The Inflation paradigm has been introduced as a possible solution to the hot Big Bang model problems. The last results from the Planck collaboration show that there is no evidence for dynamics beyond slow roll, while slow-roll inflationary models for large fields are already ruledout. The remaining single-field models (including the simplest and well-motivated R+R2 Starobinsky model) predict a tensor-to-scalar ratio of a few 10-3. That corresponds to the sensitivity target of the future CMB projects. But the quest for a better understanding of the early phases of the Universe requires to go far beyond this result.

One of the key discoveries, at the turn of the century, has been the acceleration of the expansion of the Universe. Still, today, the underlying physical processes are yet to be understood. To go beyond the standard parameterisation through a cosmological constant or a fluid with a distinctive equation of state, one of the current hypotheses is the modification of General Relativity (GR) on cosmological scales. Such a modification could also solve the problem of the singularities inherent to GR as well as our inability to formulate a quantum version of GR.

Cosmology gives insights on Dark Energy, but also on Dark Matter and neutrinos as different types of particles with different masses, interaction and decay properties do affect the power spectrum (or correlation function) at characteristic scales. his represents a unique opportunity to test the robustness of the ΛCDM model and look for new particles or fields beyond the high-energy (particle) physics standard model.