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We present a method for furnishing flat Friedman-Robertson-Walker spacetimeswith nearly arbitrary dynamics in an important subclass of cubic Horndeskitheory -- specifically shift-symmetric, cubic Horndeski theory with a vanishingconserved current. This builds on insight from previous work on theconstruction of static and spherically-symmetric hairy spacetimes in the samesector. The method is explicitly demonstrated by deriving exact analyticalsolutions describing an inflating universe and several power-law expansionscenarios, and by showing how the predicted evolution of the Hubble parameterin $\Lambda$CDM can be fit to a particular choice of Horndeski model function.We fully characterize the classes of cosmological models that cannot begenerated purely by selecting a Horndeski model function.

Tailoring cosmologies in cubic shift-symmetric Horndeski gravity