Relating Spectral Indices to Tensor and Scalar Amplitudes in Inflation

Abstract

Within an expansion in slow-roll inflation parameters, we derive the complete second-order expressions relating the ratio of tensor to scalar density perturbations and the spectral index of the scalar spectrum. We find that ``corrections'' to previously derived formulae can dominate if the tensor to scalar ratio is small. For instance, if $V{V}^{\prime \prime }/(V^{\prime }{)}^2\ne 1$ or if $m_{Pl}^2/(4π) ~|V'''/V'|\ga 1$, where $V(\varphi )$ is the inflaton potential and $m_{Pl}$ is the Planck mass, then the previously used simple relations between the indices and the tensor to scalar ratio fails. This failure occurs in particular for natural inflation, Coleman--Weinberg inflation, and ``chaotic'' inflation.

18 pages, LaTeX, no figures, FNAL--PUB--94/046-A; CfPA 94-th-14 (small revisions only, esp. examples for hybrid inflation)

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• Primordial Spectral Indices from Generalized Einstein Theories
• Production and detection of relic gravitons in quintessential inflationary models
• A generic estimate of trans-Planckian modifications to the primordial power spectrum in inflation
• Induced gravity inflation in the standard model of particle physics
• The Density Perturbation Power Spectrum to Second-Order Corrections in the Slow-Roll Expansion
• Inflation: flow, fixed points and observables to arbitrary order in slow roll
• Cosmic microwave background measurements can discriminate among inflation models
• A Hamilton-Jacobi approach to non-slow-roll inflation
• Density Perturbations of Quantum Mechanical Origin and Anisotropy of the Microwave Background
• Primordial magnetic fields from inflation?
• Quasi Single Field Inflation in the non-perturbative regime
• Slow-roll parameters in braneworld cosmologies
• The precision of slow-roll predictions for the CMBR anisotropies
• Structure of Primordial Gravitational Waves Spectrum in a Double Inflationary Model
• Chaotic inflation, radiative corrections and precision cosmology
• Second-Order Reconstruction of the Inflationary Potential
• Non--Gaussian Effects in the Cosmic Microwave Background from Inflation
• The Gravitational-Wave contribution to the CMB anisotropies
• On the reliability of inflaton potential reconstruction
• Extended open inflationary universes
• Simplified Smooth Hybrid Inflation in Supersymmetric SU(5)
• Single-field inflation à la generalized Chaplygin gas
• Polynomial Hybrid Inflation
• Lambda-inflation and CMB anisotropy
• Can induced gravity isotropize Bianchi I, V, or IX Universes?
• An Alternative Framework for E-Model Inflation in Supergravity
• S-dual Inflation and the String Swampland
• Obtaining a scalar fifth force via a broken-symmetry couple between the scalar field and matter
• Quantum Smearing in Hybrid Inflation with Chaotic Potentials
• Probing single-field inflation: predictions, constraints, and theoretical viewpoints