arXiv subjects

Giuseppe Fanizza

Publications and source records attributed to Giuseppe Fanizza.

At least 19 recordsLinked to original sources

arXiv2026

Nonlinear Relativistic Effects on Cosmological Redshift Drift

Using a fully gauge-invariant approach, we compute for the first time in the literature relativistic effects on the redshift drift up to second order in cosmological perturbation theory. This is achieved by employing a set of light-cone coordinates that simplify the description of light propagation in an inhomogeneous and anisotropic universe. We show that redshift-space distortion occurs only as a second-order effect whereas, as known, it is not present among the linear perturbations. We then derive analytical expressions of the bispectrum for the leading-order perturbative contributions on sub-Hubble scales, providing some numerical evaluations. Our finding is that, at low redshift and for large momenta, the non-linearities in the bispectrum are enhanced more than the squared power spectrum.

astro-ph.CO↗

arXiv2025

Freeze-out and spectral running of primordial gravitational waves in viscous cosmology

We investigate the impact of shear viscosity on the propagation of primordial gravitational waves (pGW) after inflation. Without assuming a specific inflationary scenario we focus on the evolution of pGWs after they re-enter the horizon during a cosmological epoch characterized by the presence of shear viscosity. We show that shear viscosity introduces an additional damping term in the tensor equation, modifying both the transfer function and the energy density power spectrum. For a constant shear viscosity-to-Hubble ratio the transfer function acquires an extra red tilt, while a time-dependent viscosity leads to a running spectral index $\Omega_\text{GW}\sim k^{n_\text{eff}(k)}$ controlled by the time evolution of the mean free path of the viscous fluid. Our analysis provides a general framework to analytically quantify how shear viscosity can alter the primordial gravitational wave background in standard and non-standard post-inflationary scenarios. As a case study we evaluate the effect of viscosity of the electron-photon-baryon plasma, on both the transfer function and the normalized energy density, finding a $k$-dependent blue tilt due to gravitational wave freeze-out from the viscous phase. This effect corresponds to a fractional difference of order $10^{-3}$.

astro-ph.CO↗

arXiv2025

A Light-Cone Approach to Higher-Order Cosmological Observables

We develop a second-order cosmological perturbation theory on a background geometry expressed in terms of light-cone coordinates, extending the first-order analyses available in the literature. In particular, we investigate the gauge transformations of second-order perturbative quantities on the light-cone and establish their connection with standard perturbation theory. Through a consistent matching procedure, we identify the second-order gauge fixing that corresponds to the non-linear Geodesic Light-Cone gauge within standard perturbation theory, known as the Observational Synchronous Gauge. We then emphasize its conceptual similarities and differences wrt the standard Synchronous Gauge. Finally, within this new perturbative framework, and adopting a fully gauge-invariant approach, we compute the luminosity distance-redshift relation up to second order with anisotropic stress as seen by a free-falling observer. Remarkably, we show how divergences at the observer position can be eliminated in a completely model independent way. These results validate our perturbative framework and establish it as a novel formalism for evaluating cosmological observables at second order.

astro-ph.CO↗

arXiv2024

$δN$ formalism on the past light-cone

We apply the gradient expansion approximation to the light-cone gauge, obtaining a separate universe picture at non-linear order in perturbation theory within this framework. Thereafter, we use it to generalize the $δN$ formalism in terms of light-cone perturbations. As a consistency check, we demonstrate the conservation of the gauge invariant curvature perturbation on uniform density hypersurface $ζ$ at the completely non-linear level. The approach studied provides a self-consistent framework to connect at non-linear level quantities from the primordial universe, such as $ζ$, written in terms of the light-cone parameters, to late time observables.

gr-qc↗

arXiv2024

The skewness of the distance-redshift relation in $Λ$CDM

Starting from a recently proposed framework for the evaluation of the cosmological averages, we evaluate the higher-order moments for the distribution of a given observable. Then, we explicitly discuss the case of the Hubble-Lemaître diagram and evaluate its skewness at the leading order in the cosmological perturbative expansion of the gravitational potential. In particular, we focus on perturbations of the luminosity distance due to gravitational lensing. Finally, we discuss our findings in view of recent numerical relativistic simulations, confirming that the skewness in the Hubble-Lemaître diagram primarily originates from the late-time matter bispectrum, with other line-of-sight projection effects being sub-dominant.

astro-ph.CO↗

arXiv2023

Gauge invariance on the light-cone: curvature perturbations and radiative degrees of freedom

We derive the expressions on the observed light-cone for some relevant cosmological gauge invariant variables, such as the Mukhanov-Sasaki variable and $E$- and $B$- modes of the tensor perturbations. Since the structure of the light-cone does not reflect in a direct way the FLRW symmetries, we develop a formalism which is coordinate independent and classifies the perturbations according to their helicities. Even though we work with linear perturbations, our formalism can be readily extended to non-linear theory and put the basis to study the evolution of cosmological perturbations, since the early- until the the late- time Universe, directly along the observed light-cone.

gr-qc↗

arXiv2023

Dispersive effects in two- and three-dimensional peridynamics

In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation characterized by the nontrivial interactions between nonlocality and the regimes of low and high frequencies are studied and suitable numerical investigations are exposed.

math.AP↗

arXiv2023

Comment on "A fractal LTB model cannot explain Dark Energy''

We reply to the criticisms moved in [1] against our results presented in [2]. In particular, we show that our fractal model has none of the problems claimed in [1]. The latters can be addressed to the overlooked nonlinear behaviour of the Einstein's equations.

astro-ph.CO↗

arXiv2022

Bond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics

Peridynamic (PD) theories have gained widespread diffusion among various research areas, due to the ability of modeling discontinuities formation and evolution in materials. Bond-Based Peridynamics (BB-PD), notwithstanding some modeling limitations, is widely employed in numerical simulations, due to its easy implementation combined with physical intuitiveness and stability. In the present paper, several aspects of bond-based peridynamic models have been reviewed and investigated. A detailed description of peridynamics theory, applications and numerical models has been presented. Employed BB-PD integral kernels have been displayed, together with their differences and commonalities; then, some consequences of their mathematical structure have been discussed. The kinematic role of nonlocality, the relation between kernel structure and material impenetrability, and the role of PD kernel nonlinearity in cracks formation prediction have been critically analyzed and commented. Finally the idea of extending BB-PD to fluids is proposed and presented in the framework of fading memory material, drawing some perspectives for a deeper and more comprehensive understanding of the peridynamics in fluids.

math.NA↗

arXiv2022

Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics

We study the dispersive properties of a linear equation in one spatial dimension which is inspired by models in peridynamics. The interplay between nonlocality and dispersion is analyzed in detail through the study of the asymptotics at low and high frequencies, revealing new features ruling the wave propagation in continua where nonlocal characteristics must be taken into account. Global dispersive estimates and existence of conserved functionals are proved. A comparison between these new effects and the classical local {\it scenario} is deepened also through a numerical analysis.

math.AP↗

arXiv2022

Gravitational Wave luminosity distance in viscous cosmological models

We study the so-called Gravitational Wave luminosity distance-redshift relation $d_L^{\,GW}(z)$ during cosmological eras driven by non-perfect fluids. In particular, we show that the presence of a shear viscosity in the energy momentum tensor turns out to be the most relevant effect. Within this scenario, a constant shear viscosity imprints the gravitational wave propagation through a friction term $δ(z)$ with a uniquely given redshift dependence. This peculiar evolution predicts a specific shape for the ratio $d_{L}^{GW}/d_{L}^{EM}$ which tends to a constant value when the sources are at $z\gtrsim 1$, whereas scales linearly with the shear viscosity at lower redshifts, regardless of the value of $Ω_{m0}$. According to our final discussion, the predicted redshift dependence $δ(z)$ provided by a shear viscosity could be tested by upcoming surveys of multi-messenger sources against analogous scenarios provided by some widely studied theories of modified gravity.

gr-qc↗

arXiv2022

The gauge invariant cosmological Jacobi map from weak lensing at leading order

We compute the weak lensing Jacobi map at first order in perturbation theory and show that it is both, gauge invariant and symmetric. Linear perturbations therefore do not induce any rotation. However, vector and tensor perturbations do induce $B$-modes in the shear. We show that contrary to what is often claimed in the literature, the shear $B$-mode power spectrum is not fully determined by the rotation power spectrum. Also the $E$-mode shear power spectrum is not determined by the convergence power spectrum. While this difference is small for scalar perturbations, it becomes very relevant for tensor perturbations, i.e. gravitational waves.

astro-ph.CO↗

arXiv2021

Precision Cosmology and Hubble tension in the era of LSS surveys

We present a fully relativistic framework to evaluate the impact of stochastic inhomogeneities on the prediction of the Hubble-Lemaître diagram. In this regard, we relate the fluctuations of the luminosity distance-redshift relation in the Cosmic Concordance model to the intrinsic uncertainty associated to the estimation of cosmological parameters from high-redshift surveys (up to z = 4). Within this framework and according to the specific of forthcoming surveys as Euclid Deep Survey and LSST, we show that the cosmic variance associated with the measurement of the Hubble constant will not exceed 0.1 $\%$. Thanks to our results, we infer that deep surveys will provide an estimation of the the Hubble constant $H_0$ which will be more precise than the one obtained from local sources, at least in regard of the intrinsic uncertainty related to a stochastic distribution of inhomogeneities.

astro-ph.CO↗

arXiv2021

Cosmic variance of $H_0$ in light of forthcoming high-redshift surveys

Forthcoming surveys will extend the understanding of cosmological large scale structures up to unprecedented redshift. According to this perspective, we present a fully relativistic framework to evaluate the impact of stochastic inhomogeneities on the determination of the Hubble constant. To this aim, we work within linear perturbation theory and relate the fluctuations of the luminosity distance-redshift relation, in the Cosmic Concordance model, to the intrinsic uncertainty associated to the measurement of $H_0$ from high-redshift surveys ($0.15\le z\le3.85$). We first present the detailed derivation of the luminosity distance-redshift relation 2-point correlation function and then provide analytical results for all the involved relativistic effects, such as peculiar velocity, lensing, time delay and (integrated) Sachs-Wolfe, and their angular spectra. Hence, we apply our analytical results to the study of high-redshift Hubble diagram, according to what has been recently claimed in literature. Following the specific of Euclid Deep Survey and LSST, we conclude that the cosmic variance associated with the measurement of the Hubble constant is at most of 0.1 %. Our work extends the analysis already done in literature for closer sources, where only peculiar velocity has been taken into account. We then conclude that deep surveys will provide an estimation of the $H_0$ which will be more precise than the one obtained from local sources, at least in regard of the intrinsic uncertainty related to a stochastic distribution of inhomogeneities.

astro-ph.CO↗

arXiv2021

Qualitative aspects in nonlocal dynamics

In this paper we investigate, through numerical studies, the dynamical evolutions encoded in a linear one-dimensional nonlocal equation arising in peridynamcs. The different propagation regimes ranging from the hyperbolic to the dispersive, induced by the nonlocal feature of the equation, are carefully analyzed. The study of an initial value Riemann-like problem suggests the formation of a singularity.

nlin.PS↗

arXiv2021

Cutting out the cosmological middle man: General Relativity in the light-cone coordinates

Analytical computations in relativistic cosmology can be split into two sets: time evolution relating the initial conditions to the observer's light-cone and light propagation to obtain observables. Cosmological perturbation theory in the FLRW coordinates constitutes an efficient tool for the former task, but the latter is dramatically simpler in light-cone-adapted coordinates that trivialize the light rays towards the observer world-line. Here we point out that time evolution and observable reconstruction can be combined into a single computation that relates directly initial conditions to observables. This is possible if one works uniquely in such light-cone coordinates, thus completely bypassing the FLRW "middle-man" coordinates. We first present in detail these light-cone coordinates, extending and generalizing the presently available material in the literature, and construct a particularly convenient subset for cosmological perturbation theory. We then express the Einstein and energy-momentum conservation equations in these coordinates at the fully non-linear level. This is achieved through a careful 2+1+1 decomposition which leads to relatively compact expressions and provides good control over the geometrical interpretation of the involved quantities. Finally, we consider cosmological perturbation theory to linear order, paying attention to the remaining gauge symmetries and consistently obtaining gauge-invariant equations. Moreover, we show that it is possible to implement statistical homogeneity on stochastic fluctuations, despite the fact that the coordinate system privileges the observer world-line.

gr-qc↗

arXiv2020

The Cosmological Perturbation Theory on the Geodesic Light-Cone background

Inspired by the fully non-linear Geodesic Light-Cone (GLC) gauge, we consider its analogous set of coordinates which describes the unperturbed Universe. Given this starting point, we then build a cosmological perturbation theory on top of it, study the gauge transformation properties related to this new set of perturbations and show the connection with standard cosmological perturbation theory. In particular, we obtain which gauge in standard perturbation theory corresponds to the GLC gauge, and put in evidence how this is a useful alternative to the standard Synchronous Gauge. Moreover, we exploit several viable definitions for gauge invariant combinations. Among others, we build the gauge invariant variables such that their values equal the ones of linearized GLC gauge perturbations. This choice is motivated by two crucial properties of the GLC gauge: i) it admits simple expressions for light-like observables, e.g. redshift and angular distance, at fully non-linear level and ii) the GLC proper time coincides with the one of a free-falling observer. Thanks to the first property, exact expressions can then be easily expanded at linear order to obtain linear gauge invariant expression for the chosen observable. Moreover, the second feature naturally provides gauge invariant expressions for physical observables in terms of the time as measured by such free-falling observer. Finally, we explicitly show all these aspects for the case of the linearized angular distance-redshift relation.

gr-qc↗

arXiv2020

Regularity and energy transfer for a nonlinear beam equation

In this paper we study some key effects of a discontinuous forcing term in a fourth order wave equation on a bounded domain, modeling the adhesion of an elastic beam with a substrate through an elastic-breakable interaction. By using a spectral decomposition method we show that the main effects induced by the nonlinearity at the transition from attached to detached states can be traced in a loss of regularity of the solution and in a migration of the total energy through the scales.

math.AP↗