The peculiar Raychaudhuri equation

Abstract

Peculiar motions are commonplace in the universe. Our local group of galaxies, for example, drifts relative to the Hubble flow at about 600 km/sec. Such bulk flows are believed to fade away as we move on to progressively larger scales. Recently, however, there have been reports of peculiar motions larger and faster than typically expected. If these claims are correct, the role of peculiar flows in shaping the kinematics of our universe has been probably underestimated. Here, we use general relativistic techniques to analyse the average kinematics of large-scale bulk motions and compute the nonlinear Raychaudhuri equation of such flows. In doing so, we introduce two families of observers. One at rest with the Hubble expansion and another following the peculiar motion. We first derive the fully nonlinear expressions of the "peculiar" Raychaudhuri equation in both frames and identify a range of relative motion effects. Linearised around a Friedmann universe with pressureless dust, the full equations reduce to a simple relation with no explicit contribution from the matter component of the universe. Using cosmological perturbation theory, we obtain a scale-dependent formula, which also incorporates the effects of universe's inhomogeneity and anisotropy. When the latter are secondary, the peculiar Raychaudhuri equation can be solved analytically. Also, combining the resulting expression with data from recent peculiar-velocity surveys, we estimate the relative deceleration/acceleration rates of such bulk motions.

Typos corrected, references added. Published version

References in corpus (6)

• Relativistic cosmology and large-scale structure
• The Raychaudhuri equations: a brief review
• Geodesic deviation, Raychaudhuri equation, and tidal forces in modified gravity with an arbitrary curvature-matter coupling
• Anisotropy of Cosmic Acceleration
• Some generalizations of the Raychaudhuri equation
• Quantum gravitational optics: Effective Raychaudhuri equation

Cited by in corpus (18)

• Resembling dark energy and modified gravity with Finsler-Randers cosmology
• Observational constraints on the deceleration parameter in a tilted universe
• Is there really a Hubble tension?
• Do supernovae indicate an accelerating universe?
• The deceleration parameter in `tilted' Friedmann universes
• The Gibbs paradox, the Landauer principle and the irreversibility associated with tilted observers
• Tilted shear-free axially symmetric fluids
• Coarse-grained description of cosmic structure from Szekeres models
• Constraining the local variance of $H_0$ from directional analyses
• Relativistic approach to the kinematics of large-scale peculiar motions
• The theory of gravitation: A tale of many questions and few answers
• The Raychaudhuri equation for spinning test particles
• Dark Energy or local acceleration?
• Focusing of world-lines in Weyl gravity
• Anisotropy in the cosmic acceleration inferred from supernovae
• Gravitational convergence, shear deformation and rotation of magnetic forcelines
• Homothetic Congruences in General Relativity
• Expected redshift drift for tilted observers