Stochastic Inflation in Numerical Relativity

Abstract

A set of 3+1 equations for stochastic inflation incorporating all metric and scalar matter degrees of freedom, first presented in previous work, are re-derived in a gauge invariant manner. We then present numerical implementations of these stochastic equations, cast in the BSSN formulation of Numerical Relativity, demonstrating their efficacy in both a slow-roll and an ultra slow-roll scenario. We find the evolution is correctly reproduced for all the dynamical variables, and the energy and momentum constraints are well-satisfied. This demonstrates that the stochastic equations are theoretically and numerically robust and ready to be applied to a wider inflationary landscape. Our simulations result in real space realizations of the fully non-linear stochastic dynamics with \new{gradients and anisotropic expansion retained. This work generalizes standard stochastic inflation, inflationary numerical relativity and lattice cosmology, opening up the possibility for reliable predictions of non-perturbative phenomena and providing} precise initial conditions for subsequent cosmological eras.

Final submission to PRD after successful peer-review. 16 pages, 9 figures

References in corpus (45)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Conformal and covariant formulation of the Z4 system with constraint-violation damping
• Higgs inflation at the critical point
• Correlation Functions in Stochastic Inflation
• Higgs inflation still alive
• Enhancement of superhorizon scale inflationary curvature perturbations
• The Separate Universe Approach and the Evolution of Nonlinear Superhorizon Cosmological Perturbations
• Primordial Black Holes from a tiny bump/dip in the Inflaton potential
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Beginning inflation in an inhomogeneous universe
• Stochastic growth of quantum fluctuations during slow-roll inflation
• GRChombo : Numerical Relativity with Adaptive Mesh Refinement
• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• Robustness of Inflation to Inhomogeneous Initial Conditions
• CosmoLattice
• GRChombo: An adaptable numerical relativity code for fundamental physics
• Stochastic inflation beyond slow roll
• Constraint damping of the conformal and covariant formulation of the Z4 system in simulations of binary neutron stars
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• One loop to rule them all: Perturbativity in the presence of ultra slow-roll dynamics
• The Effects of Potential Shape on Inhomogeneous Inflation
• Review on stochastic approach to inflation
• Backreaction and Stochastic Effects in Single Field Inflation
• Stochastic inflation at all order in slow-roll parameters: foundations
• The separate-universe approach and sudden transitions during inflation
• An efficient method for solving highly oscillatory ordinary differential equations with applications to physical systems
• Ultra-Slow-Roll Inflation on the Lattice I: Backreaction and Nonlinear Effects
• Inhomogeneous initial conditions for inflation: A wibbly-wobbly timey-wimey path to salvation
• Hamiltonian formalism for cosmological perturbations: the separate-universe approach
• Numerical stochastic inflation constrained by frozen noise
• A Bumpy Start to a Smooth Ride: Onset of Inflation amid Backreaction from Inhomogeneities
• Stochastic Inflation in General Relativity
• STOLAS: STOchastic LAttice Simulation of cosmic inflation
• Starting inflation from inhomogeneous initial conditions with momentum
• Extended $\delta N$ formalism: Nonspatially Flat Separate Universe Approach
• Cosmology using numerical relativity
• Robustness of inflation to kinetic inhomogeneities
• Numerical Relativity as a New Tool for Fundamental Cosmology
• Stochastic inflation with gradient interactions
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• Quantitative classicality in cosmological interactions during inflation
• On the Hamilton-Jacobi approach to inflation beyond slow roll
• Bunch-Davies initial conditions and non-perturbative inflationary dynamics in Numerical Relativity
• Fully-relativistic evolution of vacuum tensor inhomogeneities during inflation
• Inflaton perturbations through an Ultra-Slow Roll transition and Hamilton-Jacobi attractors

Cited by in corpus (2)

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