Singular instantons in higher derivative theories

TL;DR

This paper investigates how adding quadratic and cubic curvature terms to gravitational theories affects the existence and nature of Hawking-Turok instanton solutions, which are relevant for open universe creation.

Contribution

It analyzes the impact of higher derivative terms, especially cubic ones, on instanton solutions using conformal transformations, revealing significant changes in solution constraints.

Findings

Cubic terms alter the parameter constraints for instanton solutions.

Higher derivative modifications can lead to both singular and non-singular instantons.

The analysis provides conditions for the existence of these instantons in extended theories.

Abstract

We study the Hawking-Turok (HT) instanton solutions which have been employed to describe the creation of an open inflationary universe, in the context of higher derivative theories. We consider the effects of adding quadratic and cubic terms of the forms $\alpha R^{2}$ and $\beta R^{3}$ to the gravitational action. Using a conformal transformation to convert the higher derivative theories into theories of self interacting scalar fields minimally coupled to Einstein gravity, we argue that the cubic term represents a generic perturbation of the polynomial type to the action and obtain the conditions on the parameters of these theories for the existence of singular and non-singular instanton solutions. We find that, relative to the quadratic case, there are significant changes in the nature of the constraints on the parameters for the existence of these instantons, once cubic (and higher order perturbations) are added to the action.