Complete Hamiltonian analysis of cosmological perturbations at all orders

TL;DR

This paper develops a comprehensive Hamiltonian framework for analyzing cosmological perturbations across all orders, resolving gauge issues and applicable to various scalar field models, including Galilean fields.

Contribution

It introduces a transparent Hamiltonian method for higher-order cosmological perturbations, applicable to any order and field derivatives, improving robustness over previous Lagrangian approaches.

Findings

Consistent Hamiltonian analysis at all perturbation orders.

Extension to scalar field models, including Galilean fields.

No extra degrees of freedom from higher derivatives in the models.

Abstract

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations at all orders. To make the procedure transparent, we consider a simple model and resolve the `gauge-fixing' issues and extend the analysis to scalar field models and show that our approach can be applied to any order of perturbation for any first order derivative fields. In the case of Galilean scalar fields, our procedure can extract constrained relations at all orders in perturbations leading to the fact that there is no extra degrees of freedom due to the presence of higher time derivatives of the field in the Lagrangian. We compare and contrast our approach to the Lagrangian approach (Chen et al [2006]) for extracting higher order correlations and show that our approach is quick and robust and can be applied to any model of gravity and matter fields.