Most efforts to detect signatures of dynamical dark energy are focused on late times , z \lesssim 2 , where the dark energy component begins to dominate the cosmic energy density .
Many theoretical models involving dynamical dark energy exhibit a ‘ ‘ freezing ’ ’ equation of state however , where w \to - 1 at late times , with a transition to a ‘ ‘ tracking ’ ’ behaviour at earlier times ( with w \gg - 1 at sufficiently high redshift ) .
In this paper , we study whether large-scale structure surveys in the post-reionisation matter-dominated regime , 2 \lesssim z \lesssim 6 , are sensitive to this behaviour , on the basis that the dark energy component should remain detectable ( despite being strongly subdominant ) in this redshift range given sufficiently precise observations .
Using phenomenological models inspired by parameter space studies of Horndeski ( generalised scalar-tensor ) theories , we show how existing CMB and large-scale structure measurements constrain the dark energy equation of state in the matter-dominated era , and examine how forthcoming galaxy surveys and 21cm intensity mapping instruments can improve constraints in this regime .
We also find that the combination of existing CMB and LSS constraints with DESI will already come close to offering the best possible constraints on H _ { 0 } using BAO/galaxy power spectrum measurements , and that either a spectroscopic follow-up of the LSST galaxy sample ( e.g .
along the lines of MegaMapper or SpecTel ) or a Stage 2/PUMA-like intensity mapping survey , both at z \gtrsim 2 , would offer better constraints on the class of dark energy models considered here than a comparable cosmic variance-limited galaxy survey at z \lesssim 1.5 .