Abstract
We re-examine the importance of slow-roll corrections during the evolution of cosmological perturbations in models of multi-field inflation. We find that in many instances the presence of light degrees of freedom leads to situations in which next to leading order slow-roll corrections become significant. Examples where we expect such corrections to be crucial include models in which modes exit the Hubble radius while the inflationary trajectory undergoes an abrupt turn in field space, or during a phase transition. We illustrate this with several examples — hybrid inflation, double quadratic inflation and double quartic inflation. Utilizing both analytic estimates and full numerical results, we find that corrections can be as large as 20%. Our results have implications for many existing models in the literature, as these corrections must be included to obtain accurate observational predictions — particularly given the level of accuracy expected from CMB experiments such as Planck.
Highlights
The inflationary paradigm [1, 2] remains a convincing causal mechanism for providing the needed initial conditions of the early universe – despite scrutiny from a wealth of precision cosmological observations [3, 4]
We emphasize that the isocurvature modes will source the curvature perturbations, but this is a next-order effect in the slow-roll parameters not involving ηss and can be neglected around Hubble radius crossing, as we have argued previously7
Taking N to be the e-fold at which the mode of interest crossed the Hubble radius and applying Eqs.(3.10a)–(3.10c), we find that the instantaneous power spectra for R and S can be written as PR = P 1 +
Summary
The inflationary paradigm [1, 2] remains a convincing causal mechanism for providing the needed initial conditions of the early universe – despite scrutiny from a wealth of precision cosmological observations [3, 4] (see [5, 6] for reviews). These fields typically influence the dynamics and may even help drive inflation, leading to multi-field models (early examples are [9, 10]) In such situations the curvature perturbation does not necessarily remain constant on super-Hubble scales, resulting in new theoretical challenges as well as richer possibilities for observations [11,12,13,14,15,16,17,18,19]. A common and useful tool for analyzing multi-field models is the so-called δN formalism [26,27,28], which allows to calculate the power spectrum of the curvature perturbations to leading order in the gradient expansion and to all orders in the slow-roll parameters This approach has led to interesting and quite restrictive bounds on multi-field inflation models from primordial non-gaussianity [29,30,31,32]. The appendix collects additional formulae necessary to compute the power spectra
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