f(R) Gravities, Killing Spinor Equations, "BPS" Domain Walls and Cosmology

TL;DR

This paper explores specific f(R) gravity models that admit Killing spinor equations, enabling the construction of exact solutions like domain walls and cosmologies, revealing new insights into their geometric and physical properties.

Contribution

It identifies conditions for f(R) gravities to admit Killing spinor equations and constructs explicit solutions including domain walls and cosmologies with varying scalar curvature.

Findings

Exact BPS domain wall solutions including Randall-Sundrum II and AdS wormholes

Cosmological solutions evolving from inflation to expansion with different cosmological constants

Discovery of two different f(R) gravities producing the same BPS solutions

Abstract

We derive the condition on f(R) gravities that admit Killing spinor equations and construct explicit such examples. The Killing spinor equations can be used to reduce the fourth-order differential equations of motion to the first order for both the domain wall and FLRW cosmological solutions. We obtain exact "BPS" domain walls that describe the smooth Randall-Sundrum II, AdS wormholes and the RG flow from IR to UV. We also obtain exact smooth cosmological solutions that describe the evolution from an inflationary starting point with a larger cosmological constant to an ever-expanding universe with a smaller cosmological constant. In addition, We find exact smooth solutions of pre-big bang models, bouncing or crunching universes. An important feature is that the scalar curvature R of all these metrics is varying rather than a constant. Another intriguing feature is that there are two different f(R) gravities that give rise to the same "BPS" solution. We also study linearized f(R) gravities in (A)dS vacua.