Scalar-field potential for viable models in $f(R)$ theory

Abstract

The $f(R)$ theory of gravity can be expressed as a scalar tensor theory with a scalar degree of freedom $\varphi$. By a conformal transformation, the action and its Gibbons-York-Hawking boundary term are written in the Einstein frame and the field equations are found. An effective potential is defined from part of the trace of the field equations in such a way that it can be calculated as an integral of a purely geometric term. This potential as well as the scalar potential are found, plotted and analyzed for some viable models of $f(R)$ and for two other proposed new, shown viable, models.

arXiv comment20 pages, 8 figures

References in corpus (38)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Dynamics of dark energy
• The Cosmological Constant and Dark Energy
• f(R) Theories Of Gravity
• Dark Energy and the Accelerating Universe
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Curvature Quintessence
• Disappearing cosmological constant in f(R) gravity
• Conditions for the cosmological viability of f(R) dark energy models
• The Large Scale Structure of f(R) Gravity
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• One-loop f(R) gravity in de Sitter universe
• COBE, Gravitational Waves, Inflation and Extended Inflation
• Dark energy cosmology from higher-order, string-inspired gravity and its reconstruction
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• Solar System tests DO rule out 1/R gravity
• A Singularity Problem with f(R) Dark Energy
• Testing Gravity Against Early Time Integrated Sachs-Wolfe Effect
• The matter power spectrum in f(R) gravity
• Cosmological Constraints on f(R) Acceleration Models
• Viability of f(R) Theories with Additional Powers of Curvature
• Constraining f(R) theories with the energy conditions
• Illusions of general relativity in Brans-Dicke gravity
• Rotational Velocity Curves in the Milky Way as a Test of Modified Gravity
• Modified gravity as an alternative for Lambda-CDM cosmology
• The Imaginary Starobinsky Model
• Constraints on f(R) Cosmology in the Palatini Formalism
• Cosmological constraints and comparison of viable $f(R)$ models
• Exacerbating the cosmological constant problem with interacting dark energy
• New Models of f(R) Theories of Gravity
• Reinterpretation of the Starobinsky model
• Acceleration of the Universe via f(R) Gravities and The Stability of Extra Dimensions
• How delicate are the $f(R)$ gravity models with disappearing cosmological constant?
• Equation of state of dark energy in f(R) gravity
• Thermodynamics of Black Holes in Brans-Dicke Gravity