Constraints on features in the inflationary potential from future Euclid
  data
  With Planck cosmic microwave background observations, we established the
spectral amplitude and tilt of the primordial power spectrum. Evidence of a red
spectral tilt ($n_\mathrm{s}=0.96$) at $8\sigma$ provides strong support for
the inflationary mechanism, especially the slow-roll of the effective scalar
field in its nearly flat potential as the generator of scalar primordial
perturbations. With the next generation of large-scale structure surveys, we
expect to probe primordial physics beyond the overall shape and amplitude of
the main, smooth and slowly-changing part of the inflaton potential. Using the
specifications for the upcoming Euclid survey, we investigate to what extent we
can constrain the inflation potential beyond its established slow-roll
behaviour. We provide robust forecasts with Euclid and Planck mock data from
nine fiducial power spectra that contain suppression and wiggles at different
cosmological scales, using the Wiggly Whipped Inflation (WWI) framework to
generate these features in the primordial spectrum. We include both Euclid
cosmic shear and galaxy clustering, with a conservative cut-off for non-linear
scales. Using Markov chain Monte Carlo simulations, we obtain an improvement in
constraints in the WWI potential, as well an improvement for the background
cosmology parameters. We find that apart from improving the constraints on the
overall scale of the inflationary potential by 40-50 per cent, we can also
identify oscillations in the primordial spectrum that are present within
intermediate to small scales ($k\sim0.01-0.2\,\mathrm{Mpc^{-1}}$).
