Impact of spatial curvature on forecast constraints from standard and differential redshift drift measurements

TL;DR

This paper investigates how relaxing the flat universe assumption affects the ability of redshift drift measurements to constrain cosmological parameters, highlighting the comparable sensitivity to curvature and matter.

Contribution

It analyzes the impact of spatial curvature on redshift drift constraints, including differential measurements, and compares sensitivities at different redshifts and universe geometries.

Findings

Redshift drift sensitivity to curvature is comparable to matter at low redshifts.

Sensitivity to curvature exceeds that to dark energy equation of state.

Asymmetry exists in sensitivity between open and closed universes with same |Ω_k|.

Abstract

The redshift drift of objects following the cosmological expansion is a unique model-independent probe of background cosmology, detectable by astrophysical facilities presently under construction. Previous forecasts for such measurements assume flat universes. We explore the impact of relaxing this assumption on the constraining power of the redshift drift, focusing on the two most promising routes for its measurement: the SKA at low redshifts, and the Golden Sample for the ELT's ANDES spectrograph at higher redshifts. We also discuss the cosmological sensitivity of possible differential redshift drift measurements, both on their own and, for the specific case of the Golden Sample, in combination with the standard method. Overall, we find that the sensitivity of the redshift drift to curvature is comparable to that of matter (especially at low redshifts) and higher than the sensitivity to the dark energy equation of state. We also show that the sensitivity of redshift drift measurements to these cosmological parameters is asymmetric with respect to the curvature parameter, being different for open and closed universes with the same absolute value of the curvature parameter $\Omega_k$.