Reconstruction of the singularity-free $f(\mathcal{R})$ gravity via Raychaudhuri equations

Abstract

We study the bounce cosmology to construct a singularity-free $f(\mathcal{R})$ model using the reconstruction technique. The formulation of the $f(\mathcal{R})$ model is based on the Raychaudhari equation, a key element employed in reconstructed models to eliminate singularities. We explore the feasibility of obtaining stable gravitational Lagrangians, adhering to the conditions $f_{\mathcal{R}}>0$ and $f_{\mathcal{RR}}>0$. Consequently, both models demonstrate stability, effectively avoiding the Dolgov-Kawasaki instability. Our assessment extends to testing the reconstructed model using energy conditions and the effective equation-of-state (EoS). Our findings indicate that the reconstructed super-bounce model facilitates the examination of a singularity-free accelerating universe for both phantom and non-phantom phases. However, in the case of the reconstructed oscillatory bounce model, two scenarios are considered with $\omega =-1/3$ and $\omega =-2/3$. While the model proves suitable for studying a singular-free accelerating universe in the $\omega =-1/3$ case, it fails to demonstrate such behavior under energy conditions for the $\omega =-2/3$ scenario. The reconstructed models accommodate early-time bouncing behavior and late-

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References in corpus (61)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Extended Theories of Gravity
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• The Case for a Positive Cosmological Lambda-term
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Curvature Quintessence
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters
• Covariant Galileon
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Cosmic Evolution in a Cyclic Universe
• Can modified gravity explain accelerated cosmic expansion?
• 1/R gravity and Scalar-Tensor Gravity
• Curvature quintessence matched with observational data
• Do consistent $F(R)$ models mimic General Relativity plus $\Lambda$?
• Reconciling dark energy models with f(R) theories
• Is there Supernova Evidence for Dark Energy Metamorphosis ?
• Quantum effects can render w<-1 on cosmological scales
• Approaches to Understanding Cosmic Acceleration
• Cosmological reconstruction of realistic modified F(R) gravities
• Inflationary cosmology in modified gravity theories
• Cosmological dynamics of R^n gravity
• Solar system and equivalence principle constraints on f(R) gravity by chameleon approach
• Cosmography of f(R) gravity
• Curing singularities in cosmological evolution of F(R) gravity
• Bounce cosmology from $F(R)$ gravity and $F(R)$ bigravity
• Designing Cyclic Universe Models
• Recent Advances on Inflation
• The Raychaudhuri equations: a brief review
• Energy conditions in modified gravity
• Bouncing cosmology in modified Gauss-Bonnet gravity
• Singular Bouncing Cosmology from Gauss-Bonnet Modified Gravity
• Inflationary Cosmology: Exploring the Universe from the Smallest to the Largest Scales
• Cosmological perturbations from multi-field inflation in generalized Einstein theories
• Generic instabilities of non-singular cosmologies in Horndeski theory: a no-go theorem
• A Cosmological Super-Bounce
• Cluster Cepheids with High Precision Gaia Parallaxes, Low Zeropoint Uncertainties, and Hubble Space Telescope Photometry
• Cosmological bouncing solutions in f(T,B) gravity
• The Pantheon+ Analysis: Evaluating Peculiar Velocity Corrections in Cosmological Analyses with Nearby Type Ia Supernovae
• Inflation and non-minimal scalar-curvature coupling in gravity and supergravity
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• A new approach to reconstruction methods in $f(R)$ gravity
• Large Scale Structure Constraints for a Class of f(R) Theories of Gravity
• Multiple measurements of quasars acing as standard probes: exploring the cosmic distance duality relation at higher redshift
• Bouncing cosmology in modified gravity with higher-order curvature terms
• Reconstruction of Slow-roll $F(R)$ Gravity Inflation from the Observational Indices
• Superbounce and Loop Quantum Cosmology Ekpyrosis from Modified Gravity
• A new approach to the analysis of the phase space of f(R)-gravity
• Correction to Lagrangian for Bouncing Cosmologies in $f(Q)$ Gravity
• Reconstruction of $f(R)$ gravity models for an accelerated universe using Raychaudhuri equation
• Bounce and cyclic cosmology in new gravitational scalar-tensor theories
• Solar System tests and chameleon effect in f (R) gravity
• Bouncing solutions in $f(T)$ gravity
• Intricacies of Cosmological bounce in polynomial metric $f(R)$ gravity for flat FLRW spacetime
• Raychaudhuri-based reconstruction of anisotropic Einstein-Maxwell equation in 1+3 covariant formalism of $f(R)$-gravity
• Transitioning from a bounce to $R^2$ inflation