The deceleration parameter in `tilted' universes: generalising the Friedmann background

TL;DR

This paper investigates how large-scale peculiar velocities affect local measurements of the universe's deceleration parameter, revealing that relative motion can significantly alter perceived cosmic acceleration within a certain critical scale.

Contribution

It generalizes previous models to all Friedmann backgrounds, demonstrating that peculiar velocities can influence local cosmological measurements across various universe models.

Findings

Local deceleration parameter sign can differ from the global value due to relative motion.

The transition scale varies between a few hundred to several hundred Mpc.

Effects are universal across different Friedmann backgrounds regardless of curvature or equation of state.

Abstract

Large-scale bulk peculiar motions introduce a characteristic length scale, inside which the local kinematics are dominated by peculiar-velocity perturbations rather than by the background Hubble expansion. Regions smaller than the aforementioned critical length, which typically varies between few hundred and several hundred Mpc, can be heavily "contaminated" by the observers' relative motion. For example, at the critical length -- hereafter referred to as the "transition scale", the sign of the locally measured deceleration parameter can change from positive to negative, while the surrounding universe is still decelerating globally. Overall, distant observers can assign very different values to their local deceleration parameters, entirely because of their relative motion. In practice, this suggests that information selected from regions inside and close to the transition scale hold only locally and they should not be readily extrapolated to the global universe. We show that this principle applies to essentially all Friedmann backgrounds, irrespective of their equation of state and spatial curvature. Put another way, the transition scale and the related effects are generic to linear peculiar-velocity perturbations. This study generalises previous work applied, primarily for reasons of mathematical simplicity, to a perturbed Einstein-de Sitter universe.