Redshift drift in a universe with structure I: Lemaitre-Tolman-Bondi structures with arbitrary angle of entry of light

TL;DR

This paper analyzes redshift and position drifts in a universe with LTB structures, showing that Ricci and Weyl curvature dominate the signals, which can help probe the strong energy condition through cosmological measurements.

Contribution

It develops a formalism for calculating redshift and position drifts in arbitrary spacetimes and applies it to LTB structures with arbitrary light entry angles, simplifying the analysis of such signals.

Findings

Redshift drift is dominated by Ricci and Weyl curvature contributions.

Mean redshift drift can be approximated by a Ricci focusing term.

Redshift drift measurements can probe the strong energy condition.

Abstract

We consider the redshift drift and position drift associated with astrophysical sources in a formalism that is suitable for describing emitters and observers of light in an arbitrary spacetime geometry, while identifying emitters of a given null-geodesic bundle that arrives at the observer worldline. We then restrict the situation to the special case of a Lemaitre-Tolman-Bondi (LTB) geometrical structure, and solve for light rays propagating through the structure with arbitrary impact parameters, i.e., with arbitrary angles of entry into the LTB structure. The redshift drift signal emitted by comoving sources and viewed by a comoving observer turns out to be dominated by Ricci curvature and electric Weyl curvature contributions as integrated along the connecting light ray. This property simplifies the computations of the redshift drift signal tremendously, and we expect that the property extends to more complicated models including Swiss-cheese models. When considering several null rays with random impact parameters, the mean redshift drift signal is well approximated by a single Ricci focusing term. This suggests that the measurement of cosmological redshift drift can be used as a direct probe of the strong energy condition in a realistic universe where photons pass through many successive structures.