Giuseppe Fanizza

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.

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 Ω _GW ∼ k ^{n _eff 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 .

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 w.r.t. 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.

The paper deals with the design of a Digital Twin model of an energy harvesting cantilever beam for low frequency energy harvesting applications and specifically with a digital model matching simulations corresponding with Finite Element Method solutions in order to validate the model. The physical behavior is based on the main parameters to be investigated. The finite elements analysis is geometrically and parametrically carried out for a small PZT5A device of the orders of millimeters and is optimized to take into consideration the relationships between tip displacement, generated voltages and vibration gravitational forces for standard industrial applications in the acceleration range between 0.5 and 2 g. Then a procedure to integrate the Digital Twin into a design framework has been developed, including an artificial intelligence algorithm that supports the modelling of the real behavior of the device. The paper is devoted to help researchers involved in a Digital Twin adoption in the field of electronic design and of the physical characterization of low frequency energy harvesting devices exclusively using open-source tools.

We discuss a recently proposed fit of the 15-year data set obtained from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) in terms of a relic stochastic background of primordial gravitons, produced in the context of the string cosmology pre-big bang scenario. We show that such interpretation cannot be reconciled with a phenomenologically viable minimal version of such scenario, while it can be allowed if one considers an equally viable but generalised, non-minimal version of pre-big bang evolution. Maintaining the S-duality symmetry throughout the high-curvature string phase is possible although somewhat disfavoured. The implications of this non-minimal scenario for the power spectrum of curvature perturbations are also briefly discussed.

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.

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.