Gauge-Invariant Perturbations at a Quantum Gravity Bounce

We study the dynamics of gauge-invariant scalar perturbations in cosmological scenarios with a modified Friedmann equation, such as quantum gravity bouncing cosmologies. We work within a separate universe approximation which captures wavelengths larger than the cosmological horizon; this approximation has been successfully applied to loop quantum cosmology and group field theory. We consider two variables commonly used to characterise scalar perturbations: the curvature perturbation on uniform-density hypersurfaces zeta and the comoving curvature perturbation R. For standard cosmological models in general relativity as well as in loop quantum cosmology, these quantities are conserved and equal on super-horizon scales for adiabatic perturbations. Here we show that while these statements can be extended to a more general form of modified Friedmann equations similar to that of loop quantum cosmology, in other cases, such as the simplest group field theory bounce scenario, zeta is conserved across the bounce whereas R is not. We relate our results to approaches based on a second-order equation for a single perturbation variable, such as the Mukhanov-Sasaki equation.

Automated summary

We investigate the behavior of scalar perturbations in cosmological scenarios with modified Friedmann equations. We use a separate universe approximation to study wavelengths larger than the cosmological horizon and examine the conservation of curvature perturbation (zeta) and comoving curvature perturbation (R). While these quantities are conserved on super-horizon scales in standard cosmological models, we find that this is not always the case in scenarios like quantum gravity bouncing cosmologies. Our results provide insights for understanding the dynamics of scalar perturbations in modified cosmological scenarios.