The no-go theorem for non-singular cosmologies is extended from single scalar Horndeski theories to multiple scalar fields (multi-Galileons).

While it was previously established that a single scalar degree of freedom cannot drive a classically stable, singularity-free cosmological background (e.g. with a bounce in the early Universe instead of a Big Bang), one may have wondered whether multiple, potentially interacting, scalar fields may have avoided the no-go theorem. Here it is shown that, for generalized multi-Galileons, it remains impossible to have a singularity-free cosmology (potentially up to some finely tuned boundary conditions). Therefore, it would seem that, in order to have a stable bounce with scalar fields, one needs to include genuinely higher derivative interactions (rather than just more degrees of freedom).