Higher Powers in Gravitation

Abstract

We consider the Friedmann-Robertson-Walker cosmologies of theories of gravity that generalise the Einstein-Hilbert action by replacing the Ricci scalar, R, with some function, f(R). The general asymptotic behaviour of these cosmologies is found, at both early and late times, and the effects of adding higher and lower powers of R to the Einstein-Hilbert action is investigated. The assumption that the highest powers of R should dominate the Universe's early history, and that the lowest powers should dominate its future is found to be inaccurate. The behaviour of the general solution is complicated, and while it can be the case that single powers of R dominate the dynamics at late times, it can be either the higher or lower powers that do so. It is also shown that it is often the lowest powers of R that dominate at early times, when approach to a bounce or a Tolman solution are generic possibilities. Various examples are considered, and both vacuum and perfect fluid solutions investigated.

30 pages, 9 figures

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Cited by in corpus (19)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• f(R) theories
• Dynamical systems applied to cosmology: dark energy and modified gravity
• Initial and final de Sitter universes from modified $f(R)$ gravity
• Dynamics of f(R)-cosmologies containing Einstein static models
• Neutrino coupling to cosmological background: A review on gravitational Baryo/Leptogenesis
• Cosmological dynamics in f(R) gravity
• On The Existence Of Anisotropic Cosmological Models In Higher-Order Theories Of Gravity
• Finite Action Principle Revisited
• Effects of modified theories of gravity on neutrino pair annihilation energy deposition near neutron stars
• Implications of non-analytical f(R) gravity at Solar-System scales
• Neutrino spin oscillations in conformally gravity coupling models and quintessence surrounding a black hole
• Cosmological evolution of thermal relic particles in $f(R)$ gravity
• Neutrino pair annihilation ($\nu \bar{\nu }\to e^{-}{e}^{+}$) in the presence of quintessence surrounding a black hole
• Consequences of f(R)-theories of gravity on gravitational leptogenesis
• Constraints on a $f(R)$ gravity dark energy model with early scaling evolution
• A radiation-like era before inflation
• A class of simple bouncing and late-time accelerating cosmologies in f(R) gravity