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Mattia Scomparin

Publications and source records attributed to Mattia Scomparin.

12 recordsLinked to original sources
arXiv2026

Spectral separation of variables from equivalent Lagrangian systems

We investigate the dynamical equivalence of quadratic Lagrangians and its relation to separation of variables. We show that requiring two quadratic Lagrangians to generate the same Euler--Lagrange equations imposes a compatibility condition between the kinetic matrices and the potential. For constant symmetric kinetic matrices, this condition reduces to a commutation relation with the Hessian of the potential, yielding an orthogonal spectral decomposition of the configuration space. The equations of motion then decouple into independent subsystems: generically in block-separated form, and completely when the spectrum is simple. Applications include the Sawada--Kotera system and an $n$-dimensional extension of the H\'{e}non--Heiles model, where the classical integrable parameter regimes are recovered.

math-ph↗
arXiv2024

Cosmic structures in Ricci-inverse theories of gravity

We discuss a no-go theorem for the novel Ricci-inverse theory of modified gravity. By considering a static spherically symmetric matter distribution embedded within a de Sitter cosmology, we demonstrate that achieving a stable Sub-Horizon non-relativistic Weak-Field limit is unattainable in any of the models previously proposed to mitigate certain cosmological and inflationary instabilities. We explore potential strategies to address this challenge, suggesting a novel methodology for constructing stable models that adhere to the Sub-Horizon non-relativistic Weak-Field limit. These models are shown to maintain full consistency with the predictions of General Relativity at small scales.

astro-ph.CO↗
arXiv2024

Circumventing the Ricci-inverse no-go theorem with complexifiable singularities: a novel dark energy model

Ricci-inverse gravity is a new type of fourth-order gravity theory based on the anti-curvature tensor, that is, the inverse of the Ricci tensor. In this context, we introduce a novel method to circumvent the binding effects of a well-known no-go theorem for cosmic trajectories that cannot smoothly join a decelerated cosmic age with the current accelerated expansion of the universe. We therefore design a new class of Ricci-inverse theories whose cosmologies, without falling into no-go singularities, achieve the observed expansion as a stable attractor solution. This new perspective retrains Ricci-inverse cosmologies as viable dark energy models.

gr-qc↗
arXiv2023

First integrals of nonlinear differential equations from nonlocal constants

A new method to find first integrals of nonlinear differential equations in Jacobi-type form is presented. The basic idea of our approach is to use one-parameter perturbed motions to find well-conceived nonlocal constants that are conserved along solutions. By means of such nonlocal framework we derive a set of theorems that we apply to look for the first integrals of some relevant cases, where moreover a solution is obtained. Applications also include some equations of the Painlevé-Gambier classification.

nlin.SI↗
arXiv2022

Cadabra and Python algorithms in General Relativity and Cosmology I: Generalities

The aim of this work is to present a series of concrete examples which illustrate how the computer algebra system Cadabra can be used to manipulate expressions appearing in General Relativity and other gravitational theories. We highlight the way in which Cadabra's philosophy differs from other systems with related functionality. The use of various new built-in packages is discussed, and we show how such packages can also be created by end-users directly using the notebook interface. The current paper focuses on fairly generic applications in gravitational theories, including the use of differential forms, the derivation of field equations and the construction of their solutions. A follow-up paper discusses more specific applications related to the analysis of gravitational waves.

gr-qc↗
arXiv2022

Cadabra and Python algorithms in General Relativity and Cosmology II: Gravitational Waves

Computer Algebra Systems (CASs) like Cadabra Software play a prominent role in a wide range of research activities in physics and related fields. We show how Cadabra language is easily implemented in the well established Python programming framework, gaining excellent flexibility and customization to address the issue of tensor perturbations in General Relativity. We obtain a performing algorithm to decompose tensorial quantities up to any perturbative order of the metric. The features of our code are tested by discussing some concrete computational issues in research activities related to first/higher-order gravitational waves.

gr-qc↗
arXiv2022

Conserved currents from nonlocal constants in relativistic scalar field theories

Nonlocal constants are functions that are constant along motion but whose value depends on the past history of the motion itself. They are a powerful tool to provide first integrals in classical mechanics and, in this respect, a new approach to get nonlocal constants within the framework of lagrangian scalar field theory is introduced. We derive locally-conserved currents from them, and we prove the consistency of our results by recovering some standard Noetherian results. Applications include the real/complex nonlinear interacting theory and the real dissipative Klein-Gordon theory.

math-ph↗
arXiv2021

Nonlocal constants of motion in Lagrangian Dynamics of any order

We describe a recipe to generate "nonlocal" constants of motion for ODE Lagrangian systems. As a sample application, we recall a nonlocal constant of motion for dissipative mechanical systems, from which we can deduce global existence and estimates of solutions under fairly general assumptions. Then we review a generalization to Euler-Lagrange ODEs of order higher than two, leading to first integrals for the Pais-Uhlenbeck oscillator and other systems. Future developments may include adaptations of the theory to Euler-Lagrange PDEs.

math.DS↗
arXiv2019

Damping of cosmological tensor modes in Horndeski theories after GW170817

This paper investigates the propagation of cosmological gravitational waves interacting with free-streaming neutrinos within the context of Horndeski theories of gravity constrained by the detection of GW170817. We apply the theory of cosmological perturbations to explicitly derive the Einstein-Boltzmann equation for the damped propagation of first-order transverse traceless gravitational waves. In contrast to general relativity, we argue that modified gravity can give rise to non-vanishing free-streaming damping effects during the cosmological matter dominated era. We also provide an analytic formula for the main multipole order with which modified gravity and free-streaming neutrinos damp the variety of tensor correlation functions of the cosmic microwave background.

gr-qc↗
arXiv2017

Cosmic structures and gravitational waves in ghost-free scalar-tensor theories of gravity

We study cosmic structures in the quadratic Degenerate Higher Order Scalar Tensor (qDHOST) model, which has been proposed as the most general scalar-tensor theory (up to quadratic dependence on the covariant derivatives of the scalar field), which is not plagued by the presence of ghost instabilities. We then study a static, spherically symmetric object embedded in de Sitter space-time for the qDHOST model. This model exhibits breaking of the Vainshtein mechanism inside the cosmic structure and Schwarzschild-de Sitter space-time outside, where General Relativity (GR) can be recovered within the Vainshtein radius. We then look for the conditions on the parameters on the considered qDHOST scenario which ensure the validity of the Vainshtein screening mechanism inside the object and the fulfilment of the recent GW170817/GRB170817A constraint on the speed of propagation of gravitational waves. We find that these two constraints rule out the same set of parameters, corresponding to the Lagrangians that are quadratic in second-order derivatives of the scalar field, for the shift symmetric qDHOST.

gr-qc↗