# Hamiltonian formalism for cosmological perturbations: the separate-universe approach

@inproceedings{Artigas2021HamiltonianFF, title={Hamiltonian formalism for cosmological perturbations: the separate-universe approach}, author={Danilo Artigas and Julien Grain and Vincent Vennin}, year={2021} }

The separate-universe 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 large-scale fluctuations. It is also a prerequisite for the stochastic-inflation formalism. In this work, we formulate the separate-universe approach in the…

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## References

SHOWING 1-10 OF 67 REFERENCES

Hamiltonian formalism and gauge invariance for linear perturbations in inflation

- Physics
- 1994

A Hamiltonian treatment of gauge-invariant cosmological perturbations is presented. In this framework the gauge-invariant perturbations as well as their evolution equations are obtained with minimal…

Stochastic inflation beyond slow roll

- PhysicsJournal of Cosmology and Astroparticle Physics
- 2019

We study the stochastic formalism of inflation beyond the usual slow-roll approximation. We verify that the assumptions on which the stochastic formalism relies still hold even far from the slow-roll…

Anisotropic separate universe and Weinberg's adiabatic mode

- PhysicsJournal of Cosmology and Astroparticle Physics
- 2021

In the separate universe approach, an inhomogeneous universe is rephrased as a set of glued numerous homogeneous local patches. This is the essence of the gradient expansion and the δN formalism,…

Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation

- Physics
- 2021

We study the impact of stochastic noise on the generation of primordial black hole (PBH) seeds in ultra-slow-roll (USR) inflation with numerical simulations. We consider the non-linearity of the…

Massive scalar field in de Sitter spacetime: a two-loop calculation and a comparison with the stochastic approach

- Physics
- 2021

We examine long-wavelength correlation functions of massive scalar fields in de Sitter spacetime. For the theory with a quartic self-interaction, the twopoint function is calculated up to two loops.…

Stochastic inflation at all order in slow-roll parameters: foundations

- Physics
- 2021

In this paper we develop the formalism for the stochastic approach to inflation at all order in slow-roll parameters. This is done by including the momentum and Hamiltonian constraints into the…

Ultra-slow-roll inflation with quantum diffusion

- Physics
- 2021

We consider the effect of quantum diffusion on the dynamics of the inflaton during a period of ultra-slow-roll inflation. We extend the stochastic-δ𝒩 formalism to the ultra-slow-roll regime and show…

A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation

- PhysicsJournal of Cosmology and Astroparticle Physics
- 2020

Stochastic inflation is an effective theory describing the super-Hubble, coarse-grained, scalar fields driving inflation, by a set of Langevin equations. We previously highlighted the difficulty of…

Stochastic nonattractor inflation

- Physics
- 2020

We extend the formalism of stochastic inflation to the setup of non-attractor inflation with a sound speed $c_s$. We obtain the Langevin equations for the superhorizon perturbations and calculate the…

Unavoidable shear from quantum fluctuations in contracting cosmologies

- Physics
- 2020

Contracting cosmologies are known to be flawed with a shear instability, where the contribution from the anisotropic stress to the overall energy density grows as $a^{-6}$, with $a$ the scale factor.…