Power Spectrum and Signatures for Cascade Inflation

Abstract

The power spectrum of M-theory cascade inflation is derived. It possesses three distinctive signatures: a decisive power suppression at small scales, oscillations around the scales that cross the horizon when the inflaton potential jumps and stepwise decrease in the scalar spectral index. All three properties result from features in the inflaton potential. Cascade inflation realizes assisted inflation in heterotic M-theory and is driven by non-perturbative interactions of N M5-branes. The features in the inflaton potential are generated whenever two M5-branes collide with the boundaries. The derived small-scale power suppression serves as a possible explanation for the dearth of observed dwarf galaxies in the Milky Way halo. The oscillations, furthermore, allow to directly probe M-theory by measurements of the spectral index and to distinguish cascade inflation observationally from other string inflation models.

Figures (2)

• Figure 1: The left graph shows the dependence of $\log P_s(k)$ on $\log k$ for the scales that have crossed the horizon at least once during the last $60$ e-foldings and are still outside the horizon at the end of inflation. It clearly displays the stepwise decrease in the amplitude of the power spectrum. The right graph shows $\log P_s(k)$ vs. $\log k$ around the first transition. The amplitude of oscillations decreases as $k$ increases.
• Figure 2: The left graph shows the dependence of $n_s$ on $\log k$ for the first five inflationary bouts. It clearly displays the stepwise decrease in the spectral index. The right graph shows $n_s$ vs. $\log k$ around the first transition. The period of oscillations decreases as $k$ increases.