A generalized linear Hubble law for an inhomogeneous barotropic Universe

TL;DR

This paper introduces a generalized linear Hubble law for inhomogeneous, spherically symmetric universes that accounts for anisotropic effects like acceleration and shear, potentially explaining large-scale cosmic flows.

Contribution

It proposes a new Hubble law incorporating anisotropic terms due to inhomogeneity, expanding the understanding of cosmic expansion beyond FLRW models.

Findings

The new Hubble law includes dipolar and quadrupolar terms.

It can explain large-scale matter flows without peculiar velocities.

The matter dipole aligns with the CBR dipole.

Abstract

In this work, I present a generalized linear Hubble law for a barotropic spherically symmetric inhomogeneous spacetime, which is in principle compatible with the acceleration of the cosmic expansion obtained as a result of high redshift Supernovae data. The new Hubble function, defined by this law, has two additional terms besides an expansion one, similar to the usual volume expansion one of the FLRW models, but now due to an angular expansion. The first additional term is dipolar and is a consequence of the existence of a kinematic acceleration of the observer, generated by a negative gradient of pressure or of mass-energy density. The second one is quadrupolar and due to the shear. Both additional terms are anisotropic for off-centre observers, because of to their dependence on a telescopic angle of observation. This generalized linear Hubble law could explain, in a cosmological setting, the observed large scale flow of matter, without to have recourse to peculiar velocity-type newtonian models. It is pointed out also, that the matter dipole direction should coincide with the CBR dipole one.