The Hot Big Bang model of cosmology requires very finely-tuned initial conditions in order to explain the degree of flatness and homogeneity we observe in the Universe today. This has led the community to embrace the theory of inflation, since it readily explains these features. But are the initial conditions required to initiate inflation more or less finely-tuned than those required by the Hot Big Bang? Although there are several qualitative arguments to suggest that inflation should happen generically, attempts to quantify these have led to ambiguous answers due to the infinite measure of the total phase space. Previous studies have regularised this measure to get an unambiguous answer, but the results are strongly dependent on the regularisation technique used with some authors concluding that inflation is exponentially likely while others conclude that it is exponentially unlikely.
The Eisenhart lift, which was recently applied to field theories for the first time, is a technique that allows one to convert a theory described by a Lagrangian into an equivalent geometric system. Applying the Eisenhart lift to inflation, one can construct a manifold such that each point represents a different initial condition. Both the total volume of this manifold and the volume that leads to inflation is finite. Thus, we can finally answer quantitatively how finely-tuned the initial conditions of inflation are without the need for a regulator.