Hermitian Gravity and Cosmology

Abstract

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.

23 pages, 7 eps figures

References in corpus (10)

• Superluminary Universe: A Possible Solution to the Initial Value Problem in Cosmology
• Solving the Flatness and Quasi-flatness Problems in Brans-Dicke Cosmologies with a Varying Light Speed
• Constraining Torsion with Gravity Probe B
• Reciprocal relativity of noninertial frames and the quaplectic group
• Instabilities in the nonsymmetric theory of gravitation
• The cosmology of the nonsymmetric theory of gravitation
• World-line Quantisation of a Reciprocally Invariant System
• Reciprocal relativity of noninertial frames: quantum mechanics
• Gravity in Complex Hermitian Space-Time
• Antisymmetric Metric Field as Dark Matter

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• Antiscreening in perturbative quantum gravity and resolving the Newtonian singularity
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• More About Branes on a General Magnetized Torus
• Predictions of the pseudo-complex theory of Gravity for EHT observations- II. Theory and predictions
• The seed of magnetic monopoles in the early inflationary universe from a 5D vacuum state
• Die Kerr-Metrik in pseudokomplexer Allgemeiner Relativitätstheorie
• Die Reissner-Nordström-Metrik in der Pseudokomplexen Allgemeinen Relativitätstheorie
• Constraining Gravitational and Cosmological Parameters with Astrophysical Data