Schrödinger type formulation of FRW cosmology using scalar field and barotropic fluid within Rastall gravity

Abstract

The purpose of this paper is to uncover a connection between the dynamics associated with cosmological models and the radially symmetric nonlinear Schrödinger (NLS) equation. The link is made possible due to the central role played by a nonlinear, second-order ordinary differential equation (ODE) known as Milne–Ermakov–Pinney (EMP) equation. To this end, we describe the standard Friedmann–Robertson–Walker (FRW) cosmology of canonical scalar field (CSF) with two barotropic fluids (BFs) in terms of time-independent NLS type formulation within Rastall’s theory of gravity (RTG). We derive all cosmological dynamical quantities including scalar field [Formula: see text], scalar potential [Formula: see text], total Schrödinger energy [Formula: see text], wave function [Formula: see text] and NLS potential [Formula: see text], of EMP equation in terms of Schrödinger quantities. We consider bouncing and power-law models to find the exact solutions to these quantities in terms of cosmic time. It is found that RTG is a good candidate to discuss NLS type FRW formulation as the obtained results are in good compatibility with the standard theory of gravity.