  We explore entanglement entropy of a cap-like region for a generic quantum
field theory residing in the Bunch-Davies vacuum on de Sitter space.
Entanglement entropy in our setup is identical with the thermal entropy in the
static patch of de Sitter, and we derive a simple relation between the vacuum
expectation value of the energy-momentum tensor trace and the RG flow of
entanglement entropy. In particular, renormalization of the cosmological
constant and logarithmic divergence of the entanglement entropy are
interrelated in our setup. We confirm our findings by recovering known
universal contributions for a free field theory deformed by a mass operator as
well as obtain correct universal behaviour at the fixed points. Simple examples
of entanglement entropy flows are elaborated in $d=2,3,4$. In three dimensions
we find that while the renormalized entanglement entropy is stationary at the
fixed points, it is not monotonic. We provide a computational evidence that the
universal `area law' for a conformally coupled scalar is different from the
known result in the literature, and argue that this difference survives in the
limit of flat space. Finally, we carry out the spectral decomposition of
entanglement entropy flow and discuss its application to the F-theorem.
