How many efolds should we expect from highscale inflation?
Abstract
We address the issue of how many efolds we would naturally expect if inflation occurred at an energy scale of order ^{1016} GeV. We use the canonical measure on trajectories in classical phase space, specialized to the case of flat universes with a single scalar field. While there is no exact analytic expression for the measure, we are able to derive conditions that determine its behavior. For a quadratic potential V_{(ϕ)=m2ϕ2/2 with m =2×1013 GeV and cutoff at MPl}=2.4×^{1018} GeV, we find an expectation value of 2×10^{10} efolds on the set of FriedmannRobertsonWalker trajectories. For cosine inflation V(ϕ)=Λ4[1cos(ϕ/f)] with f =1.5×10^{19} GeV, we find that the expected total number of efolds is 50, which would just satisfy the observed requirements of our own Universe; if f is larger, more than 50 efolds are generically attained. We conclude that one should expect a large amount of inflation in largefield models and more limited inflation in smallfield (hilltop) scenarios.
 Publication:

Physical Review D
 Pub Date:
 September 2014
 DOI:
 10.1103/PhysRevD.90.063517
 arXiv:
 arXiv:1405.5538
 Bibcode:
 2014PhRvD..90f3517R
 Keywords:

 98.80.Cq;
 98.80.Jk;
 98.80.Bp;
 Particletheory and fieldtheory models of the early Universe;
 Mathematical and relativistic aspects of cosmology;
 Origin and formation of the Universe;
 High Energy Physics  Theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 13 pages, 4 figures. PRD version