Giovanni Tambalo

We continue our series of papers where we study the quasinormal modes, and their excitation, of black holes in the simplest beyond general relativity model in which first-principle calculations are tractable: a nonrotating black hole in an effective-field-theory extension of general relativity with cubic-in-curvature terms. In this theory, the equivalence between the quasinormal mode spectra associated with metric perturbations of polar and axial parities (“isospectrality”) of the Schwarzschild black hole in general relativity no longer holds. How does this loss of isospectrality translate into the time-domain ringdown of gravitational waves? Given such a ringdown, can we identify the two “fundamental quasinormal modes” associated to the two metric-perturbation parities? We study these questions through a large suite of time-domain numerical simulations, by a prescription on how to relate the gauge-invariant master functions that describe metric perturbations of each parity with the gravitational polarizations. Under the assumptions made in our calculations, we find that it is in general difficult to identify either of the two fundamental modes from the time series, although finding evidence for a non-general-relativistic mode is possible sometimes. We discuss our results in light of our assumptions and speculate about what may occur when they are relaxed.

We investigate a qualitatively new regime of inflationary models with small and rapid oscillations in the potential — resonant non-Gaussianity. In contrast to the standard scenario, where most of the observable information is encoded in the power spectrum, in this regime the oscillatory signal predominantly appears in higher-order correlation functions with large n . This behavior emerges when the oscillation frequency ω exceeds the naive cutoff of the theory, 4 π f . However, as noted by Hook and Rattazzi [1], the actual cutoff is somewhat higher — though only logarithmically — when the amplitude of the oscillations is small. We identify a phenomenologically relevant window in which n -point functions with 3 ≲ n ≲ 9 are potentially observable. In this regime, the signal exhibits 350–1000 oscillations per decade in k .

We consider evolving, spatially flat isotropic and homogeneous (FLRW) cosmologies in ghost-free (dRGT) massive gravity. In this theory, no dynamical flat FLRW background exists if the reference metric is chosen to be Minkowski and the Stueckelberg fields are homogeneous. Relaxing the assumptions on the Stueckelberg profiles gives access to dynamical backgrounds. We propose a classification of the viable flat FLRW cosmological solutions of dRGT massive gravity. Instead of specifying an initial ansatz for the Stueckelberg fields ϕ ^a and the reference metric f _ab , we show that imposing homogeneity and isotropy on the square root tensor X ^μ _v = (√(g ^-1∂ϕ^a∂ϕ^b f _ab ))^μ _v leads to dynamical cosmological solutions, and we characterize their properties. These solutions become dynamical only when the Stueckelberg fields acquire a sufficiently inhomogeneous and/or anisotropic profile. We explore the consequences for the minimal model and the complete dRGT theory, and show that perturbations are strongly coupled, at the quadratic level, on these backgrounds.

Wave-optics phenomena in gravitational lensing occur when the signal’s wavelength is commensurate to the gravitational radius of the lens. Although potentially detectable in lensed gravitational waves, fast radio bursts and pulsars, accurate numerical predictions are challenging to compute. Here we present novel methods for wave-optics lensing that allow the treatment of general lenses. In addition to a general algorithm, specialized methods optimize symmetric lenses (arbitrary number of images) and generic lenses in the single-image regime. We also develop approximations for simple lenses (point-like and singular isothermal sphere) that drastically outperform known solutions without compromising accuracy. These algorithms are implemented in (o); an accurate, flexible, and fast code. o efficiently computes the frequency-dependent amplification factor for generic lens models and arbitrary impact parameters in O ( 1 ms ) to O ( 10 ms ) depending on the lens configuration and complexity. o is readily applicable to model lensing diffraction on gravitational-wave signals, offering new means to investigate the distribution of dark-matter and large-scale structure with signals from ground and space detectors.

Wave-optics phenomena in gravitational lensing occur when the signal's wavelength is commensurate to the gravitational radius of the lens. Although potentially detectable in lensed gravitational waves, fast radio bursts and pulsars, accurate numerical predictions are challenging to compute. Here we present novel methods for wave-optics lensing that allow the treatment of general lenses. In addition to a general algorithm, specialized methods optimize symmetric lenses (arbitrary number of images) and generic lenses in the single-image regime. We also develop approximations for simple lenses (point-like and singular isothermal sphere) that drastically outperform known solutions without compromising accuracy. These algorithms are implemented in Gravitational Lensing of Waves (GLoW): an accurate, flexible, and fast code. GLoW efficiently computes the frequency-dependent amplification factor for generic lens models and arbitrary impact parameters in O(1 ms) to O(10 ms) depending on the lens configuration and complexity. GLoW is readily applicable to model lensing diffraction on gravitational-wave signals, offering new means to investigate the distribution of dark-matter and large-scale structure with signals from ground and space detectors.

We study the statistics of scalar perturbations in models of inflation with small and rapid oscillations in the inflaton potential (resonant non-Gaussianity). We do so by deriving the wavefunction Ψ[ζ( x )] non-perturbatively in ζ, but at first order in the amplitude of the oscillations. The expression of the wavefunction of the universe (WFU) is explicit and does not require solving partial differential equations. One finds qualitative deviations from perturbation theory for |ζ| ≳ α ⁻², where α ≫ 1 is the number of oscillations per Hubble time. Notably, the WFU exhibits distinct behaviours for negative and positive values of ζ (troughs and peaks respectively). While corrections for ζ < 0 remain relatively small, of the order of the oscillation amplitude, positive ζ yields substantial effects, growing exponentially as e ^πα/2 in the limit of large ζ. This indicates that even minute oscillations give large effects on the tail of the distribution.

We revisit the classic problem of gravitational wave emission by a test particle plunging into a Schwarzschild black hole both in the frequency-domain Regge-Wheeler-Zerilli formalism and in the semirelativistic approximation. We use, and generalize, a transformation due to Nakamura, Sasaki, and Shibata to improve the falloff of the source term of the Zerilli function. The faster decay improves the numerical convergence of quantities of interest, such as the energy radiated at spatial infinity through gravitational waves. As a test of the method, we study the gravitational radiation produced by test particles that plunge into the black hole with impact parameters close to the threshold for scattering. We recover and expand upon previous results that were obtained using the Sasaki-Nakamura equation. In particular, we study the relative contributions to the total energy radiated due to waves of axial and polar parity, and uncover an universal behavior in the waveforms at late times. We complement our study with a semirelativistic analysis of the problem, and we compare the two approaches. The generalized Nakamura-Sasaki-Shibata transformation presented here is a simple and practical alternative for the analysis of gravitational-wave emission by unbound orbits in the Schwarzschild spacetime using the frequency-domain Regge-Wheeler-Zerilli formalism. Published by the American Physical Society 2024

Every signal propagating through the universe is at least weakly lensed by the intervening gravitational field. In some situations, wave-optics phenomena (diffraction, interference) can be observed as frequency-dependent modulations of the waveform of gravitational waves (GWs). We will denote these signatures as Wave-Optics Features (WOFs) and analyze them in detail. Our framework can efficiently and accurately compute WOF in the single-image regime, of which weak lensing is a limit. The phenomenology of WOF is rich and offers valuable information: the dense cusps of individual halos appear as peaks in Green's function for lensing. If resolved, these features probe the number, effective masses, spatial distribution and inner profiles of substructures. High signal-to-noise GW signals reveal WOFs well beyond the Einstein radius, leading to a fair probability of observation by upcoming detectors such as LISA. Potential applications of WOF include reconstruction of the lens' projected density, delensing standard sirens and inferring large-scale structure morphology and the halo mass function. Because WOF are sourced by light halos with negligible baryonic content, their detection (or lack thereof) holds promise to test dark matter scenarios.