Complete Hamiltonian analysis of cosmological perturbations at all orders

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.

Accepted in JCAP

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• Bounce from Inflation
• Complete Hamiltonian analysis of cosmological perturbations at all orders II: Non-canonical scalar field
• Stability of a viable non-minimal bounce
• Vector Galileon and inflationary magnetogenesis
• Inflationary magnetogenesis: solving the strong coupling and its non-Gaussian signatures
• BRST Quantization of Cosmological Perturbations
• Hamiltonian formalism of cosmological perturbations and higher derivative theories
• Unifying inflationary and reheating solution
• Higher derivative quartic vertex of $f(R)$ gravity in light-cone gauge