Redshift drift exploration for interacting dark energy
  By detecting redshift drift in the spectra of Lyman-$\alpha$ forest of
distant quasars, Sandage-Loeb (SL) test directly measures the expansion of the
universe, covering the "redshift desert" of $2 \lesssim z \lesssim5$. Thus this
method is definitely an important supplement to the other geometric
measurements and will play a crucial role in cosmological constraints. In this
paper, we quantify the ability of SL test signal by a CODEX-like spectrograph
for constraining interacting dark energy. Four typical interacting dark energy
models are considered: (i) $Q=\gamma H\rho_c$, (ii) $Q=\gamma H\rho_{de}$,
(iii) $Q=\gamma H_0\rho_c$, and (iv) $Q=\gamma H_0\rho_{de}$. The results show
that for all the considered interacting dark energy models, relative to the
current joint SN+BAO+CMB+$H_0$ observations, the constraints on $\Omega_m$ and
$H_0$ would be improved by about 60\% and 30--40\%, while the constraints on
$w$ and $\gamma$ would be slightly improved, with a 30-yr observation of SL
test. We also explore the impact of SL test on future joint geometric
observations. In this analysis, we take the model with $Q=\gamma H\rho_c$ as an
example, and simulate future SN and BAO data based on the space-based project
WFIRST. We find that in the future geometric constraints, the redshift drift
observations would help break the geometric degeneracies in a meaningful way,
thus the measurement precisions of $\Omega_m$, $H_0$, $w$, and $\gamma$ could
be substantially improved using future probes.
