Eur. Phys. J. Plus (2020) 135: 529
https://doi.org/10.1140/epjp/s13360-020-00513-6

Regular Article

Hyperbolic symmetries, inflaton–phantom cosmology, and inflation

¹ Instituto de Física, Universidad Autónoma de Puebla, Apartado postal J-48, 72570, Puebla, Puebla, Mexico
² Universidad de las Américas Puebla, Ex-hda Sta. Catarina Mártir, C.P. 72810, San Andrés Cholula, Puebla, Mexico

^* e-mail: aescalan@ifuap.buap.mx

Received: 20 February 2020
Accepted: 5 June 2020
Published online: 27 June 2020

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 such 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 non-compact 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 comparison is made. Moreover, the homotopy constraints of the topology induced on the corresponding vacuum manifolds restrict 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 non-relativistic limit of the model is identified with a hyperbolic version of the nonlinear Schrödinger equation.