'Constraint consistency' at all orders in Cosmological perturbation theory

Understand

We study the equivalence of two - order-by-order Einstein's equation and Reduced action - approaches to cosmological perturbation theory at all orders for different models of inflation.

• We point out a crucial consistency check which we refer to as 'Constraint consistency' that needs to be satisfied.
• We propose a quick and efficient method to check the consistency for any model including modified gravity models.
• Our analysis points out an important feature which is crucial for inflationary model building i.e., all `constraint' inconsistent models have higher order Ostrogradsky's instabilities but the reverse is not true.