From Physical Review D:
We investigate the initial conditions of inflation in a Bianchi I universe that is homogeneous but not isotropic. We use the Eisenhart lift to describe such a theory geometrically as geodesics on a field-space manifold. We construct the phase-space manifold of the theory by considering the tangent bundle of the field space and equipping it with a natural metric. We find that the total volume of this manifold is finite for a wide class of inflationary models. We therefore take the initial conditions to be uniformly distributed over it in accordance with Laplace’s principle of indifference. This results in a normalizable, reparametrization invariant measure on the set of initial conditions of inflation in a Bianchi I universe. We find that this measure favors an initial state in which the inflaton field is at or near its minimum, with a mild preference for some initial anisotropy. Since inflation requires an initial field value with a large displacement from its minimum, we therefore conclude that the theory of inflation requires finely tuned initial conditions.
Kieran Finn, Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
Note: “Since inflation requires an initial field value with a large displacement from its minimum, we therefore conclude that the theory of inflation requires finely tuned initial conditions.”
“Thus, under this measure, initial conditions that lead to significant inflation are indeed finely tuned.”
“It is therefore far from clear that inflation truly solves the fine-tuning puzzles that it was designed for.”
Paper. (paywall)
A number of popular science writers will not like this. They love to talk about a universe accidentally barfing itself into existence.