## 3.6 Summary and outlook

We have summarized aspects of the initial conditions for the growth of cosmological perturbations that
Euclid will enable us to probe. In particular we have considered the shape of the primordial power
spectrum and its connection to inflationary models, primordial non-Gaussianity and isocurvature
perturbations.
A survey like Euclid will greatly improve our knowledge of the initial conditions for the growth of
perturbations and will help shed light on the mechanism for the generation of primordial perturbations.
The addition of Euclid data will improve the Planck satellite’s cosmic microwave background
constraints on parameters describing the shape of the primordial power spectrum by a factor of
2 – 3.

Primordial non-Gaussianity can be tested by Euclid in three different and complementary ways: via the
galaxy bispectrum, number counts of nonlinear structures and the non-Gaussian halo bias. These
approaches are also highly competitive with and complementary to CMB constraints. In combination with
Planck, Euclid will not only test a possible scale-dependence of non-Gaussianity but also its shape. The
shape of non-Gaussianity is the key to constrain and classify possible deviations for the simplest single-field
slow roll inflation.

Isocurvature modes affect the interpretation of large-scale structure clustering in two ways. The power
spectrum shape is modified on small scales due to the extra perturbations although this effect however can
be mimicked by scale-dependent bias. More importantly isocurvature modes can lead to an incorrect
inferred value for the sound horizon at radiation drag from CMB data. This then predicts an incorrect
location of the baryon acoustic feature. It is through this effect that Euclid BAO measurements improve
constraints on isocurvature modes.