K-mouflage Cosmology: the Background Evolution
  We study the cosmology of K-mouflage theories at the background level. We
show that the effects of the scalar field are suppressed at high matter density
in the early Universe and only play a role in the late time Universe where the
deviations of the Hubble rate from its $\Lambda$-CDM counterpart can be of the
order five percent for redshifts $1 \lesssim z \lesssim 5$. Similarly, we find
that the equation of state can cross the phantom divide in the recent past and
even diverge when the effective scalar energy density goes negative and
subdominant compared to matter, preserving the positivity of the squared Hubble
rate. These features are present in models for which Big Bang Nucleosynthesis
is not affected. We analyze the fate of K-mouflage when the nonlinear kinetic
terms give rise to ghosts, particle excitations with negative energy. In this
case, we find that the K-mouflage theories can only be considered as an
effective description of the Universe at low energy below $1$ keV. In the safe
ghost-free models, we find that the equation of state always diverges in the
past and changes significantly by a few percent since $z\lesssim 1$.
