Perturbative analysis of multiple-field cosmological inflation (Q2368904)

\noindent Cosmological observations suggest that the early universe underwent a period of accelerated expansion called inflation. In current cosmology, the inflationary paradigm is considered as an elegant solution of various problems arising in the context of the standard hot big-bang. In addition to providing a causal mechanism for the generation and evolution of large-scale structure formation, inflation also leads to solutions of a number of cosmological problems such as the isotropy, horizon and flatness problem of the universe [\textit{A. D. Linde}, Particle Physics and Inflationary Cosmology. Harwood Academic Publishers, Chur, Switzerland (1990); \textit{P. J. E. Peebles}, Principles of Physical Cosmology. Princeton University Press, Princeton, New Jersey (1993); \textit{A. R. Liddle, D. H. Lyth}, Cosmological Inflation and Large-Scale Structure. Cambridge University Press, (Cambridge, New York, Melbourne) (2000; Zbl 0952.83001)]. A necessary condition for the cosmological inflation phenomenon to occur is that the energy density of the early stage of the universe be dominated by the vacuum energy of a scalar field. The quantum fluctuations of the scalar field generated during the inflation process become classical after crossing the event horizon, seeding the observed density perturbations. The paper under review presents the equations describing multi-component scalar fields with a non--trivial field metric and non-minimal kinetic terms coupled to Einstein gravity. Such a kinetic term appears in various models of high-energy physics. By introducing families of orthogonal projectors, multiple--field effects can be discriminated from single-field effects. The article also studies metric perturbations which are conveniently decomposed into scalar, vector, and tensor modes [\textit{N. Straumann}, On the cosmological constant problems and the astronomical evidence for a homogeneous energy density with negative pressure. Poincaré Seminar 2002, Vacuum Energy, Renormalization, Birkhäuser Verlag, Basel, 7--51 (2003; Zbl 1054.83044)], as well as post-inflationary, adiabatic and isocurvature perturbations. In this context, the power spectra and spectral indices for adiabatic, isocurvature, correlated, and tensor modes are calculated at the first order slow-roll approximation for a comparison of the theoretical predictions of various inflationary models with cosmological observations.