Abstract: The KM3NeT neutrino telescope is currently being deployed at two different sites in the Mediterranean Sea. First searches for astrophysical neutrinos have been performed using data taken with the partial detector configuration already in operation. The paper presents the results of two independent searches for neutrinos from compact binary mergers detected during the third observing run of the LIGO and Virgo gravitational wave interferometers. The first search looks for a global increase in the detector counting rates that could be associated with inverse beta decay events generated by MeV-scale electron anti -neutrinos. The second one focuses on upgoing track -like events mainly induced by muon (anti -)neutrinos in the GeV-TeV energy range. Both searches yield no significant excess for the sources in the gravitational wave catalogs. For each source, upper limits on the neutrino flux and on the total energy emitted in neutrinos in the respective energy ranges have been set. Stacking analyses of binary black hole mergers and neutron star -black hole mergers have also been performed to constrain the characteristic neutrino emission from these categories.

Abstract: This paper focuses on how the production and polarization of gravitational waves are affected by spontaneous Lorentz symmetry breaking, which is driven by a self-interacting vector field. Specifically, we examine the impact of a smooth quadratic potential and a non-minimal coupling, discussing the constraints and causality features of the linearized Einstein equation. To analyze the polarization states of a plane wave, we consider a fixed vacuum expectation value (VEV) of the vector field. Remarkably, we verify that a space-like background vector field modifies the polarization plane and introduces a longitudinal degree of freedom. In order to investigate the Lorentz violation effect on the quadrupole formula, we use the modified Green function. Finally, we show that the space-like component of the background field leads to a third-order time derivative of the quadrupole moment, and the bounds for the Lorentz-breaking coefficients are estimated as well.

Abstract: We discuss how tensor polarizations of gravitational waves can suffer Landau damping in the presence of velocity birefringence, when parity symmetry is explicitly broken. In particular, we analyze the role of the Nieh-Yan and Chern-Simons terms in modified theories of gravity, showing how the gravitational perturbation in collisionless media can be characterized by a subluminal phase velocity, circumventing the well-known results of General Relativity and allowing for the appearance of the kinematic damping. We investigate in detail the connection between the thermodynamic properties of the medium, such as temperature and mass of the particles interacting with the gravitational wave, and the parameters ruling the parity violating terms of the models. In this respect, we outline how the dispersion relations can give rise in each model to different regions of the wavenumber space, where the phase velocity is subluminal, superluminal or does not exist. Quantitative estimates on the considered models indicate that the phenomenon of Landau damping is not detectable given the sensitivity of present-day instruments.

Abstract: In the context of the metric-affine Chern-Simons gravity endowed with projective invariance, we derive analytical solutions for torsion and nonmetricity in the homogeneous and isotropic cosmological case, described by a flat Friedmann-Robertson-Walker metric. We discuss in some details the general properties of the cosmological solutions in the presence of a perfect fluid, such as the dynamical stability and the emergence of big bounce points, and we examine the structure of some specific solutions reproducing de Sitter and power law behaviours for the scale factor. Then, we focus on first-order perturbations in the de Sitter scenario, and we study the propagation of gravitational waves in the adiabatic limit, looking at tensor and scalar polarizations. In particular, we find that metric tensor modes couple to torsion tensor components, leading to the appearance, as in the metric version of Chern-Simons gravity, of birefringence, characterized by different dispersion relations for the left and right circularized polarization states. As a result, the purely tensor part of torsion propagates like a wave, while nonmetricity decouples and behaves like a harmonic oscillator. Finally, we discuss scalar modes, outlining as they decay exponentially in time and do not propagate.

Abstract: We use the latest constraints on the population of stellar origin binary black holes (SOBBH) from LIGO/Virgo/KAGRA (LVK) observations, to estimate the stochastic gravi-tational wave background (SGWB) they generate in the frequency band of LISA. In order to account for the faint and distant binaries, which contribute the most to the SGWB, we extend the merger rate at high redshift assuming that it tracks the star formation rate. We adopt different methods to compute the SGWB signal: we perform an analytical evaluation, we use Monte Carlo sums over the SOBBH population realisations, and we account for the role of the detector by simulating LISA data and iteratively removing the resolvable signals until only the confusion noise is left. The last method allows the extraction of both the expected SGWB and the number of resolvable SOBBHs. Since the latter are few for signal-to-noise ratio thresholds larger than five, we confirm that the spectral shape of the SGWB in the LISA band agrees with the analytical prediction of a single power law. We infer the probability dis-tribution of the SGWB amplitude from the LVK GWTC-3 posterior of the binary population model: at the reference frequency of 0.003 Hz it has an interquartile range of h(2 Omega)GW(f = 3 x 10(-3) Hz) is an element of [5.65, 11.5] x 10(-13), in agreement with most previous estimates. We then perform a MC analysis to assess LISA's capability to detect and characterise this signal. Ac-counting for both the instrumental noise and the galactic binaries foreground, with four years of data, LISA will be able to detect the SOBBH SGWB with percent accuracy, narrowing down the uncertainty on the amplitude by one order of magnitude with respect to the range of possible amplitudes inferred from the population model. A measurement of this signal by LISA will help to break the degeneracy among some of the population parameters, and pro-vide interesting constraints, in particular on the redshift evolution of the SOBBH merger rate.