https://doi.org/10.1140/epjc/s10052-021-08917-z
Regular Article – Theoretical Physics
Isotropic exact solutions in 
gravity via Noether symmetries
1
Prince Mohammad Bin Fahd University, Khobar, Kingdom of Saudi Arabia
2
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan
c drmzubair@cuilahore.edu.pk, mzubairkk@gmail.com
Received:
3
December
2020
Accepted:
24
January
2021
Published online:
8
February
2021
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 
gravity, where R is the Ricci scalar and Y denotes the curvature invariant term defined by 
, while 
represents scalar field. For this purpose, we assume different general cases of generic function and explore its possible forms along with field potential 
by taking constant and variable coupling function of scalar field 
. 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.
© The Author(s) 2021
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