Nonlinear perturbations of cosmological scalar fields with non-standard kinetic terms

Abstract

We adopt a covariant formalism to derive exact evolution equations for nonlinear perturbations, in a universe dominated by two scalar fields. These scalar fields are characterized by non-canonical kinetic terms and an arbitrary field space metric, a situation typically encountered in inflationary models inspired by string theory. We decompose the nonlinear scalar perturbations into adiabatic and entropy modes, generalizing the definition adopted in the linear theory, and we derive the corresponding exact evolution equations. We also obtain a nonlinear generalization of the curvature perturbation on uniform density hypersurfaces, showing that on large scales it is sourced only by the nonlinear version of the entropy perturbation. We then expand these equations to second order in the perturbations, using a coordinate based formalism. Our results are relatively compact and elegant and enable one to identify the new effects coming from the non-canonical structure of the scalar fields Lagrangian. We also explain how to analyze, in our formalism, the interesting scenario of multifield Dirac-Born-Infeld inflation.

31 pages, no figures. Discussion on multi-field DBI inflation added. Version to be published in JCAP

References in corpus (13)

• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• String Cosmology: A Review
• 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
• Non-gaussianity from the second-order cosmological perturbation
• Multiple field inflation
• Spinflation
• Primordial Non-Gaussianities of General Multiple Field Inflation
• Multifield DBI Inflation and Non-Gaussianities
• N-flation from multiple DBI type actions
• Nonlinear perturbations for dissipative and interacting relativistic fluids

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• Strongly Coupled Perturbations in Two-Field Inflationary Models
• On Classification of Models of Large Local-Type Non-Gaussianity
• A note on the equivalence of a barotropic perfect fluid with a K-essence scalar field
• On the full quantum trispectrum in multi-field DBI inflation
• A general mechanism for producing scale-invariant perturbations and small non-Gaussianity in ekpyrotic models
• Primordial Trispectrum from Entropy Perturbations in Multifield DBI Model
• Primordial Perturbations from Multifield Inflation with Nonminimal Couplings
• Primordial Non-Gaussianities from the Trispectra in Multiple Field Inflationary Models
• Strong scale dependent bispectrum in the Starobinsky model of inflation
• Local non-Gaussianity from rapidly varying sound speeds
• Fields Annihilation and Particles Creation in DBI inflation
• Non-Gaussian Shape Discrimination with Spectroscopic Galaxy Surveys
• The Possibility of Tachyons as Soliton Solutions in 3+1 Dimensions via k-field Models