Exact hyperbolic-sine scalar-field cosmology
In
a flat
universe containing
a homogeneous canonical
scalar field, the
ansatzhas the exact solution
H=λMPl2ϕ02coth(2λt),a=a0[sinh(2λt)]ϕ02/(2MPl2).
It interpolates between decelerating
power-law expansion at early
times and exponential accelerated expansion at late
times when
2/3<ϕ02/MPl2<2.