  With future galaxy surveys, a huge number of Fourier modes of the
distribution of the large scale structures in the Universe will become
available. These modes are complementary to those of the CMB and can be used to
set constraints on models of the early universe, such as inflation. Using a
MCMC analysis, we compare the power of the CMB with that of the combination of
CMB and galaxy survey data, to constrain the power spectrum of primordial
fluctuations generated during inflation. We base our analysis on the Planck
satellite and a spectroscopic redshift survey with configuration parameters
close to those of the Euclid mission as examples. We first consider models of
slow-roll inflation, and show that the inclusion of large scale structure data
improves the constraints by nearly halving the error bars on the scalar
spectral index and its running. If we attempt to reconstruct the inflationary
single-field potential, a similar conclusion can be reached on the parameters
characterizing the potential. We then study models with features in the power
spectrum. In particular, we consider ringing features produced by a break in
the potential and oscillations such as in axion monodromy. Adding large scale
structures improves the constraints on features by more than a factor of two.
In axion monodromy we show that there are oscillations with small amplitude and
frequency in momentum space that are undetected by CMB alone but can be
measured by including galaxy surveys in the analysis.
