Hamiltonian formalism for cosmological perturbations: the separateuniverse approach
Abstract
The separateuniverse approach provides an effective description of cosmological perturbations at large scales, where the universe can be described by an ensemble of independent, locally homogeneous and isotropic patches. By reducing the phase space to homogeneous and isotropic degrees of freedom, it greatly simplifies the analysis of largescale fluctuations. It is also a prerequisite for the stochasticinflation formalism. In this work, we formulate the separateuniverse approach in the Hamiltonian formalism, which allows us to analyse the full phasespace structure of the perturbations. Such a phasespace description is indeed required in dynamical regimes which do not benefit from a background attractor, as well as to investigate quantum properties of cosmological perturbations. We find that the separateuniverse approach always succeeds in reproducing the same phasespace dynamics for homogeneous and isotropic degrees of freedom as the full cosmological perturbation theory, provided that the wavelength of the modes under consideration are larger than some lower bound that we derive. We also compare the separateuniverse approach and cosmological perturbation theory at the level of the gaugematching procedure, where the agreement is not always guaranteed and requires specific matching prescriptions that we present.
 Publication:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 February 2022
 DOI:
 10.1088/14757516/2022/02/001
 arXiv:
 arXiv:2110.11720
 Bibcode:
 2022JCAP...02..001A
 Keywords:

 cosmological perturbation theory;
 physics of the early universe;
 alternatives to inflation;
 inflation;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 Discussion around equation (4.12) expanded, few minor changes (main conclusions unchanged)