Alternative effective mass functions in the modified Mukhanov-Sasaki equation of loop quantum cosmology

Abstract

Modifications to the Mukhanov-Sasaki equation in loop quantum cosmology (LQC) have been phenomenologically explored using polymerization of the connection and related variables in the classical expressions in order to capture the quantum gravity effects in cosmological perturbations which replace the classical big bang by a big bounce. Examples of this strategy include the dressed metric and the hybrid approaches whose inter-relationship at an effective level was demonstrated by the authors recently. In this manuscript, we propose a new family of the effective mass functions in the modified Mukhanov-Sasaki equation of LQC by investigating the polymerization of a particular form of the classical mass function in terms of variable $z_s$($=a\dot \phi/H$) which relates the Mukhanov-Sasaki variable with the comoving curvature perturbation. Using a generalized ansatz motivated by quantum gravity effects in the background dynamics we find alternative effective mass functions which are distinct from those used in the dressed metric and the hybrid approaches with differences originating from the non-commutativity of the evaluation of the Poisson brackets and the polymerization procedures. The new effective mass functions acquire four correction terms in the effective potential whose exact forms are closely tied up with the ansatz used for polymerizing the inverse Hubble rate. In contrast to earlier works, one of these correction terms can in principle produce sizable effects even when the bounce is kinetic dominated. Our investigation opens a new window to explore the phenomenological implications of a large family of effective mass functions in LQC which can potentially lead to significant departures from the dressed metric and the hybrid approaches in the bounce regime.