Power-Law Bounces in $f(R)$ Gravity: Analysis of the Ekpyrosis and Accelerating Regimes

Abstract

We investigate the dynamics of the Friedmann-Lemaître-Robertson-Walker spacetime within the framework of $f(R)$ gravity using a compact, model-independent dynamical systems approach. By assuming a power-law scale factor, we explore ekpyrotic and accelerating solutions to address the big bang singularity. Our analysis demonstrates that a cosmological bounce, characterized by a transition from contraction to expansion, possibly avoids the singularity without directly using the Raychaudhuri equation, unlike previous approaches using specific $f(R)\simeq R^n$ forms. We identify a key fixed point in the phase space corresponding to the bounce, supported by perturbation analysis and qualitative description of trajectories in the phase space. The results suggest that $f(R)$ gravity provides a robust framework for non-singular cosmologies.

arXiv commentv3: Corrected minor typos and removed an unused table from the appendix

References in corpus (26)

• f(R) Theories Of Gravity
• f(R) theories
• Disappearing cosmological constant in f(R) gravity
• Cosmic Evolution in a Cyclic Universe
• Dynamical systems applied to cosmology: dark energy and modified gravity
• New Ekpyrotic Cosmology
• Singularity Theorems and Their Consequences
• Cosmography of f(R) gravity
• Bounce cosmology from $F(R)$ gravity and $F(R)$ bigravity
• Cosmology with a stiff matter era
• On the theory and applications of modern cosmography
• Homogeneous cosmologies with cosmological constant
• Generalized Galileons: instabilities of bouncing and Genesis cosmologies and modified Genesis
• Bouncing Cosmology made simple
• Some remarks on the dynamical systems approach to fourth order gravity
• Small-Field and Scale-Free: Inflation and Ekpyrosis at their Extremes
• Towards the Raychaudhuri Equation Beyond General Relativity
• Reheating after S-Brane Ekpyrosis
• A model independent approach to the study of $f(R)$ cosmologies with expansion histories close to $\Lambda$CDM
• Closed Trapped Surfaces in Cosmology
• A critical appraisal of the singularity theorems
• Can $f(R)$ gravity isotropize a pre-bounce contracting universe?
• A note on the dynamical system formulations in $f(R)$ gravity
• A model-independent compact dynamical system formulation for exploring bounce and cyclic cosmological evolutions in $f(R)$ gravity
• Consistent Cosmic Bubble Embeddings
• Cosmological Singularity and Power-Law Solutions in Modified Gravity