Modified Lyth bound and implications of BICEP2 results

Abstract

To reconcile the BICEP2 measurement on the tensor-to-scalar ratio $r$ with Planck constraint, a large negative running of scalar spectral index $n_s$ is needed. So the inflationary observable such as $n_s$ should be expanded at least to the second-order slow-roll parameters for single-field inflationary models. The large value of $r$ and the Lyth bound indicate that it is impossible to obtain the sub-Planckian excursion for the inflaton. However, we derive an absolutely minimal bound $\Delta \varphi /M_{\mathrm{Pl}}>\sqrt{r/2}$ on the inflaton excursion for single-field inflationary models, which can be applied to non-slow-roll inflationary models as well. This bound excludes the possibility of the small-field inflation with $\Delta \varphi <0.1M_{\mathrm{Pl}}$ if the BICEP2 result on $r$ stands and it opens the window of sub-Planckian excursion with $\Delta \varphi <M_{\mathrm{Pl}}$ even if $r$ is as large as $0.1$. To get the sub-Planckian excursion with $\Delta \varphi <0.1M_{\mathrm{Pl}}$, our modified bound requires $r<0.02$. Using a fifth-order polynomial potential as an explicit example, we show that it not only agrees with the observational results, but also violates the Lyth bound.

arXiv commentv2: major revision, more discussion on the derivation of the modified Lyth bound is added,main conclusions remain unchanged. PRD in press

References in corpus (102)

• Planck 2013 results. XVI. Cosmological parameters
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• Particle Physics Models of Inflation and the Cosmological Density Perturbation
• Planck 2013 results. I. Overview of products and scientific results
• BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales
• Hybrid Inflation
• Planck 2013 results. XXII. Constraints on inflation
• False Vacuum Inflation with Einstein Gravity
• Encyclopaedia Inflationaris
• What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?
• Large Scale Structure and Supersymmetric Inflation without Fine Tuning
• A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation
• A Measurement of the Damping Tail of the Cosmic Microwave Background Power Spectrum with the South Pole Telescope
• Natural Chaotic Inflation in Supergravity
• Hilltop Inflation
• A universal attractor for inflation at strong coupling
• Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity
• The Atacama Cosmology Telescope: Temperature and Gravitational Lensing Power Spectrum Measurements from Three Seasons of Data
• No-Scale Supergravity Realization of the Starobinsky Model of Inflation
• Inflation, Supergravity and Superstrings
• New models of chaotic inflation in supergravity
• General inflaton potentials in supergravity
• Higgs inflation still alive
• The Density Perturbation Power Spectrum to Second-Order Corrections in the Slow-Roll Expansion
• F-term Axion Monodromy Inflation
• D7-Brane Chaotic Inflation
• Supergravity based inflation models: a review
• String Inflation After Planck 2013
• Non-Bunch-Davies Initial State Reconciles Chaotic Models with BICEP and Planck
• Polynomial Chaotic Inflation in the Planck Era
• The Imaginary Starobinsky Model
• Observable gravitational waves from inflation with small field excursions
• Aligned Natural Inflation in String Theory
• Reconciliation of High Energy Scale Models of Inflation with Planck
• M-flation: Inflation From Matrix Valued Scalar Fields
• Cosmic Microwave Background Observables of Small Field Models of Inflation
• Trace-anomaly driven inflation in modified gravity and the BICEP2 result
• An accurate bound on tensor-to-scalar ratio and the scale of inflation
• Polynomial Chaotic Inflation in Supergravity
• The Lyth Bound Revisited
• Natural Chaotic Inflation and UV Sensitivity
• A No-Scale Framework for Sub-Planckian Physics
• Solving the $\eta$-Problem in Hybrid Inflation with Heisenberg Symmetry and Stabilized Modulus
• Hierarchical Axion Inflation
• Resurrecting Quadratic Inflation in No-Scale Supergravity in Light of BICEP2
• New inflation in supergravity with a chaotic initial condition
• Can topological defects mimic the BICEP2 B-mode signal?
• Chaotic Inflation in Supergravity with Heisenberg Symmetry
• Towards large r from [p,q]-inflation
• Observational implications of mattergenesis during inflation
• ${\varphi }^2$ or Not ${\varphi }^2$: Testing the Simplest Inflationary Potential
• BICEP2 implications for single-field slow-roll inflation revisited
• Polynomial inflation models after BICEP2
• Suppressing the impact of a high tensor-to-scalar ratio on the temperature anisotropies
• Discovery of Large Scale Tensor Mode and Chaotic Inflation in Supergravity
• Gauged M-flation, its UV sensitivity and Spectator Species
• Natural Double Inflation in Supergravity
• Supergravity Inflation with Broken Shift Symmetry and Large Tensor-to-Scalar Ratio
• Running Spectral Index from Large-field Inflation with Modulations Revisited
• New inflation in supergravity after Planck and LHC
• Complexified Starobinsky Inflation in Supergravity in the Light of Recent BICEP2 Result
• Comprehensive analysis of the simplest curvaton model
• Axion monodromy inflation with multi-natural modulations
• Steps to Reconcile Inflationary Tensor and Scalar Spectra
• The challenge for single field inflation with BICEP2 result
• Higgs Chaotic Inflation and the Primordial B-mode Polarization Discovered by BICEP2
• Is Higgs Inflation Dead?
• Dynamical Chaotic Inflation in the Light of BICEP2
• Supersymmetric topological inflation model
• Constraining $\mathcal{N}=1$ supergravity inflation with non-minimal Kähler operators using $\delta N$ formalism
• Inflation, Symmetry, and B-Modes
• Sub-Planckian Two-Field Inflation Consistent with the Lyth Bound
• Primordial tensor modes from quantum corrected inflation
• Gravitational quantum effects on power spectra and spectral indices with higher-order corrections
• Inflation After False Vacuum Decay: New Evidence from BICEP2
• Towards Matter Inflation in Heterotic String Theory
• Notes on natural inflation
• The Gravitational Wave Background and Higgs False Vacuum Inflation
• Testing Hybrid Natural Inflation with BICEP2
• Sneutrino Chaotic Inflation and Landscape
• No-Scale Ripple Inflation Revisited
• Evading the Lyth Bound in Hybrid Natural Inflation
• S-dual Inflation: BICEP2 data without unlikeliness
• Axion monodromy inflation with sinusoidal corrections
• TeV scale seesaw from supersymmetric Higgs-lepton inflation and BICEP2
• Gravitational quantum effects in the light of BICEP2 results
• Chaotic Inflation in No-Scale Supergravity with String Inspired Moduli Stabilization
• Reconstructing the Local Potential of Inflation with BICEP2 data
• Chaotic inflation with curvaton induced running
• Natural Inflation with Natural Trans-Planckian Axion Decay Constant from Anomalous $U(1{)}_X$
• Observational Consequences of a Landscape: Epilogue
• The Simple Single Field Inflation Models and the Running of Spectral Index
• Fractional chaotic inflation in the lights of PLANCK and BICEP2
• Do Mixed States save Effective Field Theory from BICEP?
• Killing the Straw Man: Does BICEP Prove Inflation at the GUT Scale?
• Large tensor spectrum of BICEP2 in the natural SUSY hybrid model
• Does the BICEP2 Observation of Cosmological Tensor Modes Imply an Era of Nearly Planckian Energy Densities?
• Primordial gravitational wave of BICEP2 from dynamical double hybrid inflation
• Hint of relic gravitational waves in the Planck and WMAP data
• Tensor-induced B modes with no temperature fluctuations
• Radiative Inflation and Dark Energy RIDEs Again after BICEP2
• Intermediate inflation under the scrutiny of recent data

Cited by in corpus (21)

• Primordial black holes and second order gravitational waves from ultra-slow-roll inflation
• Higgs inflation from Standard Model criticality
• Inflationary models with non-minimally derivative coupling
• The reconstruction of inflationary potentials
• Reconstruction of constant slow-roll inflation
• Gauge transformation of scalar induced tensor perturbation during matter domination
• Reconstruction of extended inflationary potentials for attractors
• Can CMB data constrain the inflationary field range?
• PPN parameters in gravitational theory with nonminimally derivative coupling
• Perfect fluid and F(T) gravity descriptions of inflationary universe and comparison with obervational data
• $\alpha$-attractor from superconformal E-models in brane inflation
• Energy Density, Temperature and Entropy Dynamics in Perturbative Reheating
• Variable Inflaton Equation of State and Reheating
• Clearing the Brush: The Last Stand of Solo Small Field Inflation
• Natural Higgs Inflation, Gauge Coupling Unification, and Neutrino Masses
• Lyth Bound, eternal inflation and future cosmological missions
• Generically large nongaussianity in small multifield inflation
• Confronting the Potential-driven DBI-inspired nonminimal kinetic coupling (Dinkic) inflation to the observational data
• Classical and quantum cosmology of $f(R)$ gravity's rainbow in Schutz's formalism
• The Upper Bound on the Tensor-to-Scalar Ratio Consistent with Quantum Gravity
• A note on supergravity inflation in braneworld