Hermitian Gravity and Cosmology
In an attempt to generalize general relativity, we propose a new Hermitian theory of gravity. Space-time is generalized to space-time-momentum-energy and both the principles of general covariance and equivalence are extended. The theory is endowed with a Hermitian metric on a complex manifold. The Hermitian metric contains, apart from the symmetric metric, an anti-symmetric part, which describes dynamical torsion. The causality structure is changed in a way such that there is a minimal time for events to be in causal contact and a maximal radius for a non-local instantaneous causally related volume. The speed of light can exceed the conventional speed of light in non-inertial frames and accelerations are bounded. We have indications that the theory of Hermitian gravity yields general relativity at large scales and a theory equivalent to general relativity at very small scales, where the momenta and energies are very large. As an example, we study cosmology in Hermitian gravity, where matter is described by two scalar fields. While at late times Hermitian gravity reproduces the standard cosmological FLRW models, at early times it differs significantly: quite generically the Universe of Hermitian cosmology exhibits a bounce where a maximal expansion rate (Ricci curvature) is attained. Moreover, we prove that no cosmological constant is permitted at the classical level within our model of Hermitian cosmology.