COBE, Gravitational Waves, Inflation and Extended Inflation

Abstract

We analyse the implications for inflationary models of the cosmic microwave background (cmb) anisotropy measured by COBE. Vacuum fluctuations during inflation generate an adiabatic density perturbation, and also gravitational waves. The ratio of these two contributions to the cmb anisotropy is given for an arbitrary slow-roll inflaton potential. Results from the IRAS/QDOT and POTENT galaxy surveys are used to normalise the spectrum of the density perturbation on the scale $20h^{-1}\Mpc$, so that the COBE measurement on the scale $10^3h^{-1}\Mpc$ provides a lower bound on the spectral index $n$. For `power law' and `extended' inflation, gravitational waves are significant and the bound is $n>0.84$ at the $2$-sigma level. For `natural' inflation, gravitational waves are negligible and the constraint is weakened to $n>0.70$, at best marginally consistent with a recent proposal for explaining the excess clustering observed in the APM galaxy survey. Many versions of extended inflation, including those based on the Brans--Dicke theory, are ruled out, because they require $n\lsim 0.75$ in order that bubbles formed at the end of inflation should not be observed now in the cmb.

References in corpus (3)

• Cosmic Microwave Background Probes Models of Inflation
• The gravitational wave contribution to CMB anisotropies and the amplitude of mass fluctuations from COBE results
• Graceful Exit in Extended Inflation and Implications for Density Perturbations

Cited by in corpus (281)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• f(R) theories
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Particle Physics Models of Inflation and the Cosmological Density Perturbation
• Generating the curvature perturbation without an inflaton
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation
• False Vacuum Inflation with Einstein Gravity
• Reconstructing the Inflaton Potential --- an Overview
• A Probe of Primordial Gravity Waves and Vorticity
• What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?
• The Cold Dark Matter Density Perturbation
• Formalising the Slow-Roll Approximation in Inflation
• Teleparallel Gravity: From Theory to Cosmology
• Determination of Inflationary Observables by Cosmic Microwave Background Anisotropy Experiments
• Cosmological-Parameter Determination with Microwave Background Maps
• Science with the space-based interferometer LISA. IV: Probing inflation with gravitational waves
• The Four-Year COBE Normalization and Large-Scale Structure
• Cosmic Confusion: Degeneracies among Cosmological Parameters Derived from Measurements of Microwave Background Anisotropies
• Features of heavy physics in the CMB power spectrum
• Black Hole Relics and Inflation: Limits on Blue Perturbation Spectra
• Scalar perturbation spectra from warm inflation
• CMB polarization from secondary vector and tensor modes
• Relativistic cosmology and large-scale structure
• Inflation, Supergravity and Superstrings
• Metric perturbations in two-field inflation
• Tensor Perturbations in Inflationary Models as a Probe of Cosmology
• Inflationary Models with Logarithmic Potentials
• Detectability of inflation-produced gravitational waves
• Approximation Methods for Non-linear Gravitational Clustering
• General Relativity and Cosmology: Unsolved Questions and Future Directions
• Perturbation Spectra from Intermediate Inflation
• The Imprint of Gravitational Waves on the Cosmic Microwave Background
• Reconstructing the Inflaton Potential---in Principle and in Practice
• Constraints on Warm Dark Matter from Cosmological Reionization
• Sneutrino Cold Dark Matter With Lepton-Number Violation
• Is cosmology consistent?
• Fluctuations of the Gravitational Constant in the Inflationary Brans-Dicke Cosmology
• The Cosmic Microwave Background and Particle Physics
• Kinematic Constraints to the Key Inflationary Observables
• Inflation models and observation
• Four-year COBE normalization of inflationary cosmologies
• Constraints from Inflation on Scalar-Tensor Gravity Theories
• Can We See Lorentz-Violating Vector Fields in the CMB?
• The Curvaton as a Pseudo-Nambu-Goldstone Boson
• Third Generation Familons, B Factories, and Neutrino Cosmology
• Infrared Correlations in de Sitter Space: Field Theoretic vs. Stochastic Approach
• Current cosmological constraints from a 10 parameter CMB analysis
• Model-Independent Reconstruction of the Primordial Power Spectrum from WMAP Data
• Measuring Cosmological Parameters with Cosmic Microwave Background Experiments
• New CMB constraints on the cosmic matter budget: trouble for nucleosynthesis?
• Black hole formation and slow-roll inflation
• Detectability of Inflationary Gravitational Waves with Microwave Background Polarization
• String Inflation After Planck 2013
• Relic gravitational waves and their detection
• Cold Dark Matter Models
• The Number of Supernovae from Primordial Stars in the Universe
• Singular Inflationary Universe from $F(R)$ Gravity
• The curvature perturbation in a box
• Observing the Inflaton Potential
• Slow-roll parameters in braneworld cosmologies
• Inflation versus Cyclic Predictions for Spectral Tilt
• Using Cosmology to Establish the Quantization of Gravity
• Extended Slow-Roll Conditions and Rapid-Roll Conditions
• The spectrum of cosmological perturbations produced by a multi-component inflaton to second order in the slow-roll approximation
• Testing Supersymmetric Grand Unified Models of Inflation
• The Inflationary Perturbation Spectrum
• More varieties of hybrid inflation
• The precision of slow-roll predictions for the CMBR anisotropies
• Reconstructing the Inflaton Potential---Perturbative Reconstruction to Second Order
• Cosmological constraints from current CMB and SN 1a data: a brute force 8 parameter analysis
• Emergent Cosmology, Inflation and Dark Energy
• Primordial gravitational waves in supersolid inflation
• CMB Imprints of a Pre-Inflationary Climbing Phase
• Measuring the speed of cosmological gravitational waves
• Chain Inflation in the Landscape: "Bubble Bubble Toil and Trouble"
• The Inflationary Energy Scale
• Natural Chaotic Inflation and UV Sensitivity
• Running of the Scalar Spectral Index from Inflationary Models
• On the Production of Scalar and Tensor Perturbations in Inflationary Models
• Running of the Spectral Index and Violation of the Consistency Relation Between Tensor and Scalar Spectra from trans-Planckian Physics
• The Imprint of Gravitational Waves in Models Dominated by a Dynamical Cosmic Scalar Field
• Minimal Inflation
• Unimodular $F(R)$ Gravity
• Recovering the Inflationary Potential
• Detectability of Tensor Perturbations Through CBR Anisotropy (final published version)
• Prospects for Delensing the Cosmic Microwave Background for Studying Inflation
• Characterizing Inflationary Perturbations: The Uniform Approximation
• Comprehensive Analysis of a Non-Singular Bounce in $f(R,T)$ Gravitation
• The last stand before MAP: cosmological parameters from lensing, CMB and galaxy clustering
• STATIONARY SOLUTIONS IN BRANS-DICKE STOCHASTIC INFLATIONARY COSMOLOGY
• Second-Order Reconstruction of the Inflationary Potential
• Axionic Hot Dark Matter in the Hadronic Axion Window
• On what scale should inflationary observables be constrained?
• Dynamics of Interacting Scalar Fields in Expanding Space-Time
• Inflation at Low Scales: General Analysis and a Detailed Model
• CBR anisotropy from primordial gravitational waves in inflationary cosmologies
• Inflation models after WMAP year three
• On the Predictiveness of Single-Field Inflationary Models
• Multi-wavelength constraints on the inflationary consistency relation
• Unimodular-Mimetic Cosmology
• Polarization of the Microwave Background in Inflationary Cosmology
• Coleman-Weinberg Potential In Good Agreement With WMAP
• Gravitational Wave Spectrums from Pole-like Inflations based on Generalized Gravity Theories
• Is a Massive Tau Neutrino Just What Cold Dark Matter Needs?
• GUT Inflation and Proton Decay after WMAP5
• Singular Hypersurfaces in Scalar-Tensor Theories of Gravity
• Relic Gravitational Waves with A Running Spectral Index and Its Constraints at High Frequencies
• The Higgs mass range from Standard Model false vacuum Inflation in scalar-tensor gravity
• Relating Spectral Indices to Tensor and Scalar Amplitudes in Inflation
• Extended Inflation with a Curvature-Coupled Inflaton
• On the Tensor/Scalar Ratio in Inflation with UV Cutoff
• Particle physics models of inflation
• Standard Model False Vacuum Inflation: Correlating the Tensor-to-Scalar Ratio to the Top Quark and Higgs Boson masses
• Multiple-field inflation and the CMB
• Precision cosmology and the stiff-amplified gravitational-wave background from inflation: NANOGrav, Advanced LIGO-Virgo and the Hubble tension
• Inflationary Perturbations and Precision Cosmology
• Inflationary Affleck-Dine Scalar Dynamics and Isocurvature Perturbations
• Inflation model constraints from data released in 2015
• Analytic Spectra of CMB Anisotropies and Polarization Generated by Relic Gravitational Waves with Modification due to Neutrino Free-Streaming
• Transport equations for the inflationary spectral index
• Implications of the B-mode Polarization Measurement for Direct Detection of Inflationary Gravitational Waves
• Probing the power spectrum bend with recent CMB data
• A New Method of Generating Exact Inflationary Solutions
• Inflating with Large Effective Fields
• Blue perturbation spectra from inflation
• Constraining topological defects with temperature and polarization anisotropies
• Constraining Warm Inflation with the Cosmic Microwave Background
• Absence of isentropic expansion in various inflation models
• Extended Effective Field Theory of Inflation
• Black holes and gravitational waves in string cosmology
• Mutated Hilltop Inflation : A Natural Choice for Early Universe
• Future cosmic microwave background delensing with galaxy surveys
• On the Statistics of CMB Fluctuations Induced by Topological Defects
• Gravitational waves and extra dimensions: a short review
• The Detectability of Departures from the Inflationary Consistency Equation
• On the accuracy of slow-roll inflation given current observational constraints
• Singular $F(R)$ Cosmology Unifying Early and Late-time Acceleration with Matter and Radiation Domination Era
• On the reliability of inflaton potential reconstruction
• Non-Gaussianity in braneworld and tachyon inflation
• Approximate Analytic Spectra of Reionized CMB Anisotropies and Polarization generated by Relic Gravitational Waves
• Forecasting sensitivity on tilt of power spectrum of primordial gravitational waves after Planck satellite
• Modifications by QCD transition and $e^{+}{e}^{-}$ annihilation on analytic spectrum of relic gravitational waves in accelerating universe
• Constraints in the Context of Induced-gravity Inflation
• CMB Polarization Data and Galactic Foregrounds: Estimation of Cosmological Parameters
• Basics of inflationary cosmology
• The Big Bang and Inflation United by an Analytic Solution
• Large Gravitational Waves and Lyth Bound in Multi Brane Inflation
• Running of the Scalar Spectral Index and Observational Signatures of Inflation
• Vacuum and Gravitons of Relic Gravitational Waves, and Regularization of Spectrum and Energy-Momentum Tensor
• Axion Inflation, Proton Decay and Leptogenesis in $SU(5)\times U(1{)}_{PQ}$
• "Graceful" Old Inflation
• The Hubble Slow Roll Expansion for Multi Field Inflation
• Can the Gravitational Wave Background from Inflation be Detected Locally?
• Naturalness of the relaxion mechanism
• Inflationary slow-roll formalism and perturbations in the Randall-Sundrum Type II braneworld
• Toward inflation models compatible with the no-boundary proposal
• Two scalar fields inflation from scale-invariant gravity with modified measure
• Constraints upon the spectral indices of relic gravitational waves by LIGO S5
• Curvaton in large field inflation
• Observational constraints on the inflaton potential combined with flow-equations in inflaton space
• Weyl Symmetry Inspired Inflation and Dark Matter
• Dynamical Fractional Chaotic Inflation -- Dynamical Generation of a Fractional Power-Law Potential for Chaotic Inflation
• First-order formalism for dark energy and dust
• Inflationary Tensor Perturbations After BICEP
• Swampland conjectures in hybrid metric-Palatini gravity
• Observational constraints on tachyon and DBI inflation
• Topological inflation induced by a non-minimally coupled massive scalar field
• Can Inflation be Falsified?
• Conditions for Successful Extended Inflation
• Dynamics of Modified Chaplygin Gas Inflation on the Brane with Bulk Viscous Pressure
• The consistency equation hierarchy in single-field inflation models
• Irreversible thermodynamical description of warm inflationary cosmological models
• Primordial Power Spectra of Cosmological Fluctuations with Generalized Uncertainty Principle and Maximum Length Quantum Mechanics
• Global fits for the spectral index of the cosmological curvature perturbation
• Testing Inflation with the Cosmic Microwave Background
• Unifying Inflation with early and late Dark Energy in Multi-Fields: Spontaneously broken scale invariant TMT
• Stewart-Lyth Inverse Problem
• Cosmological Constraints on Dissipative Models of Inflation
• Two scalar field cosmology from coupled one-field models
• Acceleration of the Universe
• On the Stewart-Lyth Inverse Problem
• Phenomenological approaches of inflation and their equivalence
• Improved calculation of relic gravitational waves
• No-boundary measure and preference for large e-foldings in multi-field inflation
• Brane Inflation, Solitons and Cosmological Solutions: I
• Inflation Based on the Tsallis Entropy
• Detection and Fundamental Applications of Individual First Galaxies
• New Primordial-Magnetic-Field Limit from The Latest LIGO S5 data
• Effects of the Modified Uncertainty Principle on the Inflation Parameters
• No evidence for the blue-tilted power spectrum of relic gravitational waves
• Primordial curvature perturbation during and at the end of multi-field inflation
• Reconstructing the inflaton potential for an almost flat COBE spectrum
• Lyth bound revisited
• A semi-analytical approach to perturbations in mutated hilltop inflation
• An Observational Test of Quantum Cosmology
• The Scalar Field Potential in Inflationary Models: Reconstruction and Further Constraints
• Constraints on inflation in closed universe
• Complete power spectrum for an induced gravity open inflation model
• Primordial Gravitational Waves and Inflation: CMB and Direct Detection With Space-Based Laser Interferometers
• Constraining Cosmic Inflation with Observations: Prospects for 2030
• On the degree of scale invariance of inflationary perturbations
• Singular Accelerated Evolution in Massive $F(R)$ Bigravity
• Magnon Inflation: Slow Roll with Steep Potentials
• Primordial Gravitational Waves Assisted by Cosmological Scalar Perturbations
• Classification of Inflationary Einstein--Scalar--Field--Models via Catastrophe Theory
• Quintessential Inflation with Dynamical Higgs Generation as an Affine Gravity
• Measuring the spectral running from cosmic microwave background and primordial black holes
• Constraints on Higher Dimensional Models for viable Extended Inflation
• Mutated hybrid inflation in $f(R,\square R)$-gravity
• Testing Cold Dark Matter Models At Moderate to High Redshift
• Gravitational Waves From Dark Sectors, Oscillating Inflatons, and Mass Boosted Dark Matter
• Analytic Spectra of CMB Anisotropies and Polarization Generated by Scalar Perturbations in Synchronous Gauge
• Constraints on the Tensor-to-Scalar ratio for non-power-law models
• Gravitational wave generation in power-law inflationary models
• Kähler moduli inflation and WMAP7
• Revisit relic gravitational waves based on the latest CMB observations
• CMB imprints of non-canonical anisotropic inflation
• Relic gravitational waves in the frame of slow-roll inflation with a power-law potential and the detection
• The Tilt of Primordial Gravitational Waves Spectra from BICEP2
• Goldilocks Models of Higher-Dimensional Inflation (including modulus stabilization)
• Observational constraint on the fourth derivative of the inflaton potential
• Introduction to the number of $e$-folds in slow-roll inflation
• The End for Extended Inflation?
• Chaotic Inflation with Time-Variable Space Dimensions
• Constraint on inflation model from BICEP2 and WMAP 9-year data
• Can power spectrum observations rule out slow-roll inflation?
• Quantum Fluctuations in Cosmology and How They Lead to a Multiverse
• CBR Anisotropy from Primordial Gravitational Waves in Two-Component Inflationary Cosmology
• Primordial gravitational wave of BICEP2 from dynamical double hybrid inflation
• Minimal-supersymmetric extended inflation field in Horava-Lifshitz gravity
• Modulated Inflation Models and Primordial Black Holes
• Warm Modified Chaplygin Gas Shaft Inflation
• The inflationary scenario in the $f(R)$ gravity model with a $R^4$ term
• The Berry phase in inflationary cosmology
• Slow-roll inflationary senario in the maximally extended background
• Limits on the gravity wave contribution to microwave anisotropies
• MeV Tau Neutrino: Astrophysical and Cosmological Constraints and Mischief
• The Andante Regime of Scalar Field Dynamics
• Cosmological consequences of a scalar field with oscillating equation of state. III. Unifying inflation with dark energy and small tensor-to-scalar ratio
• Observing the Structure of the Landscape with the CMB Experiments
• Signals of Inflation in a Friendly String Landscape
• The role of the quantum properties of gravitational radiation in the dete ction of gravitational waves
• Inflation for Bianchi IX model
• Consistency Relations for Large Field Inflation
• Statistical Constraints on the Inflation Effective Potential from the COBE DMR Results
• Gravitational lensing on the Cosmic Microwave Background by gravity waves
• The observational position of simple non-minimally coupled inflationary scenarios
• Optimistic estimation on probing primordial gravitational waves with CMB B-mode polarization
• Cosmological Zoom-In Simulations of Milky Way Host Mass Dark Matter Halos with a Blue-Tilted Primordial Power Spectrum
• Thermodynamics of the Primordial Universe
• An updated dark energy view of inflation
• Measuring the modified gravitational waves propagation beyond general relativity from CMB observations
• Slow-roll, acceleration, the Big Rip and WKB approximation in NLS-type formulation of scalar field cosmology
• Inflation in the Generalized Inverse Power Law Scenario
• Polarization of the Microwave Background: theoretical framework
• Density and Graviton Perturbations in the Cosmic Microwave Background
• On the prior dependence of constraints on the tensor-to-scalar ratio
• Compactification driven Hilltop Inflation in Einstein-Yang-Mills
• Primordial Gravitational Waves in Quadratic Gravity
• Shape of the inflaton potential and the efficiency of the universe heating
• Measuring CMB polarisation with the Planck mission
• Analytic Solutions of Scalar Field Cosmology, Mathematical Structures for Early Inflation and Late Time Accelerated Expansion
• Warm Inflation in $f(Q)$ gravity
• The nature of cosmological singularities in isotropic universes and braneworlds
• What can the anthropic principle tell us about the future of the dark energy universe?
• Probing the primordial Universe from the low-multipole CMB data
• Skewness in the Cosmic Microwave Background Anisotropy from Inflationary Gravity Wave Background
• Inflation and Leptogenesis in a $U(1)$-enhanced supersymmetric model
• Inflation and the cosmic microwave background
• Inflation and Unification
• Cosmic Microwave Background Tests of Inflation
• Simulating first-order phase transition during inflation
• Are latest detected events of gravitational waves in favor of some models of inflation based on string theory?
• Ultra slow-roll with a black hole
• Constraints on the generalized natural inflation after Planck 2018
• The Spectral Index in the CDM Cosmogony
• Scalar-field potential for viable models in $f(R)$ theory
• Symmetry Analysis In Inflationary Cosmology
• On inflationary parameters in scalar-tensor theories
• Dark matter and dark energy from pockets of gravity created by quantum tunneling of the inflaton potential
• Theoretical and observational aspects of cosmological inflation