Cosmological Acceleration and Gravitational Collapse

Abstract

The acceleration parameter defined through the local volume expansion is negative for a pressureless, irrotational fluid with positive energy density. In the presence of inhomogeneities or anisotropies the volume expansion rate results from averaging over various directions. On the other hand, the observation of light from a certain source in the sky provides information on the expansion along the direction to that source. If there are preferred directions in the underlying geometry one can define several expansion parameters. We provide such definitions for the case of the Tolman-Bondi metric. We then examine the effect of a localized inhomogeneity on the surrounding cosmological fluid. Our framework is similar in spirit to the model of spherical collapse. For an observer in the vicinity of a central overdensity, the perceived local evolution is consistent with acceleration in the direction towards the center of the overdensity, and deceleration perpendicularly to it. A negative mass leads to deceleration along the radial direction, and acceleration perpendicularly to it. If the observer is located at the center of an overdensity the null geodesics are radial. The form of the luminosity distance as a function of the redshift is consistent with acceleration for a certain range of redshifts.

24 pages, 8 figures (uses iopart style/class files); new references are added; (v3) minor corrections to match published version in JCAP

References in corpus (4)

• Mimicking Dark Energy with Lemaitre-Tolman-Bondi Models: Weak Central Singularities and Critical Points
• Constraints on backreaction in dust universes
• Primordial inflation explains why the universe is accelerating today
• Accelerating Universe via Spatial Averaging

Cited by in corpus (11)

• Lemaitre-Tolman-Bondi model and accelerating expansion
• Accelerated expansion from structure formation
• CMB multipole measurements in the presence of foregrounds
• The supernova Hubble diagram for off-center observers in a spherically symmetric inhomogeneous universe
• Mapping Luminosity-Redshift Relationship to LTB Cosmology
• The Possibility of Cosmic Acceleration via Spatial Averaging in Lemaitre-Tolman-Bondi Models
• Description of our cosmological spacetime as a perturbed conformal Newtonian metric and implications for the backreaction proposal for the accelerating universe
• LTB universes as alternatives to dark energy: does positive averaged acceleration imply positive cosmic acceleration?
• Analytical Estimate of the Effect of Spherical Inhomogeneities on Luminosity Distance and Redshift
• Exploiting scale dependence in cosmological averaging
• Is the physics within the Solar system really understood?