This White Paper for the CNRS IN2P3 Prospective 2020 focuses on realistic and timely situations of cosmic inflation in connection with the CMB, gravitational and particle physics, adding inter-disciplinarity and unification values within a strongly predictive physical approach. The formulation of inflation in the Ginsburg-Landau approach developed by de Vega and Sanchez [1] and by Boyanovsky, de Vega, Sanchez and Destri [2-4] clarifies and places inflation in the setting of the effective field theories of particle physics. In addition, it sets up a clean way to directly confront the inflationary predictions with the available and forthcoming CMB data and select a definitive model. All CMB + LSS data until now show how powerful is the Ginsburg-Landau effective theory of inflation in predicting observables in agreement with observations, including the inflation energy scale and the inflaton potential, and which has much more to provide in the future. It paves the way to discoveries, new learning and understanding .