Emergence of dynamical dark energy from polynomial $f(R)$ theory in Palatini formalism

Abstract

We consider FRW cosmology in $f(R)=R+\gamma R^2+\delta R^3$ modified framework. The Palatini approach reduces its dynamics to the simple generalization of Friedmann equation. Thus we study the dynamics in two-dimensional phase space with some details. After reformulation of the model in the Einstein frame, it reduces to the FRW cosmological model with a homogeneous scalar field and vanishing kinetic energy term. This potential determines the running cosmological constant term as a function of the Ricci scalar. As a result we obtain the emergent dark energy parametrization from the covariant theory. We study also singularities of the model and demonstrate that in the Einstein frame some undesirable singularities disappear.

arXiv comment8 pages, 15 figures

References in corpus (21)

• The Cosmological Constant and Dark Energy
• f(R) Theories Of Gravity
• f(R) theories
• Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Covariant conservation of energy momentum in modified gravities
• Limit to General Relativity in f(R) theories of gravity
• Accelerated Cosmological Models in Ricci squared Gravity
• Solar System experiments do not yet veto modified gravity models
• Why the cosmological constant is small and positive
• Wormholes and nonsingular space-times in Palatini $f(R)$ gravity
• Physical non-equivalence of the Jordan and Einstein frames
• Nonsingular Black Holes in $f(R)$ Theories
• Correspondence of $F(R)$ Gravity Singularities in Jordan and Einstein Frames
• What is a singular black hole beyond General Relativity?
• Starobinsky cosmological model in Palatini formalism
• Cosmological implications of the transition from the false vacuum to the true vacuum state
• Tensor perturbations in a general class of Palatini theories
• Robustness of braneworld scenarios against tensorial perturbations
• Dynamical system approach to running $\Lambda$ cosmological models
• Extended Cosmologies

Cited by in corpus (22)

• Stellar structure models in modified theories of gravity: lessons and challenges
• Palatini inflation in models with an $R^2$ term
• Palatini formulation of $f(R,T)$ gravity theory, and its cosmological implications
• Rescuing Quartic and Natural Inflation in the Palatini Formalism
• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar
• Minimum main sequence mass in quadratic Palatini $f(\mathcal{R})$ gravity
• On stability of a neutron star system in Palatini gravity
• Stability criterion for white dwarfs in Palatini $f(R)$ gravity
• Polytropic stars in Palatini gravity
• Early evolutionary tracks of low-mass stellar objects in modified gravity
• Cooling process of brown dwarfs in Palatini f(R) gravity
• Lithium abundance is a gravitational model dependent quantity
• Metric-affine gravity effects on terrestrial (exo-)planets profiles
• White dwarf stars in modified gravity
• Jupiter and jovian (exo)-planets in Palatini $f(\bar{R})$ gravity
• Extended Cosmology in Palatini f(R)-theories
• The Palatini star: exact solutions of the modified Lane-Emden equation
• Giant planet formation in Palatini gravity
• Polynomial $f(R)$ Palatini cosmology -- dynamical system approach
• Cooling Process of White Dwarf Stars in Palatini $f(R)$ Gravity
• Simple cosmological model with inflation and late times acceleration
• Propagation and lensing of gravitational waves in Palatini $f(\hat{R})$ gravity