Relativistic quantum geometry from a 5D geometrical vacuum: Gravitational waves from preinflation

Abstract

In this work we introduce Relativistic Quantum Geometry (RQG) on a Modern Kaluza-Klein theory by studying the boundary conditions on a extended Einstein-Hilbert action for a 5D vacuum defined on a 5D (background) Riemannian manifold. We introduce a connection which describes a displacement from the background manifold to the extended one, on which the 5D vacuum Einstein equations with cosmological constant included, describes the dynamics of the scalar field σ, which is responsible of describing the mentioned displacement and complies with a relativistic quantum algebra that depends on the relativistic observers. In our formalism the extra dimension is considered as space-like, and therefore is a noncompact one. After considering a static foliation on the extra dimension, we obtain the dynamics for the gravitational waves that propagates on a 4D (curved) background, defined on the 4D induced curved Riemannian manifold. Finally, an example, in which we study a pre-inflationary model of the early universe is developed. We obtain some constraints from Planck2018 observations.

Dark energy from a geometrical gauge scalar-tensor theory of gravity

“…Geometrical scalar fields have been even used in some theories of gravity with extra dimensions. Induced matter theory and relativistic quantum approaches in non-Riemannian geometries are good examples [32,33]. The interest in non-Riemannian geometries and in particular in the Weyl class of geometries has recently increased due to their proposal to solve, for example, the frame equivalence issue.…”

Quantum thermodynamics in the interior of a Reissner–Nordström black-hole

“…In this last framework have been studied several topics. Some of them are inflationary back reaction effects [19], charged and electromagnetic fields [20], geometric back-reaction in pre-inflationary scenarios [21,22] and to study the initial state of the universe [23], among others.…”

Quantum thermodynamics in the interior of a Reissner-Nordström black-hole

“…In this last framework have been studied several topics. Some of them are inflationary back reaction effects [15], charged and electromagnetic fields [16], geometric back-reaction in pre-inflationary scenarios [17,18] and to study the initial state of the universe [19], among others. In Sect.…”