Abstract
The pre-inflationary evolution of the universe describes the beginning of the expansion from a static initial state, such that the Hubble parameter is initially zero, but increases to an asymptotic constant value, in which it could achieve a de Sitter (inflationary) expansion. The expansion is driven by a background phantom field. The back-reaction effects at this moment should describe vacuum geometrical excitations, which are studied in detail in this work using relativistic quantum geometry.
Highlights
Geometrodynamics [8,9] is a picture of general relativity that studies the evolution of the spacetime geometry
The significant advantages of geometrodynamics usually have come at the expense of manifest local Lorentz symmetry [10]
Recently we have introduced a new method to study the scalar perturbations of the metric in a non-perturbative manner [14] by introducing relativistic quantum geometry (RQG)
Summary
Geometrodynamics [8,9] is a picture of general relativity that studies the evolution of the spacetime geometry. There are no non-linearities or highderivative problems in the dynamical description, so our formalism is much easier to apply to different physical systems like inflation [14], or pre-inflation This primordial epoch is of significant interest in cosmology and deserves a detailed study. It is supposed that during pre-inflation the universe began to expand from some Planck-size initial volume, to thereafter pass to an inflationary epoch In this framework RQG should be very useful when we try to study the evolution of the geometrical back-reaction effects given that we are dealing with Planck energetic scales, and back-reaction effects should be very intense at these scales. As was demonstrated in [15] the Einstein tensor can be written
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