Covariant second-order perturbations in generalized two-field inflation

Abstract

We examine the covariant properties of generalized models of two-field inflation, with non-canonical kinetic terms and a possibly non-trivial field metric. We demonstrate that kinetic-term derivatives and covariant field derivatives do commute in a proper covariant framework, which was not realized before in the literature. We also define a set of generalized slow-roll parameters, using a unified notation. Within this framework, we study the most general class of models that allows for well-defined adiabatic and entropic sound speeds, which we identify as the models with parallel momentum and field velocity vectors. For these models we write the exact cubic action in terms of the adiabatic and isocurvature perturbations. We thus provide the tool to calculate the exact non-Gaussianity beyond slow-roll and at any scale for these generalized models. We illustrate our general results by considering their long-wavelength limit, as well as with the example of two-field DBI inflation.

39 pages, no figures, minor changes and clarifications

References in corpus (29)

• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Primordial Non-Gaussianities from Inflation Models
• Non-Gaussianities in two-field inflation
• Primordial perturbations and non-Gaussianities in DBI and general multi-field inflation
• Perturbations in generalized multi-field inflation
• Primordial fluctuations and non-Gaussianities in multi-field DBI inflation
• Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --
• Multi-brid inflation and non-Gaussianity
• Primordial Bispectrum from Multifield Inflation with Nonminimal Couplings
• Non-gaussianity from the second-order cosmological perturbation
• Scale-dependent non-Gaussianity probes inflationary physics
• Large non-Gaussianity from multi-brid inflation
• Spinflation
• Primordial Non-Gaussianity in Multi-Scalar Slow-Roll Inflation
• Primordial Non-Gaussianities of General Multiple Field Inflation
• On the Issue of the ζSeries Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part I: the Bispectrum
• Nflation: non-gaussianity in the horizon-crossing approximation
• On the full quantum trispectrum in multi-field DBI inflation
• Lorentz boost and non-Gaussianity in multi-field DBI-inflation
• Primordial Trispectrum from Entropy Perturbations in Multifield DBI Model
• N-flation from multiple DBI type actions
• Non-Gaussianities in Multifield Inflation: Superhorizon Evolution, Adiabaticity, and the Fate of fnl
• Primordial Non-Gaussianities from the Trispectra in Multiple Field Inflationary Models
• Multi-field G-inflation
• Non-Gaussianity of superhorizon curvature perturbations beyond $\delta$ N formalism
• Note on Non-Gaussianities in Two-field Inflation
• Separable and non-separable multi-field inflation and large non-Gaussianity
• Local non-Gaussianity from rapidly varying sound speeds
• Non-Gaussianities in multi-field DBI inflation with a waterfall phase transition

Cited by in corpus (5)

• Revisiting non-Gaussianity in multifield inflation with curved field space
• Multifield inflation beyond $N_{\mathrm{field}}=2$: non-Gaussianities and single-field effective theory
• The Non-Minimal Ekpyrotic Trispectrum
• Non-Gaussianity in two-field inflation beyond the slow-roll approximation
• Separate universe in multifield inflation: a phase-space approach