We study the phenomenological implications of the modular symmetry Γ(3) A 4 of lepton flavors facing recent experimental data of neutrino oscillations. The mass matrices of neutrinos and charged leptons are essentially given by fixing the expectation value of modulus τ , which is the only source of modular invariance breaking. We introduce no flavons in contrast with the conventional flavor models with A 4 symmetry. We classify our neutrino models along with the type I seesaw model, the Weinberg operator model and the Dirac neutrino model. In the normal hierarchy of neutrino masses, the seesaw model is available by taking account of recent experimental data of neutrino oscillations and the cosmological bound of sum of neutrino masses. The predicted sin 2 θ 23 is restricted to be larger than 0.54 and δ CP = ±(50 • -180 • ). Since the correlation of sin 2 θ 23 and δ CP is sharp, the prediction is testable in the future. It is remarkable that the effective mass m ee of the neutrinoless double beta decay is around 22 meV while the sum of neutrino masses is predicted to be 145 meV. On the other hand, for the inverted hierarchy of neutrino masses, only the Dirac neutrino model is consistent with the experimental data.

We consider domain walls in the Z 3 symmetric next-to-minimal supersymmetric standard model. The spontaneous Z 3 discrete symmetry breaking produces domain walls, and the stable domain walls are problematic. Thus, we assume the Z 3 symmetry is slightly but explicitly broken and the domain walls decay. Such a decay causes a large late-time entropy production. We study its cosmological implications on unwanted relics such as the moduli, gravitino, lightest superparticle, and axion.

Toward a test of parity violation in a gravity theory, possible effects of Chern-Simons (CS) gravity on an interferometer have been recently discussed. Continuing work initiated in an earlier publication [Okawara, Yamada and Asada, Phys. Rev. Lett. 109, 231101 (2012)], we study possible altitudinal and directional dependence of relativistic Sagnac effect in CS modified gravity.We compare the CS effects on Sagnac interferometers with the general relativistic Lense-Thirring (LT) effects. Numerical calculations show that the eastbound Sagnac interferometer might be preferred for testing CS separately, because LT effects on this interferometer cancel out. The size of the phase shift induced in the CS model might have an oscillatory dependence also on the altitude of the interferometer through the CS mass parameter m CS . Therefore, the international space station site as well as a ground-based experiment is also discussed.

We study an axion inflation model recently proposed within the framework of type IIB superstring theory, where we pay a particular attention to a sub-Planckian axion decay constant. Our axion potential can lead to the small field inflation with a small tensor-to-scalar ratio, and a typical reheating temperature can be as low as GeV.

We study general class of small-field axion inflations which are the mixture of polynomial and sinusoidal functions suggested by the natural and axion monodromy inflations. The axion decay constants leading to the successful axion inflations are severely constrained in order not to spoil the Big-Bang nucleosynthesis and overproduce the isocurvature perturbation originating from the QCD axion. We in turn find that the cosmologically favorable axion decay constants are typically of order the grand unification scale or the string scale which is consistent with the prediction of closed string