Semi-Classical limit and quantum corrections in noncoincidence power-law $f(Q)$-Cosmology

TL;DR

This paper explores quantum cosmology within $f(Q)$ gravity, deriving the Wheeler-DeWitt equation for a power-law model and analyzing quantum corrections in the semi-classical limit.

Contribution

It derives the Wheeler-DeWitt equation in $f(Q)$ gravity with a non-coincidence gauge and investigates quantum corrections for a power-law model.

Findings

Wavefunction of the universe calculated for the power-law model

Quantum correction terms analyzed in semi-classical limit

Insights into quantum effects in $f(Q)$-cosmology

Abstract

Within the framework of symmetric teleparallel $f\left( Q\right) $-gravity for a connection defined in the non-coincidence gauge we derive the Wheeler-DeWitt equation of quantum cosmology. Because the gravitational field equation in $f\left( Q\right) $-gravity admits a minisuperspace description the Wheeler-DeWitt equation is a single inhomogeneous partial differential equations. We assume the power-law $f\left( Q\right) =f_{0}Q^{\mu}$ model and with the application of linear quantum observables we calculate the wavefunction of the universe. Finally, we investigate the effects of the quantum correction terms in the semi-classical limit.