Rapid numerical solutions for the Mukhanov-Sasaki equation

Abstract

We develop a novel technique for numerically computing the primordial power spectra of comoving curvature perturbations. By finding suitable analytic approximations for different regions of the mode equations and stitching them together, we reduce the solution of a differential equation to repeated matrix multiplication. This results in a wavenumber-dependent increase in speed which is orders of magnitude faster than traditional approaches at intermediate and large wavenumbers. We demonstrate the method's efficacy on the challenging case of a stepped quadratic potential with kinetic dominance initial conditions.

arXiv comment10 pages, 8 figures, Submitted to Physical Review D

References in corpus (42)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Planck 2018 results. X. Constraints on inflation
• The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes
• Planck 2013 results. I. Overview of products and scientific results
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectrum
• Oscillations in the CMB from Axion Monodromy Inflation
• A note on inflation and transplanckian physics
• Suppressing the lower Multipoles in the CMB Anisotropies
• Primordial black hole dark matter from single field inflation
• TASI Lectures on Inflation
• Initial Conditions for Inflation
• Bayesian Analysis of Inflation II: Model Selection and Constraints on Reheating
• Transplanckian energy production and slow roll inflation
• CMB polarization features from inflation versus reionization
• Bayesian Analysis of Inflation: Parameter Estimation for Single Field Models
• BINGO: A code for the efficient computation of the scalar bi-spectrum
• A note on alpha-vacua and interacting field theory in de Sitter space
• A Note on Calm Excited States of Inflation
• Kinetic Initial Conditions for Inflation
• Vacuum Choices and the Predictions of Inflation
• The Fate of the Alpha-Vacuum
• Bayesian Analysis of Inflation III: Slow Roll Reconstruction Using Model Selection
• Boundary Effective Field Theory and Trans-Planckian Perturbations: Astrophysical Implications
• Symmetry Constraints in Inflation, $\alpha$-vacua, and the Three Point Function
• Non-Gaussianities in the Cosmological Perturbation Spectrum due to Primordial Anisotropy
• Taming the alpha-vacuum
• Non-Gaussianities in the Cosmological Perturbation Spectrum due to Primordial Anisotropy II
• Novel quantum initial conditions for inflation
• Constraining the kinetically dominated Universe
• A remark on alpha vacua for quantum field theories on de Sitter space
• Observational Constraints on Constant Roll Inflation
• A case for kinetically dominated initial conditions for inflation
• The Inflationary Wavefunction and its Initial Conditions
• Extracting New Physics from the CMB
• The Standard Model of Cosmology: A Skeptic's Guide
• Quantum initial conditions for inflation and canonical invariance
• Improved cosmological fits with quantized primordial power spectra
• Perturbations and the Future Conformal Boundary
• Just enough inflation
• The Runge-Kutta-Wentzel-Kramers-Brillouin Method
• Two-point correlators revisited: Fast and slow scales in multifield models of inflation

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• Constraining Quantum Initial Conditions before Inflation
• Primordial power spectra from $k$-inflation with curvature
• Logolinear series expansions with applications to primordial cosmology
• Kinetic dominance and the wavefunction of the universe
• Analytic Approximations for the Primordial Power Spectrum with Israel Junction Conditions
• Dense output for highly oscillatory numerical solutions