Non-screening of the Cosmological Background in K-mouflage modified
  gravity
  We describe the effects of the cosmological background on the K-mouflage
screening properties of an astrophysical structure. We show that the K-mouflage
screening of the spatial gradients of the scalar field, i.e. the screening of
the fifth force, happens inside a dynamically generated screening radius. This
radius is smaller than the location where the quasistatic approximation, i.e.
where the spatial gradients exceed the time derivative, holds. Even though this
quasistatic radius is much smaller than the size of the matter overdensity,
spatial gradients remain well described by the quasistatic approximation up to
the horizon. Cosmologically we find that the time derivatives can remain
dominant at redshifts $z\gtrsim 2$, when the cosmic web shows a faster growth.
Despite the existence of K-mouflage screening, we confirm that the values of
the scalar field itself are still dominated by the cosmological background,
down to the center of the matter overdensity, and that for instance the time
drift of Newton's constant due to the large-scale cosmological evolution highly
constrains K-mouflage models.
