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

• Published in: Journal of cosmology and astroparticle physics Vol. 2009; no. 1; p. 012
• Main Authors: Renaux-Petel, Sébastien, Tasinato, Gianmassimo
• Format: Journal Article
• Language: English
• Published: United States IOP Publishing 01.01.2009; Institute of Physics (IOP)
• Subjects: Astrophysics; ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BORN-INFELD THEORY; Cosmology and Extra-Galactic Astrophysics; DISTURBANCES; ENTROPY; General Relativity and Quantum Cosmology; High Energy Physics - Theory; INFLATIONARY UNIVERSE; LAGRANGIAN FUNCTION; MATHEMATICAL EVOLUTION; METRICS; NONLINEAR PROBLEMS; Physics; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; SCALAR FIELDS; Sciences of the Universe; STRING MODELS; STRING THEORY
• ISSN: 1475-7516; 1475-7508; 1475-7516
• DOI: 10.1088/1475-7516/2009/01/012

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 multi-field Dirac-Born-Infeld inflation.