The effective two-dimensional phase space of cosmological scalar fields

It has been shown by Remmen and Carroll that, for a model universe which contains only a kinetically canonical scalar field minimally coupled to gravity it is possible to choose 'special coordinates' to describe a two-dimensional effective phase space. The special, non-canonical, coordinates are $ϕ$,$\dotϕ$ and the ability to describe an effective phase space with these coordinates empowers the common usage of $ϕ-\dotϕ$ as the space to define inflationary initial conditions. This paper extends the result to the full Horndeski action. The existence of a two-dimensional effective phase space is shown for the general case. Subsets of the Horndeski action, relevant to cosmology are considered as particular examples to highlight important aspects of the procedure.

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