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The geometry of inflationary observables: lifts, flows, equivalence classes. (arXiv:2308.00032v1 [gr-qc])

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The Eisenhart lift allows to formulate the dynamics of a scalar field in a
potential as pure geodesic motion in a curved field-space manifold involving an
additional fictitious vector field. Making use of the formalism in the context
of inflation, we show that the main inflationary observables can be expressed
in terms of the geometrical properties of a two-dimensional uplifted
field-space manifold spanned by the time derivatives of the scalar and the
temporal component of the vector. This allows to abstract from specific
potentials and models and describe inflation solely in terms of the flow of
geometric quantities. Our findings are illustrated through several inflationary
examples previously considered in the literature.

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