Real-time cosmology

In recent years, improved astrometric and spectroscopic techniques have opened the possibility of measuring the temporal change of radial and transverse position of sources in the sky over relatively short time intervals. This has made at least conceivable to establish a novel research domain, which we dub “real-time cosmology”. We review for the first time most of the work already done in this field, analysing the theoretical framework as well as some foreseeable observational strategies and their capability to constrain models. We first focus on real-time measurements of the overall redshift drift and angular separation shift in distant sources, which allows the observer to trace the background cosmic expansion and large scale anisotropy, respectively. We then examine the possibility of employing the same kind of observations to probe peculiar and proper accelerations in clustered systems, and therefore their gravitational potential. The last two sections are devoted to the future change of the cosmic microwave background on “short” time scales, as well as to the temporal shift of the temperature anisotropy power spectrum and maps. We conclude revisiting in this context the usefulness of upcoming experiments (like CODEX and Gaia) for real-time observations.