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

Oct 7, 2014
12 pages
Published in:
  • Phys.Lett.B 748 (2015) 132-143
  • Published: Jul 2, 2015
e-Print:
Report number:
  • MIT-CTP-4499

Citations per year

2014201720202023202401234
Abstract: (Elsevier)
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 Δ(x) . We show that for large N , the two-point function is 〈δt(x)δt(0)〉∝Δ2(|x|)/N and the three-point function is 〈δt(x)δt(y)δt(0)〉∝Δ(|x−y|)Δ(|x|)Δ(|y|)/N2 . 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 .
Note:
  • 15 pages in double column format, 6 figures. V2: Further clarifications, updated to coincide with version published in Physics Letters B
  • density: perturbation
  • inflation: hybrid
  • power spectrum: density
  • model: hybrid
  • inflation: model
  • power spectrum: primordial
  • defect: stability
  • n-point function: 3
  • correlation function
  • cosmic background radiation