“…In Einstein's theory, an effective perfect fluid description can be given for a canonical, minimally coupled scalar field φ [11][12][13][14][15], and this fact is well known for special spacetimes, such as the Friedmann-Lemaître-Robertson-Walker (FLRW) spaces used in cosmology. Roughly speaking, fixing the scalar field potential V (φ) corresponds to prescribing the equation of state of the fluid, but this is not a one-to-one correspondence [12,[16][17][18][19]. The effective fluid description of more general theories containing a scalar field, such as k-essence and special cases of Horndeski gravity, has been worked out in detail with respect to cosmological perturbations or to general spacetimes [18][19][20][21].…”