Testing inflation on all scales: a case study with α-attractors

A plethora of inflationary models have been shown to produce interesting small-scale phenomenology, such as enhanced scalar fluctuations leading to primordial black hole (PBH) production and large scalar-induced gravitational waves (GW). Nevertheless, good models must simultaneously explain current observations on all scales. In this work, we showcase our methodology to establish the small-scale phenomenology of inflationary models on firm grounds. We consider the case of hybrid cosmological α-attractors, and focus on a reduced parameter space featuring the two potential parameters which roughly determine the position of the peak in the scalar power spectrum, 𝒫ζ, and its amplitude. We first constrain the parameter space by comparing the large-scale predictions for 𝒫ζ with current CMB anisotropies measurements and upper limits on μ-distortions. We take into account uncertainties due to the reheating phase, and observe that the parameter-space area compatible with large-scale constraints shrinks for extended reheating stages. We then move to smaller scales, where we find that non-Gaussianity at peak scales is of the local type and has amplitude fNL ∼ 𝒪(0.1). This ensures that non-linear effects are subdominant, motivating us to employ the tree-level 𝒫ζ to compute the abundance of PBHs and the spectrum of induced GWs for models consistent with large-scale tests. The former allows us to further constrain the parameter space, by excluding models which over-produce PBHs. We find that a subset of viable models can lead to significant production of PBHs, and a fraction of these is within reach for LISA, having a signal-to-noise ratio larger than that of astrophysical foregrounds. Our first-of-its-kind study systematically combines tests at different scales, and exploits the synergy between cosmological observations and theoretical consistency requirements. As such, it represents the first step towards establishing a paradigm for constraining inflation on all scales.