Focusing of geodesic congruences in an accelerated expanding Universe
arXiv:1208.4201 · doi:10.1088/1475-7516/2012/12/020
Abstract
We study the accelerated expansion of the Universe through its consequences on a congruence of geodesics. We make use of the Raychaudhuri equation which describes the evolution of the expansion rate for a congruence of timelike or null geodesics. In particular, we focus on the space-time geometry contribution to this equation. By straightforward calculation from the metric of a Robertson-Walker cosmological model, it follows that in an accelerated expanding Universe the space-time contribution to the Raychaudhuri equation is positive for the fundamental congruence, favoring a non-focusing of the congruence of geodesics. However, the accelerated expansion of the present Universe does not imply a tendency of the fundamental congruence to diverge. It is shown that this is in fact the case for certain congruences of timelike geodesics without vorticity. Therefore, the focusing of geodesics remains feasible in an accelerated expanding Universe. Furthermore, a negative contribution to the Raychaudhuri equation from space-time geometry which is usually interpreted as the manifestation of the attractive character of gravity is restored in an accelerated expanding Robertson-Walker space-time at high speeds.
11 pages, 2 figures. Final version changed to match published version in JCAP. References updated. Conclusions unchanged
References in corpus (28)
- Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
- Extra force in modified theories of gravity
- A f(R) gravity without cosmological constant
- Dark Matter from R^2-gravity
- The Raychaudhuri equations: a brief review
- On the evolution of density perturbations in f(R) theories of gravity
- A cosmic vector for dark energy
- 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
- Cosmological evolution in vector-tensor theories of 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
- Modified f(R) gravity from scalar-tensor theory and inhomogeneous EoS dark energy
- Is the CMB cold spot a gate to extra dimensions?
- Quantum Corrections to the Cosmological Evolution of Conformally Coupled Fields
- A Geometrical Approach to Strong Gravitational Lensing in f(R) Gravity
- Some model-independent phenomenological consequences of flexible brane worlds
- Raychaudhuri's equation and aspects of relativistic charged collapse
- Some generalizations of the Raychaudhuri equation
- Searching for CPT violation in top anti-top production
- Effect of Spin-Torsion Interaction on Raychaudhuri Equation
- Gravitino and Axino SuperWIMPs
- Quantum gravitational optics: Effective Raychaudhuri equation
- Revisiting a model-independent dark energy reconstruction method
- On a Raychaudhuri equation for hot gravitating fluids