Generalized effective description of loop quantum cosmology

TL;DR

This paper extends the effective description of loop quantum cosmology to include states with large dispersions, deriving generalized equations and Hamiltonian to better understand quantum geometries and their phenomenological implications.

Contribution

It introduces a generalized effective framework for LQC that accounts for states with large dispersions, broadening the scope of phenomenological studies.

Findings

Derived generalized effective Friedmann and Raychaudhuri equations.

Proposed a generalized effective Hamiltonian for broad quantum states.

Explored the relationship between dispersions in standard LQC and peaked states in modified theories.

Abstract

The effective description of loop quantum cosmology (LQC) has proved to be a convenient platform to study phenomenological implications of the quantum bounce that resolves the classical big-bang singularity. Originally, this description was derived using Gaussian quantum states with small dispersions. In this paper we present a generalization to incorporate states with large dispersions. Specifically, we derive the \emph{generalized} effective Friedmann and Raychaudhuri equations and propose a generalized effective Hamiltonian which are being used in an ongoing study of the phenomenological consequences of a broad class of quantum geometries. We also discuss an interesting interplay between the physics of states with larger dispersions in standard LQC, and of sharply peaked states in (hypothetical) LQC theories with larger area gap.