Peculiar acceleration

It has been proposed recently to observe the change in cosmological redshift of distant galaxies or quasars with the next generation of large telescope and ultra-stable spectrographs (the so-called Sandage–Loeb test). Here we investigate the possibility of observing the change in peculiar velocity in nearby clusters and galaxies. This “peculiar acceleration” could help reconstructing the gravitational potential without assuming virialization. We show that the expected effect is of the same order of magnitude of the cosmological velocity shift. Finally, we discuss how to convert the theoretical predictions into quantities directly related to observations.