Globally Stable Dark Energy in $F(R)$ Gravity

Abstract

$F(R)$ models for dark energy generally exhibit a weak curvature singularity, which can be cured by adding an $R^2$ term. This correction allows for a unified description of primordial and late-time accelerated expansions. However, most existing models struggle to achieve this, as they become unstable over certain negative ranges of the Ricci scalar, where either the first or second derivative of $F(R)$ turns negative. These instabilities may disrupt the post-inflationary evolution when the Ricci scalar oscillates about the vacuum state after the $R^2$ inflation. In this work, we introduce a new model-building to guarantee global stability, i.e., the first and second derivatives are positive for all real Ricci scalars. By extending the idea from Appleby and Battye, we demonstrate that viable models can be constructed by imposing a positive, bounded first derivative of $F(R)$ with a sigmoid shape. As examples, we first reformulate and generalize the original Appleby-Battye model. Then, we propose a new dark energy model, which successfully explains the acceleration of cosmic expansion and passes local gravity tests.

31 pages, 5 figures. Published in Chinese Physics C 50 (2026) 015106

References in corpus (56)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Planck 2018 results. X. Constraints on inflation
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space
• Chameleon Cosmology
• The Confrontation between General Relativity and Experiment
• Curvature Quintessence
• Disappearing cosmological constant in f(R) gravity
• Challenges for $\Lambda$CDM: An update
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Can modified gravity explain accelerated cosmic expansion?
• Conditions for the cosmological viability of f(R) dark energy models
• Unifying inflation with LambdaCDM epoch in modified f(R) gravity consistent with Solar System tests
• Are f(R) dark energy models cosmologically viable ?
• Do consistent $F(R)$ models mimic General Relativity plus $\Lambda$?
• Beyond $\Lambda$CDM: Problems, solutions, and the road ahead
• The Large Scale Structure of f(R) Gravity
• Detecting Dark Energy in Orbit -- the Cosmological Chameleon
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Tests of Chameleon Gravity
• Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday
• Solar system and equivalence principle constraints on f(R) gravity by chameleon approach
• Phantom crossing, equation-of-state singularities, and local gravity constraints in f(R) models
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Curing singularities in cosmological evolution of F(R) gravity
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• Theoretical Models of Dark Energy
• A Singularity Problem with f(R) Dark Energy
• Classifying and avoiding singularities in the alternative gravity dark energy models
• Aspects of cosmological expansion in F(R) gravity models
• Unification of Inflation with Dark Energy in $f(R)$ Gravity and Axion Dark Matter
• Can higher curvature corrections cure the singularity problem in f(R) gravity?
• Phantom boundary crossing and anomalous growth index of fluctuations in viable f(R) models of cosmic acceleration
• Generic feature of future crossing of phantom divide in viable $f(R)$ gravity models
• Future Oscillations around Phantom Divide in f(R) Gravity
• f(R) Gravity and its Cosmological Implications
• Cosmic History of Chameleonic Dark Matter in $F(R)$ Gravity
• Screened Scalar Fields in the Laboratory and the Solar System
• Phantom crossing in viable $f(R)$ theories
• Singularity phenomena in viable f(R) gravity
• Note on the equation of state of geometric dark-energy in f(R) gravity
• Big Bang Nucleosynthesis Hunts Chameleon Dark Matter
• The Nature of Dark Energy and Constraints on Its Hypothetical Constituents from Force Measurements
• Towards a unified interpretation of the early Universe in $R^2$-corrected dark energy model of $F(R)$ gravity
• Cosmological constraints on $R^2$-corrected Appleby-Battye model