The Raychaudhuri equation in homogeneous cosmologies

Abstract

In this work we address the issue of studying the conditions required to guarantee the Focusing Theorem for both null and timelike geodesic congruences by using the Raychaudhuri equation. In particular we study the case of Friedmann-Robertson-Walker as well as more general Bianchi Type I spacetimes. The fulfillment of the Focusing Theorem is mandatory in small scales since it accounts for the attractive character of gravity. However, the Focusing Theorem is not satisfied at cosmological scales due to the measured negative deceleration parameter. The study of the conditions needed for congruences convergence is not only relevant at the fundamental level but also to derive the viability conditions to be imposed on extended theories of gravity describing the different expansion regimes of the universe. We illustrate this idea for f(R) gravity theories.

13 pages, 12 figures. Minor changes. Version published in JCAP

References in corpus (39)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• A f(R) gravity without cosmological constant
• Dark Matter from R^2-gravity
• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• The Raychaudhuri equations: a brief review
• Screening Modifications of Gravity through Disformally Coupled Fields
• The evolution of density perturbations in f(R) gravity
• A cosmic vector for dark energy
• Reconstructing the Distortion Function for Nonlocal Cosmology
• On the $\Lambda$CDM Universe in $f(G)$ gravity
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Some remarks on the dynamical systems approach to fourth order gravity
• Power-law cosmic expansion in f(R) gravity models
• Photon spectra from WIMP annihilation
• Fitting formulae for photon spectra from WIMP annihilation
• Exotic Collider Signals from the Complete Phase Diagram of Minimal Universal Extra Dimensions
• The evolution of cosmological gravitational waves in f(R) gravity
• Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity
• Cosmological evolution in vector-tensor theories of gravity
• Cosmological dynamics of exponential gravity
• Resolving Cosmic Gamma Ray Anomalies with Dark Matter Decaying Now
• Finite Temperature Solitons in Non-Local Field Theories from p-Adic Strings
• Diffuse MeV Gamma-rays and Galactic 511 keV Line from Decaying WIMP Dark Matter
• Is the CMB cold spot a gate to extra dimensions?
• Focusing of geodesic congruences in an accelerated expanding Universe
• Compactifying the state space for alternative theories of gravity
• Quantum Corrections to the Cosmological Evolution of Conformally Coupled Fields
• Some model-independent phenomenological consequences of flexible brane worlds
• A dynamical system approach to higher order gravity
• Searching for CPT violation in top anti-top production
• On tidal forces in f(R) theories of gravity
• Gravitino and Axino SuperWIMPs
• On the collapse in fourth order gravities
• On Friedmann-Lema\^ıtre-Robertson-Walker cosmologies in non-standard gravity

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• Theoretical and observational constraints of viable f(R) theories of gravity
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• Strong energy condition and the repulsive character of f(R) gravity
• Preinflationary dynamics in loop quantum cosmology: Monodromy Potential
• Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss-Bonnet term
• Regular multihorizon black holes in $f(G)$ gravity with nonlinear electrodynamics
• Defocusing of Null Rays in Infinite Derivative Gravity
• Background dynamics of pre-inflationary scenario in Brans-Dicke loop quantum cosmology
• $f(\bar{R},L(X))$-gravity in the context of dark energy with power law expansion and energy conditions
• Focusing of world-lines in Weyl gravity
• Criteria for resolving the cosmological singularity in Infinite Derivative Gravity around expanding backgrounds
• Raychaudhuri Equation in an Anisotropic Universe with Anisotropic Sources