Higher-Order Gravity, Finite Action, and a Safe Beginning for the Universe

TL;DR

This paper explores how quadratic gravity naturally favors homogeneous, isotropic, and accelerated expanding universes with finite action, providing a potential semi-classical explanation for the universe's initial conditions and inflation.

Contribution

It demonstrates that quadratic gravity eliminates inhomogeneous solutions with infinite action, favoring smooth, accelerating universes and suggesting a semi-classical origin for early universe conditions.

Findings

Homogeneous, isotropic solutions undergo accelerated expansion.

Quadratic gravity solutions have finite action, unlike general relativity.

The theory may be asymptotically safe at high energies.

Abstract

General relativity allows for inhomogeneous and anisotropic universes with finite action. By contrast, in quadratic gravity such solutions obtain infinite action and are thus eliminated. What remains are homogeneous and isotropic solutions undergoing accelerated expansion, thereby automatically inducing an early inflationary phase. In this manner, semi-classical consistency may explain some of the basic, coarse-grained features of the early universe. This includes suitable initial conditions for the second law of thermodynamics, in the spirit of the Weyl curvature hypothesis. We note that quadratic gravity is a renormalisable theory and may admit an asymptotically safe regime at high energies, rendering the theory trustworthy to high energies. We also comment on theories containing curvature terms up to infinite derivative order, and on the contrast with no-boundary initial conditions.