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

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.

37 pages, discussion on gravity trapping in RSII modified, typos corrected, further comments and references added; version to appear in JHEP

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• Braneworld in $f(T)$ Gravity Theory with Noncanonical Scalar Matter Field
• Tensor perturbations of Palatini $f(\mathcal{R})$-branes
• Localization of Gravitino Field on $f(R)$ Thick Branes
• Gravitational resonances on $f(R)$-brane
• Stable Palatini $f(\mathcal{R})$ braneworld
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• Hybrid metric-Palatini brane system
• Smooth braneworld in $6$-dimensional asymptotically AdS spacetime
• Fundamental energy scale of the thick brane in mimetic gravity
• Stability of braneworlds with non-minimally coupled multi-scalar fields
• Gravity and Matters on a pure geometric thick polynomial $f(R)$ brane
• Effective action of a self-interacting scalar field on brane
• f(R) Theories of Supergravities and Pseudo-supergravities
• Localization mechanism of $q-$form field on the brane-world by coupling with gravity
• Vacuum $f(R)$ thick brane solution with a Gaussian warp function