We have discussed a particular class of exact cosmological solutions of the 4-dimensional low energy string gravity in the string frame. In the vacuum without matter and the 2-form fields, the exact cosmological solutions always give monotonically sh
rinking universes if the dilaton field is not a constant. However, in the presence of the 2-form fields and/or the radiation-like fluid in the string frame, the exact cosmological solutions show a minimum size of the universe in the evolution, but with an initial cosmological curvature singularity in the string frame.
We have found that the conformally coupled induced gravity can be an infrared fixed point of induced gravity with Yukawa couplings with matter. The late time cosmology with a uniform mean matter distribution can be described by the conformally couple
d induced gravity, which has an emergent global conformal symmetry in the cosmic scale. Aiming to resolve the puzzles for the dark energy, we have obtained exact cosmological equations and determined the dark energy density, the matter density, and the jerk parameter in the present universe based on the recent observational cosmic expansion data for $a/H^{2}$.
We have found a mechanism which regulates the dark energy in our universe. With an emergent conformal symmetry, the dark energy density is regulated to the order of a conformal anomaly parameter in the conformally coupled gravity. In the late time co
smological evolution, we have obtained a set of exact cosmological equations which deviate from the Friedmann equations significantly. Based on the recent observational cosmic expansion data, it is shown that the dark energy density is about 1/4 of the matter density at present, which is quite smaller than determined by General Relativity. The jerk parameter at present is also determined as a definite value 0.47.
A cosmic potential which can relax the vacuum energy is proposed in a framework of scalar-tensor gravity. In the phase of the gravity scalar field around the evolution with an approximate emergent conformal symmetry, we have obtained a set of cosmolo
gical equations with the dark energy regulated to the order of a conformal anomaly parameter. Through a role of the cosmic potential, the vacuum energy which could be generated in matter Lagrangian does not contribute to the dark energy in the phase.
We use the evolution operator method to find the Schwinger pair-production rate at finite temperature in scalar and spinor QED by counting the vacuum production, the induced production and the stimulated annihilation from the initial ensemble. It is
shown that the pair-production rate for each state is factorized into the mean number at zero temperature and the initial thermal distribution for bosons and fermions.
We calculate the effective potential of a strong magnetic field induced by fermions with anomalous magnetic moments which couple to the electromagnetic field in the form of the Pauli interaction. For a uniform magnetic field, we find the explicit for
m of the effective potential. It is found that the non-vanishing imaginary part develops for a magnetic field stronger than a critical field and has a quartic form which is quite different from the exponential form of the Schwinger process. We also consider a linear magnetic field configuration as an example of inhomogeneous magnetic fields. We find that the imaginary part of the effective potential is nonzero even below the critical field and shows an exponentially decreasing behavior with respect to the inverse of the magnetic field gradient, which is the non-perturbative characteristics analogous to the Schwinger process. These results imply the instability of the strong magnetic field to produce fermion pairs as a purely magnetic effect. The possible applications to the astrophysical phenomena with strong magnetic field are also discussed.
