Finite inflation in curved space

Abstract

We investigate the effects of non-zero spatial curvature on cosmic inflation in the light of cosmic microwave background (CMB) anisotropy measurements from the Planck 2018 legacy release and from the 2015 observing season of BICEP2 and the Keck Array. Even a small percentage of non-zero curvature today would significantly limit the total number of e-folds of the scale factor during inflation, rendering just-enough inflation scenarios with a kinetically dominated or fast-roll stage prior to slow-roll inflation more likely. Finite inflation leads to oscillations and a cutoff towards large scales in the primordial power spectrum and curvature pushes them into the CMB observable window. Using nested sampling, we carry out Bayesian parameter estimations and model comparisons taking into account constraints from reheating and horizon considerations. We confirm the preference of CMB data for closed universes with Bayesian odds of over $100:1$ and with a posterior on the curvature density parameter of ${\Omega }_{K,0}=-0.051\pm 0.017$ for a curvature extension of LCDM and ${\Omega }_{K,0}=-0.031\pm 0.014$ for Starobinsky inflation. Model comparisons of various inflation models give similar results as for flat universes with the Starobinsky model outperforming most other models.

arXiv comment46 pages, 32 figures, 3 tables, submitted to PRD, from chapter 5 of L. T. Hergt's doctoral thesis at https://www.repository.cam.ac.uk/handle/1810/323129, data available at https://zenodo.org/record/6547872

References in corpus (86)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Planck 2015 results. XIII. Cosmological parameters
• Planck 2013 results. XVI. Cosmological parameters
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• 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
• Planck 2018 results. I. Overview and the cosmological legacy of Planck
• The Simons Observatory: Science goals and forecasts
• Planck 2018 results. V. CMB power spectra and likelihoods
• Planck 2013 results. XXII. Constraints on inflation
• Encyclopaedia Inflationaris
• BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
• Monodromy in the CMB: Gravity Waves and String Inflation
• Reconstructing the Inflaton Potential --- an Overview
• Gravity Waves and Linear Inflation from Axion Monodromy
• What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?
• Formalising the Slow-Roll Approximation in Inflation
• Cobaya: Code for Bayesian Analysis of hierarchical physical models
• Planck evidence for a closed Universe and a possible crisis for cosmology
• How long before the end of inflation were observable perturbations produced?
• Efficient sampling of fast and slow cosmological parameters
• PolyChord: nested sampling for cosmology
• PolyChord: next-generation nested sampling
• BICEP2 / Keck Array x: Constraints on Primordial Gravitational Waves using Planck, WMAP, and New BICEP2/Keck Observations through the 2015 Season
• Suppressing the lower Multipoles in the CMB Anisotropies
• Curvature tension: evidence for a closed universe
• A Critical Review of Classical Bouncing Cosmologies
• Inflationary paradigm in trouble after Planck2013
• Planck intermediate results. LVII. Joint Planck LFI and HFI data processing
• Concordance and Discordance in Cosmology
• The evidence for a spatially flat Universe
• Is the Low CMB Quadrupole a Signature of Spatial Curvature?
• Inflation and the Scale Dependent Spectral Index: Prospects and Strategies
• Investigating Cosmic Discordance
• Inflationary schism after Planck2013
• Planck constraints on the tensor-to-scalar ratio
• Beginning inflation in an inhomogeneous universe
• Fast-Roll Inflation
• Bayesian Analysis of Inflation II: Model Selection and Constraints on Reheating
• A Detailed Description of the CamSpec Likelihood Pipeline and a Reanalysis of the Planck High Frequency Maps
• Robustness of Inflation to Inhomogeneous Initial Conditions
• WMAP data and the curvature of space
• anesthetic: nested sampling visualisation
• Inflation after Planck: Judgment Day
• Why Not Consider Closed Universes?
• Quantifying the global parameter tensions between ACT, SPT and Planck
• Closed Universes, de Sitter Space and Inflation
• Quantifying dimensionality: Bayesian cosmological model complexities
• Just enough inflation: power spectrum modifications at large scales
• Spatial Curvature Falsifies Eternal Inflation
• Kinetic Initial Conditions for Inflation
• Fast and accurate CMB computations in non-flat FLRW universes
• CMB quadrupole suppression: I. Initial conditions of inflationary perturbations
• How Many $e$-Folds Should We Expect from High-Scale Inflation?
• The CMB Quadrupole depression produced by early fast-roll inflation: MCMC analysis of WMAP and SDSS data
• CMB quadrupole suppression: II. The early fast roll stage
• Quantifying concordance of correlated cosmological data sets
• Cosmological constraints on slow-roll inflation: an update
• Primordial power spectra for curved inflating universes
• The pre-inflationary and inflationary fast-roll eras and their signatures in the low CMB multipoles
• Initial conditions for Inflation in an FRW Universe
• Predictions of just-enough inflation
• Bayesian evidence for the tensor-to-scalar ratio $r$ and neutrino masses $m_{\nu }$: Effects of uniform vs logarithmic priors
• Low power on large scales in just enough inflation models
• Inflation in the closed FLRW model and the CMB
• Quantifying Suspiciousness Within Correlated Data Sets
• Novel quantum initial conditions for inflation
• An efficient method for solving highly oscillatory ordinary differential equations with applications to physical systems
• Constraining the kinetically dominated Universe
• Linear Point and Sound Horizon as Purely Geometric standard rulers
• Optimal polarisation equations in FLRW universes
• de Sitter equilibrium as a fundamental framework for cosmology
• A case for kinetically dominated initial conditions for inflation
• ${\varphi }^4$ inflation is not excluded
• Tensor to scalar ratio and large scale power suppression from pre-slow roll initial conditions
• Tensor perturbations during inflation in a spatially closed Universe
• Transients in finite inflation
• Cosmic curvature from de Sitter equilibrium cosmology
• Signatures of the Very Early Universe: Inflation, Spatial Curvature and Large Scale Anomalies
• Viability of slow-roll inflation in light of the non-zero k_min measured in the CMB power spectrum
• Quantum initial conditions for inflation and canonical invariance
• Holographic bounds and finite inflation
• Natural inflation with natural number of e-foldings