'Constraint consistency' at all orders in Cosmological perturbation theory

TL;DR

This paper investigates the consistency of two approaches to cosmological perturbation theory at all orders, introduces a method to check this 'Constraint consistency' in inflation models, and links it to Ostrogradsky's instabilities.

Contribution

It proposes a quick method to verify 'Constraint consistency' in any inflationary model, including modified gravity, and clarifies its relation to higher-order instabilities.

Findings

Constraint inconsistent models have Ostrogradsky's instabilities.

All models with constraint lapse and shift can still have Ostrogradsky's instabilities.

Derived single-variable equations for non-canonical scalar fields during power-law inflation.

Abstract

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. In other words, one can have models with constraint lapse function and shift vector, though it may have Ostrogradsky's instabilities. We also obtain the single variable equation for non-canonical scalar field in the limit of power-law inflation for the second-order perturbed variables.