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

Understand

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.