Symmetry Constraints in Inflation, $\alpha$-vacua, and the Three Point Function

Understand

The Ward identities for conformal symmetries in single field models of inflation are studied in more detail in momentum space.

• For a class of generalized single field models, where the inflaton action contains arbitrary powers of the scalar and its first derivative, we find that the Ward identities are valid.
• We also study a one-parameter family of vacua, called $\alpha$-vacua, which preserve conformal invariance in de Sitter space.
• We find that the Ward identities, upto contact terms, are met for the three point function of a scalar field in the probe approximation in these vacua.