We study the physics potential of the detection of the Cosmic Neutrino Background via neutrino capture on tritium, taking the proposed PTOLEMY experiment as a case study. With the projected energy resolution of ∆ ∼ 0.15 eV, the experiment will be sensitive to neutrino masses with degenerate spectrum, m 1 m 2 m 3 = m ν 0.1 eV. These neutrinos are non-relativistic today; detecting them would be a unique opportunity to probe this unexplored kinematical regime. The signature of neutrino capture is a peak in the electron spectrum that is displaced by 2m ν above the beta decay endpoint. The signal would exceed the background from beta decay if the energy resolution is ∆ 0.7 m ν . Interestingly, the total capture rate depends on the origin of the neutrino mass, being Γ D 4 and Γ M 8 events per year (for a 100 g tritium target) for unclustered Dirac and Majorana neutrinos, respectively. An enhancement of the rate of up to O(1) is expected due to gravitational clustering, with the unique potential to probe the local overdensity of neutrinos. Turning to more exotic neutrino physics, PTOLEMY could be sensitive to a lepton asymmetry, and reveal the eV-scale sterile neutrino that is favored by short baseline oscillation searches. The experiment would also be sensitive to a neutrino lifetime on the order of the age of the universe and break the degeneracy between neutrino mass and lifetime which affects existing bounds.

We show that maximally helical hypermagnetic fields produced during pseudoscalar inflation can generate the observed baryon asymmetry of the universe via the B + L anomaly in the Standard Model. We find that most of the parameter space of pseudoscalar inflation that explains the cosmological data leads to baryon overproduction, hence the models of natural inflation are severely constrained. We also point out a connection between the baryon number and topology of the relic magnetic fields. Both the magnitude and sign of magnetic helicity can be detected in future diffuse gamma ray data. This will be a smoking gun evidence for a link between inflation and the baryon asymmetry of the Universe.PACS numbers: 98.80.Cq, 12.15.-y.

Superstring theory and other supersymmetric theories predict the existence of relatively light, weakly interacting scalar particles, called moduli, with a universal form of coupling to matter. Such particles can be emitted from cusps of cosmic strings, where extremely large Lorentz factors are achieved momentarily. Highly boosted modulus bursts emanating from cusps subsequently decay into gluons, they generate parton cascades which in turn produce large numbers of pions and then neutrinos. Due to very large Lorentz factors, extremely high energy neutrinos, up to the Planck scale and above, are produced. For some model parameters, the predicted flux of neutrinos with energies 10 21 eV is observable by JEM-EUSO and by the future large radio detectors LOFAR and SKA.

Superconducting cosmic strings can give transient electromagnetic signatures that we argue are most evident at radio frequencies. We investigate the three different kinds of radio bursts from cusps, kinks, and kink-kink collisions on superconducting strings. We find that the event rate is dominated by kink bursts in a range of parameters that are of observational interest, and can be quite high (several a day at 1 Jy flux) for a canonical set of parameters. In the absence of events, the search for radio transients can place stringent constraints on superconducting cosmic strings.

The anomalous conversion of leptons into baryons during leptogenesis is shown to produce a right-handed helical magnetic field; in contrast, the magnetic field produced during electroweak baryogenesis is known to be left-handed. If the cosmological medium is turbulent, the magnetic field evolves to have a present day coherence scale ∼ 10 pc and field strength ∼ 10 −18 Gauss. This result is insensitive to the energy scale at which leptogenesis took place. Observations of the amplitude, coherence scale, and helicity of the intergalactic magnetic field promise to provide a powerful probe of physics beyond the Standard Model and the very early universe.