Non-perturbative approach for curvature perturbations in stochastic-$\delta N$ formalism

Abstract

In our previous paper, we have proposed a new algorithm to calculate the power spectrum of the curvature perturbations generated in inflationary universe with use of the stochastic approach. Since this algorithm does not need the perturbative expansion with respect to the inflaton fields on super-horizon scale, it works even in highly stochastic cases. For example, when the curvature perturbations are very large or the non-Gaussianities of the curvature perturbations are sizable, the perturbative expansion may break down but our algorithm enables to calculate the curvature perturbations. We apply it to two well-known inflation models, chaotic and hybrid inflation, in this paper. Especially for hybrid inflation, while the potential is very flat around the critical point and the standard perturbative computation is problematic, we successfully calculate the curvature perturbations.

arXiv comment25 pages, 9 figures, 2 tables

References in corpus (36)

• Planck 2013 results. XVI. Cosmological parameters
• BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales
• Hybrid Inflation
• New cosmological constraints on primordial black holes
• False Vacuum Inflation with Einstein Gravity
• A General Analytic Formula for the Spectral Index of the Density Perturbations produced during Inflation
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• A general proof of the conservation of the curvature perturbation
• Large Scale Structure and Supersymmetric Inflation without Fine Tuning
• Super-Horizon Scale Dynamics of Multi-Scalar Inflation
• D-Term Inflation
• Hybrid Inflation from Supergravity D Terms
• Improved constraints on the primordial power spectrum at small scales from ultracompact minihalos
• Chaotic new inflation and formation of primordial black holes
• Generalised constraints on the curvature perturbation from primordial black holes
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Non-linear metric perturbations and production of primordial black holes
• Stochastic growth of quantum fluctuations during slow-roll inflation
• On the divergences of inflationary superhorizon perturbations
• Single-field inflation, anomalous enhancement of superhorizon fluctuations, and non-Gaussianity in primordial black hole formation
• Primordial Black Holes as a Probe of Cosmology and High Energy Physics
• A new algorithm for calculating the curvature perturbations in stochastic inflation
• Hybrid inflation along waterfall trajectories
• A new probe of the small-scale primordial power spectrum: astrometric microlensing by ultracompact minihalos
• Gamma-rays from ultracompact minihalos: potential constraints on the primordial curvature perturbation
• The hybrid inflation waterfall and the primordial curvature perturbation
• P-term, D-term and F-term inflation
• Avoiding the blue spectrum and the fine-tuning of initial conditions in hybrid inflation
• Contribution of the hybrid inflation waterfall to the primordial curvature perturbation
• Lagrangian Formulation of Stochastic Inflation: A Recursive Approach
• Perturbations in stochastic inflation
• Recursive Stochastic Effects in Valley Hybrid Inflation
• Fluctuations along supersymmetric flat directions during Inflation
• Stochastic Approach to Flat Direction during Inflation
• On the fate of coupled flat directions during inflation
• Inflationary buildup of a vector field condensate and its cosmological consequences

Cited by in corpus (57)

• Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the seeds of Galaxies
• Quantum diffusion during inflation and primordial black holes
• The exponential tail of inflationary fluctuations: consequences for primordial black holes
• Primordial Black Holes for the LIGO Events in the Axion-like Curvaton Model
• Revisiting constraints on small scale perturbations from big-bang nucleosynthesis
• Primordial black hole tower: Dark matter, earth-mass, and LIGO black holes
• Primordial Black Holes
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• Stochastic Ultra Slow Roll Inflation
• Multiple Fields in Stochastic Inflation
• Can massive primordial black holes be produced in mild waterfall hybrid inflation?
• Critical Number of Fields in Stochastic Inflation
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Statistical nature of infrared dynamics on de Sitter background
• Cancellation of quantum corrections on the soft curvature perturbations
• Review on stochastic approach to inflation
• Inflation is always semi-classical: Diffusion domination overproduces Primordial Black Holes
• The Open Effective Field Theory of Inflation
• Markovian Dynamics in de Sitter
• Gravitational Waves and Primordial Black Holes from Supersymmetric Hybrid Inflation
• Squeezed Bispectrum in the $\delta N$ Formalism: Local Observer Effect in Field Space
• Higgs vacuum (in)stability during inflation: the dangerous relevance of de Sitter departure and Planck-suppressed operators
• Stochastic dark energy from inflationary quantum fluctuations
• Tunneling in Stochastic Inflation
• Can all the infrared secular growth really be understood as increase of classical statistical variance?
• Large fluctuations and Primordial Black Holes
• Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase
• Inflationary stochastic anomalies
• Numerical stochastic inflation constrained by frozen noise
• Numerically modeling stochastic inflation in slow-roll and beyond
• Stochastic non-attractor inflation
• Revisiting Magnetogenesis during Inflation
• Stochastic Effects in Anisotropic Inflation
• STOLAS: STOchastic LAttice Simulation of cosmic inflation
• Stochastic Effects in Axion Inflation and Primordial Black Holes Formation
• Finding origins of CMB anomalies in the inflationary quantum fluctuations
• Extended $\delta N$ formalism: Nonspatially Flat Separate Universe Approach
• Boundary Crossing in Stochastic Inflation with Critical Number of Fields
• Primordial Helical Magnetic Fields from Inflation?
• Feynman Rules for Stochastic Inflationary Correlators
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Computing First-Passage Times with the Functional Renormalisation Group
• Stochastic Baryogenesis
• Stochastic inflation with gradient interactions
• Inflation with Stochastic Boundary
• Stochastic inflation and non-perturbative power spectrum beyond slow roll
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• Stochastic inflation with quantum and thermal noise
• Stochastic origin of primordial fluctuations in the Sky
• Classicality of Stochastic Noise Away From Quasi-de Sitter Inflation
• Improved quantum algorithm for calculating eigenvalues of differential operators and its application to estimating the decay rate of the perturbation distribution tail in stochastic inflation
• Stochastic-tail of the curvature perturbation in hybrid inflation
• Stochastic Inflation with Interacting Noises
• Deviations from Gaussian White Noise in Stochastic Inflation
• Time-reversed Stochastic Inflation
• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond
• Calculating the power spectrum in stochastic inflation by Monte Carlo simulation and least squares curve fitting