A Density Spike on Astrophysical Scales from an N-Field Waterfall Transition

Abstract

Hybrid inflation models are especially interesting as they lead to a spike in the density power spectrum on small scales, compared to the CMB, while also satisfying current bounds on tensor modes. Here we study hybrid inflation with $N$ waterfall fields sharing a global $SO(N)$ symmetry. The inclusion of many waterfall fields has the obvious advantage of avoiding topologically stable defects for $N>3$. We find that it also has another advantage: it is easier to engineer models that can simultaneously (i) be compatible with constraints on the primordial spectral index, which tends to otherwise disfavor hybrid models, and (ii) produce a spike on astrophysically large length scales. The latter may have significant consequences, possibly seeding the formation of astrophysically large black holes. We calculate correlation functions of the time-delay, a measure of density perturbations, produced by the waterfall fields, as a convergent power series in both $1/N$ and the field's correlation function $\Delta (x)$. We show that for large $N$, the two-point function is $<\delta t(\mathbf{x})\delta t(0)>\propto {\Delta }^2(|\mathbf{x}|)/N$ and the three-point function is $<\delta t(\mathbf{x})\delta t(\mathbf{y})\delta t(0)>\propto \Delta (|\mathbf{x}-\mathbf{y}|)\Delta (|\mathbf{x}|)\Delta (|\mathbf{y}|)/N^2$. In accordance with the central limit theorem, the density perturbations on the scale of the spike are Gaussian for large $N$ and non-Gaussian for small $N$.

15 pages in double column format, 6 figures. V2: Further clarifications, updated to coincide with version published in Physics Letters B

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• Non-minimal gravitational reheating during kination
• Primordial Black Holes from Multifield Inflation with Nonminimal Couplings
• Influence of large local and non-local bispectra on primordial black hole abundance
• Can massive primordial black holes be produced in mild waterfall hybrid inflation?
• The long-short wavelength mode coupling tightens primordial black hole constraints
• Mechanisms of Producing Primordial Black Holes By Breaking The SU(2,1)/SU(2)$\times$U(1) Symmetry
• Tensor Spectra Templates for Axion-Gauge Fields Dynamics during Inflation
• On the primordial black hole formation in hybrid inflation
• Galactic Geology: Probing Time-Varying Dark Matter Signals with Paleo-Detectors
• Hawking Radiation Signatures from Primordial Black Holes Transiting the Inner Solar System: Prospects for Detection
• Stochastic-tail of the curvature perturbation in hybrid inflation
• Calculating the power spectrum in stochastic inflation by Monte Carlo simulation and least squares curve fitting