Abstract: Deviations from unitarity in the three-neutrino mixing canonical picture are expected in many physics scenarios beyond the Standard Model. The mixing of new heavy neutral leptons with the three light neutrinos would in principle modify the strength and flavour structure of charged-current and neutral-current interactions with matter. Non-unitarity effects would therefore have an impact on the neutrino decoupling processes in the early Universe and on the value of the effective number of neutrinos, Neff. We calculate the cosmological energy density in the form of radiation with a non-unitary neutrino mixing matrix, addressing the possible interplay between parameters. Highly accurate measurements of Neff from forthcoming cosmological observations can provide independent and complementary limits on the departures from unitarity. For completeness, we relate the scenario of small deviations from unitarity to non-standard neutrino interactions and compare the forecasted constraints to other existing limits in the literature.

Abstract: We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types of non-singular cosmologies, namely bouncing and asymptotically Minkowski solutions, from a perspective that makes their features more apparent. We study in detail the propagation of gravitational waves near these non-singular solutions and carefully discuss the origin and severity of the instabilities and strong coupling problems that appear. We also investigate the role of the adiabatic sound speed of the matter sector in the regularisation of the gravitational waves evolution. We extend our analysis to more general Born-Infeld inspired theories where analogous solutions are found. As a general conclusion, we obtain that the bouncing solutions are generally more prone to instabilities, while the asymptotically Minkowski solutions can be rendered stable, making them appealing models for the early universe.

Abstract: High-energy neutrinos could be produced in the interaction of charged cosmic rays with matter or radiation surrounding astrophysical sources. Even with the recent detection of extraterrestrial high-energy neutrinos by the IceCube experiment, no astrophysical neutrino source has yet been discovered. Transient sources, such as gamma-ray bursts, core-collapse supernovae, or active galactic nuclei are promising candidates. Multi-messenger programs offer a unique opportunity to detect these transient sources. By combining the information provided by the ANTARES neutrino telescope with information coming from other observatories, the probability of detecting a source is enhanced, allowing the possibility of identifying a neutrino progenitor from a single detected event. A method based on optical and X-ray follow-ups of high-energy neutrino alerts has been developed within the ANTARES collaboration. This method does not require any assumptions on the relation between neutrino and photon spectra other than time-correlation. This program, denoted as TAToO, triggers a network of robotic optical telescopes (TAROT and ROTSE) and the Swift-XRT with a delay of only a few seconds after a neutrino detection, and is therefore well-suited to search for fast transient sources. To identify an optical or Xray counterpart to a neutrino signal, the images provided by the follow-up observations are analysed with dedicated pipelines. A total of 42 alerts with optical and 7 alerts with Xray images taken with a maximum delay of 24 hours after the neutrino trigger have been analysed. No optical or X-ray counterparts associated to the neutrino triggers have been found, and upper limits on transient source magnitudes have been derived. The probability to reject the gamma-ray burst origin hypothesis has been computed for each alert.