Hyperbolic symmetries, inflaton-phantom cosmology, and inflation

TL;DR

This paper explores hyperbolic symmetries in cosmology using a hyperbolic complex plane, unifying scalar fields, analyzing potentials, and examining topological defects, with implications for inflation and observational tests.

Contribution

It introduces a novel hyperbolic symmetry framework for scalar fields in cosmology, avoiding complex concepts and connecting to inflationary models and observational constraints.

Findings

Scalar potentials are bounded from below and exhibit spontaneous symmetry breaking.

Topological defects are restricted to those associated with discrete symmetries.

The nonrelativistic limit relates to a hyperbolic nonlinear Schrödinger equation.

Abstract

Using a hyperbolic complex plane, we study the realization of the underlying hyperbolic symmetry as an internal symmetry that enables the unification of scalar fields of cosmological and particle physics interest. Such an unification is achieved along the universal prescriptions used in physics, avoiding the use of concepts as Euclideanization, non-canonical Lagrangians and hidden structures, that have appeared in other approaches. The scalar potentials constructed within the present scheme are bounded from below, and the realization of the spontaneous symmetry breaking of the aforementioned noncompact symmetry is studied. The profiles of these potentials with exact/broken hyperbolic symmetry replicate qualitative aspects of those ones used in inflationary models, and then a detailed com\-pa\-ri\-son is made. Moreover, the homotopy constraints of the topology induced on the corresponding vacuum manifolds, restricts the existence of topological defects associated with continuous symmetries, allowing only those defects associated with discrete symmetries; the consistency of these results is contrasted with current observational tests from the LIGO/Virgo collaboration, and terrestrial experiments based on a synchronized network of atomic magnetometers. At the end, the nonre\-la\-tivistic limit of the model is identified with a hyperbolic version of the nonlinear Schr\"odinger equation.