Horizon-preserving dualities and perturbations in non-canonical scalar field cosmologies

Understand

We generalize the cosmological duality between inflation and cyclic contraction under the interchange $a \leftrightarrow H$ to the case of non-canonical scalar field theories with varying speed of sound.

• The single duality in the canonical case generalizes to a family of three dualities constructed to leave the cosmological acoustic horizon invariant.
• We find three classes of models: (I) DBI inflation, (II) the non-canonical generalization of cyclic contraction, and (III) a new cosmological solution with rapidly decreasing speed of sound and relatively slowly growing scale factor, which we dub {\it stalled} cosmology.
• We construct dual analogs to the inflationary slow roll approximation, and solve for the curvature perturbation in all three cases.