetime.

gr-qc↗

arXiv2020

Does the cosmological constant stay hidden?

We elaborate on the proposal of [Phys. Rev. Lett. 123 (2019) 13, 131302], about the possibility of hiding the cosmological constant in the complicated topology that one expects to exist at the Planck scale. We build a differential equation ruling the time evolution of $\langle K\rangle$, the spatial average of the expansion scalar. Supposing that the solution $\langle K\rangle = 0$ exists despite the presence of a large cosmological constant $Λ$, we show that such solution seems to be unstable.

gr-qc↗

arXiv2020

Rastall's theory of gravity: Spherically symmetric solutions and the stability problem

We study the stability of static, spherically symmetric solutions of Rastall's theory in the presence of a scalar field with respect to spherically symmetric perturbations. It is shown that the stability analysis is inconsistent in the sense that linear time-dependent perturbations cannot exist, and we can conclude that these solutions are stable. Possible reasons for this inconsistency are discussed.

gr-qc↗

arXiv2020

Transient weak gravity in scalar-tensor theories

Sub-horizon perturbations in scalar-tensor theories have been shown to grow generically faster than in uncoupled models due to a positive, additive Yukawa force. In such cases, the amount of clustering becomes larger than in the standard cosmological model, exacerbating the observed tension in the $σ_8$ parameter. Here we show instead that in some simple cases of conformally coupled dark energy one can obtain a transient regime of negative Yukawa force, without introducing ghosts or other instabilities.

gr-qc↗

arXiv2019

Neutron star masses in $R^{2}$-gravity

We address the issue of the existence of inequivalent definitions of gravitational mass in $R^{2}$-gravity. We present several definitions of gravitational mass, and discuss the formal relations between them. We then consider the concrete case of a static and spherically symmetric neutron star, and solve numerically the equations of motion for several values of the free parameter of the model. We compare the features of the mass-radius relations obtained for each definition of gravitational mass, and we comment on their dependence on the free parameter. We then argue that $R^{2}$-gravity is a valuable proxy to discuss the existence of inequivalent definitions of gravitational mass in a generic modified gravity theory, and present some comments on the general case.

gr-qc↗

arXiv2019

An Introduction to Particle Dark Matter

We review the features of Dark Matter as a particle, presenting some old and new instructive models, and looking for their physical implications in the early universe and in the process of structure formation. We also present a schematic of Dark Matter searches and introduce the most promising candidates to the role of Dark Matter particle.

hep-ph↗

arXiv2019

Generic slow-roll and non-gaussianity parameters in $f(R)$ theories

In this paper we establish \textit{formulae} for the inflationary slow-roll parameters $ε$, $η$ and $ζ$ as functions of the Ricci scalar $R$ for $f(R)$ theories of gravity. As examples, we present the analytic and numerical solutions of $ε$, $η$ and $ζ$ as functions of the number of e-folds $N$ in two important instances: for the Starobinsky model and for a $f(R)$ reconstruction of the $α$-Attractors. The highlight of our proposal is to rewrite the slow-roll parameters in terms of $f(R)$, which allows to find directly $n_{\rm s}$, $r$, $α_{\rm s}$ and $f^{\text{equil}}_{\text{NL}}$ as functions of $R$ itself. We obtain that both models indicate a small contribution to the non-Gaussianity parameters, which are in good agreement with current observational constraints.

gr-qc↗

arXiv2019

Cosmology and Newtonian limit in a model of gravity with nonlocally interacting metrics

We investigate the features of the cosmological expansion history described by a recent model of gravity characterised by two nonlocally interacting metrics. We perform a detailed analysis of the dynamical system formed by the field equations and we find no stable critical points at finite and infinite distance. Nonetheless, we show that even if the universe does not evolve towards a de Sitter attractor, the effective equation of state parameter $ω_{\rm eff}$ always tends to $-1$, independently from the value of the free parameter $m^2$, which characterises the nonlocality of the theory. We also address the behaviour of gravity on Solar System scales and the growth of small cosmological fluctuations on small scales, in the quasi-static approximation. We find a post-Newtonian $γ$ parameter, a slip parameter and an effective, normalised gravitational coupling different from unity. These differences all depend on $m^2$ and are negligible if one consider the cosmological solution by which $m^2 \sim H_0^2$.

gr-qc↗