Abstract
The present article investigates the existence of Noether and Noether gauge symmetries of flat Friedman–Robertson–Walker universe model with perfect fluid matter ingredients in a generalized scalar field formulation namely f(R,Y,phi ) gravity, where R is the Ricci scalar and Y denotes the curvature invariant term defined by Y=R_{alpha beta }R^{alpha beta }, while phi represents scalar field. For this purpose, we assume different general cases of generic f(R,Y,phi ) function and explore its possible forms along with field potential V(phi ) by taking constant and variable coupling function of scalar field omega (phi ). In each case, we find non-trivial symmetry generator and its related first integrals of motion (conserved quantities). It is seen that due to complexity of the resulting system of Lagrange dynamical equations, it is difficult to find exact cosmological solutions except for few simple cases. It is found that in each case, the existence of Noether symmetries leads to power law form of scalar field potential and different new types of generic function. For the acquired exact solutions, we discuss the cosmology generated by these solutions graphically and discuss their physical significance which favors the accelerated expanding eras of cosmic evolution.
Highlights
Baryon acoustic oscillation surveys etc. are some interesting examples of such astronomical experiments whose observational data sets illustrate this phenomena of cosmic expansion [1,2,3,4,5,6,7]
The possible motive of this phenomena has been considered as a hidden strange nature of energy which is seen as a dominating component in the cosmos matter structure and is refereed as dark ingredient or dark energy (DE) [8,9]
It is argued that the extension of Einstein’s gravitational framework for accommodating DE by the inclusion of extra degrees of freedom is more acceptable on cosmological landscape as compared to modified matter proposals where only the energy-momentum source is modified by adding dark ingredients as extra terms
Summary
In the context of differential equations and their exact solutions, one of the most intriguing and simple techniques considered by the researchers is the use of Noether and Noether gauge symmetries. On replacing the values of derivatives, it can be checked that only I1 is non-zero and is given by I1 = −2a3m2φ It can be solved for scale factor if one pick the power law form of scalar field φ = φ0aα and we obtain a(t) = 3. The scale factor is in power law form and its graph is provided in left panel of Fig. 11 In this case, the deceleration parameter is find to be q = 2 representing Zel’dovich universe model (stiff matter). The first integrals can be simplified by substituting the values of derivatives but the resulting equations are quite complicated which can not be solved analytically
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