New nonlinear instability for scalar fields

In this Letter, we introduce the nonlinear partial differential equation ∂2τπ∝(→∇π)2 showing a new type of instability. Such equations appear in the effective field theory (EFT) of dark energy for the k-essence model as well as in many other theories based on the EFT formalism. We demonstrate the occurrence of instability in the cosmological context using a relativistic N-body code, and we study it mathematically in 3+1 dimensions within spherical symmetry. We show that this term dominates for the low speed of sound limit where some important linear terms are suppressed