Direction and redshift drifts for general observers and their applications in cosmology

High precision astrometry now enables us to measure the time drift of astrophysical observables in real time, hence providing new ways to probe different cosmological models. This article presents a general derivation of the redshift and direction drifts for general observers. It is then applied to the standard cosmological framework of a Friedmann-Lemaître spacetime including all effects at first order in the cosmological perturbations, as well as in the class of spatially anisotropic universe models of the Bianchi I family. It shows that for a general observer, the direction drift splits into a parallax and an aberration drifts and order of magnitude estimates of these two components are provided. The multipolar decomposition of the redshift and aberration drifts is also derived and shows that the observer’s peculiar velocity contributes only as a dipole whereas the anisotropic shear contributes as a quadrupole.

Figure 1

General definitions for the two null geodesics between a general observer and source. The differences between the times contribute to the parallax part of the drift. Note that at first order in velocities $\delta {\tau }_{s,\mathrm{o}}=\delta {\tilde{t}}_{s,\mathrm{o}}$.

Figure 2

Behavior of the function $\frac{a_{\mathrm{o}}{\chi }_{s\mathrm{o}}}{D_{H_{\mathrm{o}}}}={\int }_0^z\frac{\mathrm{d}{z}^{\prime }}{E(z^{\prime })}$ as a function of $z$. Note that it saturates for large $z$. The vertical line corresponds to $z=1.48$.