A statistical approach to multifield inflation: many-field perturbations beyond slow roll

Abstract

We study multifield contributions to the scalar power spectrum in an ensemble of six-field inflationary models obtained in string theory. We identify examples in which inflation occurs by chance, near an approximate inflection point, and we compute the primordial perturbations numerically, both exactly and using an array of truncated models. The scalar mass spectrum and the number of fluctuating fields are accurately described by a simple random matrix model. During the approach to the inflection point, bending trajectories and violations of slow roll are commonplace, and 'many-field' effects, in which three or more fields influence the perturbations, are often important. However, in a large fraction of models consistent with constraints on the tilt the signatures of multifield evolution occur on unobservably large scales. Our scenario is a concrete microphysical realization of quasi-singlefield inflation, with scalar masses of order H, but the cubic and quartic couplings are typically too small to produce detectable non-Gaussianity. We argue that our results are characteristic of a broader class of models arising from multifield potentials that are natural in the Wilsonian sense.

Inflation and String Theory

“…This suggests that the basic phenomenology is again that of inflection point inflation, and a number of numerical investigations [240,255,535,642,643] have confirmed this expectation.…”

“…26 Then, as explained in Appendix C, the fluctuations of fields transverse to the inflationary trajectory make strictly positive contributions to ∆ 2 R : see (C.107). As such, the contributions of additional fields actually strengthen the Lyth bound, increasing the displacement ∆φ required to produce a given observed value of r. The bound can be (rather weakly) violated if the slow-roll, slow-turn approximations assumed above are invalid: fluctuations of additional fields can then contribute negatively to ∆ 2 R , increasing the effective value of r -see [255] for explicit examples. However, we are not aware of a plausible construction in which this effect is large enough to induce a meaningful weakening of the bound (2.106).…”

“…1 These fields fluctuation quantum-mechanically during inflation and therefore have to be included in the computation of the primordial perturbations. The phenomenology of these models of quasisingle-field inflation [490] has been explored in [118,207,208,239,255,265,267,[491][492][493][494][495][496][497].…”

“…Although numerical experiments in the particular example of warped Dbrane inflation (see §5.1) give strong evidence that six fields can be large enough for universality to take hold [240,535], much remains to be learned about the statistics of general multi-field models -see [255,488,[536][537][538][539][540][541][542] for related work.…”

“…through brane-antibrane annihilation, provides a setting in which fields that can otherwise be omitted from the effective theory play a role: strong violations of the adiabatic approximation allow very massive fields to contribute to the dynamics, as further discussed in §5.6. Furthermore, the existence of multiple light fields can lead to 'modulated reheating', in which the dominant contribution to the temperature anisotropies arises from spatial variations in the couplings between the inflaton and the visible sector, or to the conversion of entropic perturbations to curvature perturbations: investigations of these effects in string theory include [563,566] and [255,535,552], respectively. Finally, condensation of a complex tachyon produces a network of topological defects, cosmic strings, which have striking signatures, as we now explain.…”