Redshift Dipoles from Non-Geodesic Observer Congruences in Covariant Cosmology

TL;DR

This paper explores how non-geodesic observer congruences in covariant cosmology can produce redshift dipoles, offering a new way to test if observed anisotropies are due to structure kinematics or other effects.

Contribution

It introduces a covariant framework showing that non-geodesic observers induce a redshift dipole, which depends on their acceleration and can be used to distinguish different origins of anisotropies.

Findings

Non-geodesic congruences add a dipolar modulation to redshift.

This modulation depends on the observer's acceleration and its evolution.

The redshift dependence provides a test for the origin of observed dipoles.

Abstract

Recent analyses of large-scale structure and redshift surveys have reported significant dipolar anisotropies in the local Universe that are not straightforwardly attributable to a global kinematic boost. When interpreted within standard frameworks, these signals may correspond to coherent bulk flows that have been reported to exhibit tension with $\Lambda$CDM expectations. On the other hand, signals inferred from different astrophysical probes are not always consistent with the Cosmic Microwave Background (CMB) dipole, challenging the assumption of dipoles that are pure kinematical in origin. In an inhomogeneous universe, the identification of the Hubble frame with a geodesic matter flow is not guaranteed beyond the idealized FLRW limit, particularly once structure formation leads to a non-trivial distribution of velocities and gravitational fields. Within a fully covariant framework, we show that a non-geodesic observer congruence introduces an additional contribution to the propagation of redshift along the past light cone, proportional to the line-of-sight projection of the observer four-acceleration. This generates a dipolar modulation in the redshift itself, which propagates to any observable defined in redshift space. Unlike the standard kinematic dipole associated with a global Lorentz boost, this contribution arises from the kinematics of the observer congruence and depends on its evolution along the past light cone. As a result, it induces a dipolar modulation with a non-trivial redshift dependence. This behaviour provides a concrete observational test of whether the observed dipole is fully accounted for by large-scale structure kinematics or requires additional non-geodesic contributions.