Noether Symmetries in $f(Q)-$Cosmology

TL;DR

This paper uses Noether symmetry analysis to identify conserved quantities in $f(Q)$-cosmology, revealing that only power-law models admit symmetries and deriving exact solutions for these cases.

Contribution

It applies Noether symmetry analysis to $f(Q)$-cosmology, identifying conditions for symmetries and deriving exact solutions for power-law models.

Findings

Only power-law $f(Q)$ functions admit Noether symmetries.

Exact solutions are derived for these symmetric models.

The analysis applies to FLRW background with various connections.

Abstract

We apply the Noether symmetry analysis in $f\left( Q\right)$-Cosmology to determine invariant functions and conservation laws for the cosmological field equations. For the FLRW background and the four families of connections, it is found that only power-law $f\left( Q\right)$ functions admit point Noether symmetries. Finally, exact and analytic solutions are derived using the invariant functions.