General-Relativistic Path Effects and the Local Hubble Expansion

TL;DR

The work tackles how integrated general-relativistic path effects modify observed redshifts and distances in the nearby Universe, beyond standard kinematic corrections. It introduces a compact effective mapping $z_{eff}(z)=z-α f(z)$, where $f(0)=1$ and $f(z\gtrsim 0.1)\to 0$, to encode the leading Sachs redshift contributions from local tidal and shear fields without altering the background expansion. A key contribution is deriving a physically motivated suppression function from tidal-field correlations and exposing a clear multipole hierarchy (monopole and dipole dominate, higher orders suppressed) that yields testable predictions for low-$z$ surveys like LSST, DESI, and Taipan, including a bias in the locally inferred $H_0$ at the percent level. The framework preserves high-$z$ cosmology while offering concrete observational diagnostics to distinguish GR path effects from kinematic flows and calibration systematics, with potential implications for understanding nearby anisotropies and the distance ladder.

Abstract

We develop an effective mapping for low-redshift photon propagation that captures the leading path-dependent deviations from the standard FLRW redshift. Instead of relying on exact integrations of the Sachs optical equations, we introduce a minimal deformation of the redshift relation z_eff(z) = z minus alpha times f(z), where alpha is a small amplitude and f(z) suppresses the correction at z greater than approximately 0.1. This mapping does not modify the background expansion but encapsulates the leading contribution of inhomogeneous tidal fields to the accumulated Sachs redshift. We derive the implications for the luminosity distance, the low-redshift Hubble relation, and the directional dependence associated with local structure. The framework provides a clean general-relativistic description of path-dependent redshift drift and yields concrete predictions for forthcoming low-redshift surveys.