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-single-field 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.

Figures (17)

• Figure 1: A single-field inflection point potential, taken from Baumann:2007ah. If the inflaton is above the inflection point 60 e-folds before the end of inflation, $V"> 0$ and the scalar power spectrum is blue, as indicated by the shading. A red spectrum requires that the inflaton has passed the inflection point 60 or more e-folds before the end of inflation.
• Figure 2: The mass spectra of the six scalar fields, in units of $H^2$. The leftmost peak, which has support at tachyonic values, corresponds to the lightest (adiabatic) field $\psi_1$. The next peak corresponds to the second-lightest field $\psi_2$. The third peak corresponds to $\psi_3$ and $\psi_4$, which are nearly degenerate in each realization, and the broad final peak similarly corresponds to $\psi_5$ and $\psi_6$.
• Figure 3: The mass spectrum simulated in the matrix model given in equation (\ref{['abc']}), cf. MMW. Comparing to Fig. \ref{['spectrumofall']}, we see that the model is in good qualitative agreement with the results of simulations in the ensemble of inflaton potentials.
• Figure 4: Histogram showing the relative probability of the number $n_f$ of scalar fields that are light enough to fluctuate during inflation, cf. equation (\ref{['nf']}).
• Figure 5: The mass-squared of the adiabatic fluctuation in units of $H$, evaluated 60 e-folds before the end of inflation, versus the total number of e-folds, $N_e$.