Inflation in a closed universe

Abstract

To derive a power spectrum for energy density inhomogeneities in a closed universe, we study a spatially-closed inflation-modified hot big bang model whose evolutionary history is divided into three epochs: an early slowly-rolling scalar field inflation epoch and the usual radiation and non-relativistic matter epochs. (For our purposes it is not necessary to consider a final dark energy dominated epoch.) We derive general solutions of the relativistic linear perturbation equations in each epoch. The constants of integration in the inflation epoch solutions are determined from de Sitter invariant quantum-mechanical initial conditions in the Lorentzian section of the inflating closed de Sitter space derived from Hawking's prescription that the quantum state of the universe only include field configurations that are regular on the Euclidean (de Sitter) sphere section. The constants of integration in the radiation and matter epoch solutions are determined from joining conditions derived by requiring that the linear perturbation equations remain nonsingular at the transitions between epochs. The matter epoch power spectrum of gauge-invariant energy density inhomogeneities is not a power law, and depends on spatial wavenumber in the way expected for a generalization to the closed model of the standard flat-space scale-invariant power spectrum. The power spectrum we derive appears to differ from a number of other closed inflation model power spectra derived assuming different (presumably non de Sitter invariant) initial conditions.

20 pages, minor changes, Phys. Rev. D accepted version

References in corpus (113)

• Planck 2015 results. XIII. Cosmological parameters
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• Efficient Computation of CMB anisotropies in closed FRW models
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
• A 2.4% Determination of the Local Value of the Hubble Constant
• Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples
• Constraints on the redshift dependence of the dark energy potential
• A 6% measurement of the Hubble parameter at $z\sim 0.45$: direct evidence of the epoch of cosmic re-acceleration
• Cosmic Chronometers: Constraining the Equation of State of Dark Energy. I: H(z) Measurements
• Encyclopaedia Inflationaris
• Everything You Always Wanted To Know About The Cosmological Constant Problem (But Were Afraid To Ask)
• Cosmological implications of baryon acoustic oscillation (BAO) measurements
• The trouble with $H_0$
• Carnegie Hubble Program: A Mid-Infrared Calibration of the Hubble Constant
• Dark Energy vs. Modified Gravity
• Hubble parameter measurement constraints on the cosmological deceleration-acceleration transition redshift
• Hubble parameter measurement constraints on the redshift of the deceleration-acceleration transition, dynamical dark energy, and space curvature
• The Atacama Cosmology Telescope: Cosmological parameters from three seasons of data
• An Open Universe from Inflation
• Observational Constraints on Dark Energy and Cosmic Curvature
• Cosmology and Astrophysics from Relaxed Galaxy Clusters II: Cosmological Constraints
• Median Statistics, H_0, and the Accelerating Universe
• First evidence of running cosmic vacuum: challenging the concordance model
• Is the Low CMB Quadrupole a Signature of Spatial Curvature?
• Cosmographic bounds on the cosmological deceleration-acceleration transition redshift in $f(\mathcal{R})$ gravity
• Dynamical Dark Energy or Simply Cosmic Curvature?
• Cosmological Constraints from Hubble Parameter versus Redshift Data
• Hints of dynamical vacuum energy in the expanding Universe
• INFLATION WITH VARIABLE OMEGA
• Inflation with $\Omega \ne 1$
• Large Angle CMB Anisotropy in an Open Universe in the One-Bubble Inflationary Scenario
• Median statistics and the Hubble constant
• Hard Art of the Universe Creation
• Integral Solution for the Microwave Background Anisotropies in Non-fl at Universes
• Determining the Hubble constant from Hubble parameter measurements
• Null test of the cosmic curvature using $H(z)$ and supernovae data
• Probing for dynamics of dark energy and curvature of universe with latest cosmological observations
• Curvature vs Distances: testing the FLRW cosmology
• Can we have inflation with Omega > 1?
• Cosmology with gamma-ray bursts: II Cosmography challenges and cosmological scenarios for the accelerated Universe
• The Beginning and Evolution of the Universe
• Non-Gaussian Error Distribution of Hubble Constant Measurements
• LARGE SCALE PERTURBATIONS IN THE OPEN UNIVERSE
• Supernovae Ia Constraints on a Time-Variable Cosmological "Constant"
• WMAP data and the curvature of space
• An Improved Method to Measure the Cosmic Curvature
• Hubble parameter measurement constraints on dark energy
• Is there evidence for dark energy evolution?
• Cosmological Constraints from Compact Radio Source Angular Size versus Redshift Data
• Model-independent test of the FLRW metric, the flatness of the Universe, and non-local measurement of $H_0{r}_{\mathrm{d}}$
• What are $Om{h}^2(z_1,z_2)$ and $Om(z_1,z_2)$ diagnostics telling us in light of $H(z)$ data?
• Why Not Consider Closed Universes?
• Dynamical dark energy: scalar fields and running vacuum
• Binned Hubble parameter measurements and the cosmological deceleration-acceleration transition
• Closed Universes, de Sitter Space and Inflation
• Constraining cosmic curvature by using age of galaxies and gravitational lenses
• New Model-independent Method to Test the Curvature of the Universe
• Constraining the Dark Energy Equation of State with HII Galaxies
• Updated Estimates of Global Cosmological Parameters Determined Using Classical Double Radio Galaxies
• Global Cosmological Parameters Determined Using Classical Double Radio Galaxies
• Constraints on non-flat cosmologies with massive neutrinos after Planck 2015
• COBE-DMR-Normalized Open CDM Cosmogonies
• Fast and accurate CMB computations in non-flat FLRW universes
• Hubble parameter data constraints on dark energy
• Nonflat time-variable dark energy cosmology
• Constraining dark energy with gamma-ray bursts
• Towards a Precision Cosmology from Starburst Galaxies at z>2
• The impact of a new median statistics $H_0$ prior on the evidence for dark radiation
• Large-scale structure in COBE-normalized cold dark matter cosmogonies
• Constraints on Scalar-Field Dark Energy from Galaxy Cluster Gas Mass Fraction versus Redshift
• Model-independent estimations for the curvature from standard candles and clocks
• Dark Energy Evolution and the Curvature of the Universe from Recent Observations
• CBR Anisotropy in an Open Inflation, CDM Cosmogony
• Implication of Dark Energy Parametrizations on the Determination of the Curvature of the Universe
• Is there a concordance value for $H_0$?
• Observational constraints on non-flat dynamical dark energy cosmological models
• Polar Network Index as a magnetic proxy for the solar cycle studies
• Constraints on dark energy from H II starburst galaxy apparent magnitude versus redshift data
• The HII Galaxy Hubble Diagram Strongly Favors $R_{\mathrm{h}}=ct$ over $\Lambda$CDM
• Model-independent determination of curvature parameter by using $H(z)$ and $D_A(z)$ data pair from BAO measurement
• CMB Anisotropy Constraints on Open and Flat-Lambda CDM Cosmogonies from UCSB South Pole, ARGO, MAX, White Dish, and SuZIE Data
• Dark Energy Parametrizations and the Curvature of the Universe
• On the determination of curvature and dynamical Dark Energy
• COBE-DMR-normalised Open Inflation, CDM Cosmogony
• Inflation in the closed FLRW model and the CMB
• Closed Universes from Cosmological Instantons
• Constraints on dark energy from the lookback time versus redshift test
• Galaxy cluster number count data constraints on cosmological parameters
• Spatial curvature endgame: Reaching the limit of curvature determination
• Reconstructing the Properties of Dark Energy using Standard Sirens
• Dark Energy in a Hyperbolic Universe
• Dynamics of Inflationary Universes with Positive Spatial Curvature
• Dark energy and cosmic curvature: Monte-Carlo Markov Chain approach
• Testing flatness of the universe with probes of cosmic distances and growth
• Galaxy cluster angular size data constraints on dark energy
• Non-parametric Dark Energy Degeneracies
• Tentative Appraisal of Compatibility of Small-Scale CMB Anisotropy Detections in the Context of COBE-DMR-Normalized Open and Flat $\Lambda$ CDM Cosmogonies
• Using SuZIE arcminute-scale CMB anisotropy data to probe open and flat-ΛCDM cosmogonies
• Growth Rate in the Dynamical Dark Energy Models
• Cosmological constraints from large-scale structure growth rate measurements
• Cosmic Degeneracy with Dark Energy Equation of State
• Probing dynamics of dark energy with latest observations
• Time and distance constraints on accelerating cosmological models
• Quintessence with a constant equation of state in hyperbolic universes
• Causality in Inflationary Universes with Positive Spatial Curvature
• Cosmological Constraints on the DGP braneworld model with Gamma-ray bursts
• Imprint of spatial curvature on inflation power spectrum
• The Hubble constant and dark energy from cosmological distance measures
• Constraining thawing and freezing models with cluster number counts
• Quintessence and the Curvature of the Universe after WMAP
• Forecasting cosmological parameter constraints from near-future space-based galaxy surveys
• Age problem in holographic dark energy
• Constraining Thawing Dark Energy using Galaxy Cluster Number Counts

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• Cosmological constraints on slow-roll inflation: an update
• Primordial power spectra for curved inflating universes
• Planck 2015 constraints on the non-flat XCDM inflation model
• The resilience of the Etherington-Hubble relation
• Planck 2015 constraints on spatially-flat dynamical dark energy models
• CMB distance priors revisited: effects of dark energy dynamics, spatial curvature, primordial power spectrum, and neutrino parameters
• Power spectrum for perturbations in an inflationary model for a closed universe
• Current data are consistent with flat spatial hypersurfaces in the $\Lambda$CDM cosmological model but favor more lensing than the model predicts
• Lorentzian Vacuum Transitions: Open or Closed Universes?
• First study of reionization in the Planck 2015 normalized closed $\Lambda$CDM inflation model
• Observational Constraints on Dynamical Dark Energy Models
• General theory of cosmological perturbations in open and closed universes from the Horndeski action
• Scalar quantum fields in cosmologies with 2+1 spacetime dimensions
• Spatial Curvature in $f(R)$ Gravity
• Analytical approximations for curved primordial power spectra
• First study of reionization in tilted flat and untilted non-flat dynamical dark energy inflation models
• Lorentz violation with an invariant minimum speed as foundation of the tachyonic inflation within a Machian scenario
• Spatial Curvature at the Sound Horizon
• Flatness without CMB - the Entanglement of Spatial Curvature and Dark Energy Equation of State
• Tilted non-spatially-flat inflation
• Emergent universe revisited through the CSL theory
• A natural model for curved inflation
• Curved and expanding spacetime geometries in Bose-Einstein condensates
• Living in a Non-Flat Universe: Theoretical Formalism