Time drift of cosmological redshifts and its variance

The contribution of cosmological perturbations to the time drift of the cosmological redshift is derived. It is shown that the dominant correction arises from the local acceleration of both the emitter and the observer. The amplitude of this effect is estimated to be of the order of 1% of the drift signal at $z=2–4$, but can easily be lowered down to 0.1% by using many absorption lines and quasars.

Figure 1

Left: the time drift of the redshift as a function of the redshift of the source obtained from Eq. (1) for a $\Lambda \mathrm{CDM}$ model (solid line) and a model with a constant equation of state $w=-0.9$ for the dark energy (dashed line). Right: amplitude of the rms of the systematic errors ${\zeta }_{\dot{v}}$ due to cosmic acceleration effects. The contribution of ${\zeta }_O$ (dashed line) is subdominant compared to the one of ${\zeta }_E$ (dotted line). The solid lines represent the differences between a standard $\Lambda \mathrm{CDM}$ model and a cosmological model with either $w=-0.95$ (upper solid line) or $w=-0.98$ (lower solid line).

Figure 2

The coefficient $\alpha$ that enters in Eq. (13) as a function of the width of wavelengths, $\Delta \lambda$, on which the observations are average for several source redshifts, $\overline{z}=4$ (solid line), $\overline{z}=3$ (long dashed line), $\overline{z}=2$ (dashed line), and $\overline{z}=1$ (dotted line) for $\Lambda \mathrm{CDM}$ with $h=0.7$, ${\Omega }_{\mathrm{m}0}=0.3$, and ${\Omega }_{\Lambda 0}=0.7$.