A Brachistochrone Approach to Reconstruct the Inflaton Potential

We propose a new way to implement an inflationary prior to a cosmological dataset that incorporates the inflationary observables at arbitrary order. This approach employs an exponential form for the Hubble parameter $H(ϕ)$ without taking the slow-roll approximation. At lowest non-trivial order, this $H(ϕ)$ has the unique property that it is the solution to the brachistochrone problem for inflation.

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