arXiv subjects

Massimiliano Rinaldi

Publications and source records attributed to Massimiliano Rinaldi.

At least 19 recordsLinked to original sources

arXiv2026

A Strong Cosmologically Coupled Mass Growth Solution in Linearized General Relativity

DESI Data Release 2 has heightened interest in cosmologically coupled black holes (CCBHs) as an explanation for accelerating late-time expansion, but known models for CCBHs grow too slowly to drive it. We construct at linear order a solution to General Relativity whose Hernandez-Misner-Sharp mass passively grows $\propto a^κ$ as the universe expands. The constant $κ$ enters all eigenvalues of the Weyl and stress-tensor operators, so growth is unambiguously physical in both free-field and material sectors. The solution is causal over spacetime relevant for stellar collapse compact objects. A cloud of energized vacuum emerges at $κ= 3$, complementing the $a^3$ scaling predicted elsewhere for the masses of energized vacuum black holes. This first step toward $κ\sim 3$ CCBH exact solutions enables observational tests with pulsar binaries.

gr-qc↗

arXiv2026

Evaporating cosmologically coupled black holes

Cosmologically coupled black holes (CCBHs), whose masses evolve in response to the cosmological expansion, have recently attracted significant theoretical and observational interest. Existing studies have treated CCBHs as purely classical objects, neglecting the effect of Hawking radiation (HR), which competes with the cosmological coupling (CC) mechanism. We take a first step towards studying evaporating CCBHs, adopting a quasi-adiabatic approximation in which the HR rate is evaluated at the instantaneous CCBH mass, and modeling the CC mechanism through the phenomenological scaling of the mass with the scale factor, $M \propto a^k$. We show that, depending on the coupling strength $k$, even late-time CC activation can significantly delay Hawking evaporation, or lead to asymptotic CC-dominated mass growth, with important implications. We set limits on the abundance of primordial CCBHs from $γ$-ray observations, finding limits which are weaker than their uncoupled counterparts, as CCBHs are kept farther from the endpoint of evaporation for a longer time. Unlike standard primordial black holes, the CCBH formation and present-day masses no longer approximately coincide, even for formation masses $M_{\text{form}} \gtrsim 10^{15}\,{\text{g}}$. Therefore, the same population of primordial CCBHs may be subject to evaporation limits through its past emission history, as well as to other limits (such as microlensing) through its present-day mass.

astro-ph.CO↗

arXiv2026

Black hole apparent horizons become comoving with the universe

It has been shown that static black hole event horizons cannot exist in time-dependent backgrounds without becoming naked singularities. In light of this, we are left with the question ``how does a black hole horizon evolve in an expanding universe?'' Here we offer a solution to this puzzle by showing in full generality that regular black hole apparent horizons tend to become comoving, thus confirming the necessity of a cosmological coupling and raising intriguing possibilities for the early growth of black holes.

gr-qc↗

arXiv2026

The unavoidable de Sitter fate of a scale-invariant Universe

We consider a very general scale-invariant scalar-tensor theory of gravity and its flat cosmological solutions. We show that any stable configuration with non-degenerate gravitational dynamics carries a non-vanishing cosmological constant, unless the quartic self-coupling of the scalar field vanishes. Since this condition is not protected against radiative corrections, a residual cosmological constant is expected as a generic and robust prediction of this class of theories. This result suggests that dark energy may be a natural consequence of an early scale-invariant phase of the Universe.

gr-qc↗

arXiv2026

Quintessence Dark Energy from non-perturbative Higgs-Yang-Mills mass gap

We discuss the equations that arise from a Higgs--Yang-Mills dark sector coupled to gravity on a flat Friedmann-Lemaitre-Robinson-Walker metric. We choose the simplest $SU(2)$ representation, which we show to be compatible with the Cosmological Principle. We devise a multiple time scale approach to solve the equations of motion through a hierarchy of the couplings, utilizing exact solutions in terms of Jacobi elliptic functions. This novel method implements the dynamical system approach used in the literature and can shed new light on the possibility that this model can describe dark energy.

astro-ph.CO↗

arXiv2025

Importance of being nonminimally coupled: Scalar Hawking radiation from regular black holes

In curved space-time, a scalar field $ϕ$ is generically expected to couple to curvature, via a coupling of the form $ξϕ^2R$. Yet in the study of Hawking emission from regular black holes (RBHs), where scalar fields are often introduced as simple probes of the geometry, and the Ricci scalar is generically non-zero, this non-minimal coupling is almost always ignored. We revisit this assumption by studying scalar Hawking emission from four representative RBHs (the Bardeen, Hayward, Simpson-Visser, and D'Ambrosio-Rovelli space-times), within two benchmark cases: the conformal case $ξ=1/6$, and a large negative value $ξ=-10^4$ motivated by Higgs inflation. We compute the graybody factors and emission spectra, showing that the latter can be either enhanced or suppressed, even by several orders of magnitude. A crucial role is played by the sign of the term $ξfR$, with $f(r)=-g_{tt}$ in Schwarzschild-like coordinates, as it determines whether the non-minimal coupling suppresses or enhances the geometric potential barrier. For the D'Ambrosio-Rovelli case with large negative $ξ$, the low-energy emission spectrum is enhanced by up to five orders of magnitude, since $ξfR<0$ throughout the space-time, leading to a deep potential well which broadens the transmissive window. The deviations we find can be particularly relevant in the case where primordial RBHs are dark matter candidates, given the impact of the non-minimal coupling on their evaporation history.

gr-qc↗

arXiv2025

Topological regular black holes without Cauchy horizon

Regular and spherically symmetric black holes that solve the singularity problems of the Schwarzschild solution are phenomenologically viable at large distance but usually suffer from the Cauchy horizon instability. To overcome this drawback, we extended the analysis to include hyperbolic and toroidal horizon topologies within the framework of static, topologically maximally symmetric spacetimes. We show that both hyperbolic and toroidal black holes can be constructed without Cauchy horizons and without curvature singularities, thereby avoiding the mass inflation instability. These solutions exhibit asymptotic flatness in a generalized quasi-Minkowskian sense. The phenomenological aspects of these solutions are also studied by examining their thermodynamical properties, the photon sphere, and the effective potentials, ensuring consistency with observable properties such as black hole shadows. Lastly, we investigate a reconstruction technique within a scalar-tensor gravity framework, illustrating how the discussed metrics can arise from well-defined scalar field dynamics. Our investigation presents a viable pathway for constructing physically realistic, regular black holes in both General Relativity and modified gravity, broadening the landscape of singularity-free spacetimes and offering models that may better reflect the nature of strong gravitational fields in astrophysical and cosmological settings.

gr-qc↗

arXiv2024

Implications of cosmologically coupled black holes for pulsar timing arrays

It has been argued that realistic models of (singularity-free) black holes (BHs) embedded within an expanding Universe are coupled to the large-scale cosmological dynamics, with striking consequences, including pure cosmological growth of BH masses. In this pilot study, we examine the consequences of this growth for the stochastic gravitational wave background (SGWB) produced by inspiraling supermassive cosmologically coupled BHs. We show that the predicted SGWB amplitude is enhanced relative to the standard uncoupled case, while maintaining the $Ω_{\text{gw}} \propto f^{2/3}$ frequency scaling of the spectral energy density. For the case where BH masses grow with scale factor as $M_{\text{bh}} \propto a^3$, thus contributing as a dark energy component to the cosmological dynamics, $Ω_{\text{gw}}$ can be enhanced by more than an order of magnitude. This has important consequences for the SGWB signal detected by pulsar timing arrays, whose measured amplitude is slightly larger than most theoretical predictions for the spectrum from inspiraling binary BHs, a discrepancy which can be alleviated by the cosmological mass growth mechanism.

gr-qc↗

arXiv2024

How the Schwarzschild-de Sitter horizons remain in thermal equilibrium at vastly different temperatures

The Tolman-Ehrenfest criterion of thermal equilibrium for a static fluid in a static spacetime is generalized to stationary heat conduction, in the approximation in which backreaction is negligible. Applying this generalized criterion to the Hawking radiation in the Schwarzschild-de Sitter geometry shows that the two horizons (which act as thermostats) remain in thermal equilibrium. The temperature of the radiation fluid interpolates between the temperatures at the horizons, with a static analytic profile that is given explicitly.

gr-qc↗

arXiv2024

Tracing cosmic stretch marks: probing scale invariance in the early Universe

This paper investigates a scale-invariant inflationary model characterized by a scalar field non-minimally coupled to gravity and a curvature term quadratic in the Ricci scalar. The model's dynamic is analyzed using a full numerical solution of the two-field system, going beyond previous analytical studies. We derive robust constraints on the model parameters using the latest Cosmic Microwave Background (CMB) data from Planck and BICEP/Keck. The study confirms that scale-invariance effectively reduces the system to single-field dynamics, eliminating entropy perturbations and ensuring stability. Key predictions include a minimal level of primordial gravitational waves with a tensor-to-scalar ratio r > 0.003, which upcoming CMB experiments are well-positioned to test. The model is compared to Starobinsky and $α$ - attractor inflation, with future observations of tensor modes offering a potential discriminator between them. Overall, the results suggest that scale-invariant inflation is a viable and competitive framework for explaining early universe dynamics and predicting cosmological observables.

hep-th↗

arXiv2024

Black hole event horizons are cosmologically coupled

It is shown that an exactly static and spherically symmetric black hole event horizon cannot be embedded in a time-dependent geometry. Forcing it to do so results in a naked null singularity at the would-be horizon. Therefore, since the universe is expanding, black holes must couple to the cosmological expansion, which was suggested as the growth mechanism for supermassive black holes in galaxies, with implications for the dark energy puzzle.

gr-qc↗

arXiv2024

Testing scale-invariant inflation against cosmological data

There is solid theoretical and observational motivation behind the idea of scale-invariance as a fundamental symmetry of Nature. We consider a recently proposed classically scale-invariant inflationary model, quadratic in curvature and featuring a scalar field non-minimally coupled to gravity. We go beyond earlier analytical studies, which showed that the model predicts inflationary observables in qualitative agreement with data, by solving the full two-field dynamics of the system -- this allows us to corroborate previous analytical findings and set robust constraints on the model's parameters using the latest Cosmic Microwave Background (CMB) data from Planck and BICEP/Keck. We demonstrate that scale-invariance constrains the two-field trajectory such that the effective dynamics are that of a single field, resulting in vanishing entropy perturbations and protecting the model from destabilization effects. We derive tight upper limits on the non-minimal coupling strength, excluding conformal coupling at high significance. By explicitly sampling over them, we demonstrate an overall insensitivity to initial conditions. We argue that the model \textit{predicts} a minimal level of primordial tensor modes set by $r \gtrsim 0.003$, well within the reach of next-generation CMB experiments. These will therefore provide a litmus test of scale-invariant inflation, and we comment on the possibility of distinguishing the model from Starobinsky and $α$-attractor inflation. Overall, we argue that scale-invariant inflation is in excellent health, and possesses features which make it an interesting benchmark for tests of inflation from future CMB data.

astro-ph.CO↗

arXiv2023

Stress-energy tensor correlations across regular black holes horizons

Hawking radiation can be regarded as a spontaneous and continuous creation of virtual particle-antiparticle pairs outside the event horizon of a black hole where strong tidal forces prevent the annihilation: the particle escapes to infinity contributing to the Hawking flux, while its corresponding antiparticle partner enters the event horizon and ultimately reaches the singularity. The aim of this paper is to investigate the energy density correlations between the Hawking particles and their partners across the event horizon of two models of non-singular black holes by calculating the two-point correlation function of the density operator of a massless scalar field. This analysis is motivated by the fact that in acoustic black holes particle-partner correlations are signalled by the presence of a peak in the equal time density-density correlator. Performing the calculation in a Schwarzschild black hole it was shown in [1] that the peak does not appear, mainly because of the singularity. It is then interesting to consider what happens when the singularity is not present. In the Hayward and Simpson-Visser non-singular black holes we show that the density-density correlator remains finite when the partner particle approaches the hypersurface that replaces the singularity, opening the possibility that partner-particle correlations can propagate towards other regions of spacetime instead of being lost in a singularity.

gr-qc↗

arXiv2023

Inflation and primordial gravitational waves in scale-invariant quadratic gravity with Higgs

In scale-invariant models of fundamental physics all mass scales are generated via spontaneous symmetry breaking. In this work, we study inflation in scale-invariant quadratic gravity, in which the Planck mass is generated classically by a scalar field, which evolves from an unstable fixed point to a stable one thus breaking scale-invariance. We investigate the dynamics by means of dynamical system standard techniques. By computing the spectral indices and comparing them with data, we put some constraints on the three dimensionless parameters of the theory. We show that certain regions of the parameter space will be within the range of future CMB missions like CMB-S4, LiteBIRD and STPol. The second half of the paper is dedicated to the analysis of inflationary first-order tensor perturbations and the calculation of the power spectrum of the gravitational waves. We comment on our results and compare them with the ones of mixed Starobinsky-Higgs inflation.

gr-qc↗

arXiv2023

Scale-invariant inflation

We examine a scalar-tensor model of gravity that is globally scale-invariant. When adapted to a spatially flat Robertson-Walker metric, the equations of motion describe a dynamical system that flows from an unstable de Sitter space to a stable one. We show that during this transition inflation can occur. Moreover, at the final fixed point, a mass scale naturally emerges that can be identified with the Planck mass. We compute the inflationary spectral indices and the tensor perturbation and we compare them with observations. We also study the possibility that primordial magnetic fields are generated during inflation.

gr-qc↗

arXiv2023

Inflationary helical magnetic fields with a sawtooth coupling

We study the generation of helical magnetic fields during inflation by considering a model which does not suffer from strong coupling or large back-reaction. Electromagnetic conformal invariance is broken only during inflation by coupling the gauge-invariants $F_{μν}F^{μν}$ and $F_{μν}{\tilde{F}}^{μν}$ to a time-dependent function $I$ with a sharp transition during inflation. The magnetic power spectrum is scale-invariant up to the transition and very blue-shifted after that. The subsequent evolution of the helical magnetic field is subjected to magneto-hydrodynamical processes, resulting in far larger coherence lengths than those occurring after adiabatic decay. Scale-invariant quadratic gravity is a suitable framework to test the model, providing a natural physical interpretation. We show that fully helical magnetic fields are generated with values in agreement with the lower bounds on fields in the Intergalactic Medium derived from blazar observations. This model holds even at large/intermediate energy scales of inflation, contrary to what has been found in previous works.

astro-ph.CO↗

arXiv2023

On the stability of scale-invariant black holes

Quadratic scale-invariant gravity non minimally coupled to a scalar field provides a competitive model for inflation, characterized by the transition from an unstable to a stable fixed point, both characterized by constant scalar field configurations. We provide a complementary analysis of the same model in the static, spherically symmetric setting, obtaining two Schwarzschild-de Sitter solutions, which corresponds to the two fixed points existing in the cosmological scenario. The stability of such solutions is thoroughly investigated from two different perspectives. First, we study the system at the classical level by the analysis of linear perturbations. In particular, we provide both analytical and numerical results for the late-time behavior of the perturbations, proving the stable and unstable character of the two solutions. Then we perform a semi-classical, non-linear analysis based on the Euclidean path integral formulation. By studying the difference between the Euclidean on-shell actions evaluated on both solutions, we prove that the unstable one has a meta-stable character and is spontaneously decaying into the stable fixed point which is always favoured.

gr-qc↗

arXiv2022

Vacuum decay in quadratic gravity

Metastable states decay at zero temperature through quantum tunneling at an exponentially small rate, which depends on the Coleman-de Luccia instanton, also known as bounce. In some theories, the bounce may not exist or its on-shell action may be ill-defined or infinite, thus hindering the vacuum decay process. In this paper, we test this possibility in modified theories of gravity interacting with a real scalar field. We consider an Einstein-Hilbert term with a non-minimally coupled scalar field and a quadratic Ricci scalar contribution. To tackle the problem we use a new analytic method, with which we prove that the scalar field on the bounce has a universal behaviour at large Euclidean radii, almost independently of the potential. Our main result is that the quadratic Ricci scalar prevents the decay, regardless of the other terms in the action.

gr-qc↗