Slow-roll corrections in multi-field inflation: a separate universes approach

Abstract

In view of cosmological parameters being measured to ever higher precision, theoretical predictions must also be computed to an equally high level of precision. In this work we investigate the impact on such predictions of relaxing some of the simplifying assumptions often used in these computations. In particular, we investigate the importance of slow-roll corrections in the computation of multi-field inflation observables, such as the amplitude of the scalar spectrum P ζ , its spectral tilt n s , the tensor-to-scalar ratio r and the non-Gaussianity parameter f N L . To this end we use the separate universes approach and δN formalism, which allows us to consider slow-roll corrections to the non-Gaussianity of the primordial curvature perturbation as well as corrections to its two-point statistics. In the context of the δN expansion, we divide slow-roll corrections into two categories: those associated with calculating the correlation functions of the field perturbations on the initial flat hypersurface and those associated with determining the derivatives of the e-folding number with respect to the field values on the initial flat hypersurface. Using the results of Nakamura & Stewart '96, corrections of the first kind can be written in a compact form. Corrections of the second kind arise from using different levels of slow-roll approximation in solving for the super-horizon evolution, which in turn corresponds to using different levels of slow-roll approximation in the background equations of motion. We consider four different levels of approximation and apply the results to a few example models. The various approximations are also compared to exact numerical solutions.

Scale invariant extension of the Standard Model: a nightmare scenario in cosmology

“…The crucial difference compared with refs. [104,105] is that our potential V (ϕ I ) in (3.8) boasts a river-valley like structure, which causes complications in calculating the inflationary parameters without using the valley approximation, as we will see. We solve eqs.…”

“…of eq. (3.24), such that φ⊥ φ⊥ in β sr can be small even if φ⊥ is large [105]. In the following figures, In the left panel of figure 5 we show the zoomed trajectory near S = S * (i.e., t = t * ).…”

“…Similar models have been considered for instance in refs. [104,105] to calculate the non-Gaussianity of the curvature perturbation. The crucial difference compared with refs.…”