Quintessential $\alpha$-attractor inflation: forecasts for Stage IV galaxy surveys

Single-field models of $\alpha$-attractor quintessential inflation provide a unified picture of the two periods of early- and late-time cosmic acceleration, where both inflation and dark energy are described by a single scalar degree of freedom rolling down a runaway potential. These theoretically well-motivated models have distinct observational predictions that are in agreement with existing cosmological data. We show that the next generation of large-scale structure surveys, even when no other cosmological data sets are considered, will strongly constrain the parameter space of these models, and test them against the standard cosmological model and more conventional non-quintessential inflation. In particular, we expect $\mathcal{O}(10^{-5}\mathrm{-}10^{-4})$ constraints on the present values of the dark energy equation of state and its time derivative, $w_0$ and $w_a$. We also forecast more than one order of magnitude tighter constraints on the spectral index of primordial curvature perturbations $n_s$ compared to the expectations for the standard model. This demonstrates the powerful synergy between the upcoming large-scale structure probes of inflation and those aiming to measure the tensor-to-scalar ratio $r$ through the observation of $B$-mode polarization of the cosmic microwave background.