Quantum Cosmology and Higher-Order Lagrangian Theories

TL;DR

This paper explores how adding a cubic Ricci scalar term to the Einstein-Hilbert action affects quantum cosmology, revealing that it may prevent inflation solutions unlike quadratic corrections, thus impacting early universe models.

Contribution

It introduces and analyzes the effects of a cubic Ricci scalar term in quantum cosmology, highlighting differences from quadratic theories and implications for inflation.

Findings

Cubic Ricci term acts as a more generic perturbation than quadratic corrections.

Under certain parameters, inflation may not occur with cubic terms.

Contrasts with $R^2$-theory in predicting inflationary epochs.

Abstract

In this paper the quantum cosmological consequences of introducing a term cubic in the Ricci curvature scalar $R$ into the Einstein--Hilbert action are investigated. It is argued that this term represents a more generic perturbation to the action than the quadratic correction usually considered. A qualitative argument suggests that there exists a region of parameter space in which neither the tunneling nor the no-boundary boundary conditions predict an epoch of inflation that can solve the horizon and flatness problems of the big bang model. This is in contrast to the $R^2$--theory.