Building analytical three-field cosmological models

Abstract

A difficult task to deal with is the analytical treatment of models composed of three real scalar fields, as their equations of motion are in general coupled and hard to integrate. In order to overcome this problem we introduce a methodology to construct three-field models based on the so-called "extension method". The fundamental idea of the procedure is to combine three one-field systems in a non-trivial way, to construct an effective three scalar field model. An interesting scenario where the method can be implemented is with inflationary models, where the Einstein-Hilbert Lagrangian is coupled with the scalar field Lagrangian. We exemplify how a new model constructed from our method can lead to non-trivial behaviors for cosmological parameters.

Relativistic quantum oscillators in the global monopole spacetime

“…Let us restrict the motion of the relativistic spin-1 2 fermionic and scalar fields to a region where a hard-wall confining potential is present. The hard-wall potential has been studied in rotating effects on the scalar field [10], in the KGO under effects of linear topological defects [50,53], in noninertial effects on a nonrelativistic Dirac particle [65], in a Landau-Aharonov-Casher system [66], on a Dirac neutral particle in analogous way to a quantum dot [67], on the harmonic oscillator in an elastic medium with a spiral dislocation [68], on persistent currents for a moving neutral particle with no permanent electric dipole moment [69] and in a Landau-type quantization from a Lorentz symmetry violation background with crossed electric and magnetic fields [70].…”

“…Inspired by the DO [30], Bruce and Minning have proposed a relativistic quantum oscillator model for the scalar field which it was known in the literature as the KGO [31] that, in the nonrelativistic limit, is reduced to the oscillator described by the Schröndinger equation [45]. The KGO has been studied by a PT -symmetric Hamiltonian [46], in noncommutative space [47,48], in spacetime with cosmic string [49], in a spacetime with torsion [50,51], in a Kaluza-Klein theory [52], with noninertial effects [53], under effects of linear and Coulomb-type central potentials [54][55][56], in thermodynamic properties [57,58] and in possible scenarios of Lorentz symmetry violation [59,60].…”

Effects of the Cornell-Type Potential on a Position-Dependent Mass System in Kaluza-Klein Theory

“…Position-dependent mass quantum systems have been investigated in the relativistic context, for example, the pionic atom [30], in solution of the Dirac equation [31], in implications in atomic physics [32], in the quark-antiquark interaction [33], in effects of external fields on a two-dimensional Klein Gordon particle under pseudo-harmonic oscillator interaction [34], in noncommutative space [35], in the cosmic spacetime [36,37], in the global monopole spacetime [38], in the rotating cosmic string spacetime [39], in the spacetime with torsion [40][41][42], in possible scenarios of Lorentz symmetry violation [43][44][45], on the Klein-Gordon oscillator [46][47][48][49], on the Majorana fermion [50], in the Som-Raychaudhuri spacetime [51,52] and in Kaluza-Klein theory [53].…”

Effects of a Landau-Type Quantization Induced by the Lorentz Symmetry Violation on a Dirac Field

“…which means that the radial wave function vanishes at a fixed radius ρ 0 . The hard-wall potential has been studied in noninertial effects [50][51][52][53], in relativistic scalar particle systems in a spacetime with a spacelike dislocation [54], in a geometric approach to confining a Dirac neutral particle in analogous way to a quantum dot [55], in a Landau-Aharonov-Casher system [56] and on a harmonic oscillator in an elastic medium with a spiral dislocation [57]. Then, let us consider the particular case which α 2 s ≫ 1, while the ρ 0 and the parameter of the confluent hypergeometric function b are fixed and that the parameter of the confluent hypergeometric function a to be large.…”