  We consider solutions to the Einstein-massless-scalar field system with a
positive cosmological constant, arising from sufficiently regular, near-FLRW,
initial data. We establish global existence in the future direction and derive
their precise asymptotic behavior towards infinity. As a corollary, we infer
that, unlike the FLRW background, the perturbed solutions do not describe a
regular irrotational stiff fluid with linear equation of state $p=\rho$, for
general asymptotic data at infinity. The reason for the breakdown of this
interpretation is that the gradient of the scalar field stops being timelike at
large times, eventually becoming null and then spacelike near infinity. Our
results hold for open sets of initial data in Sobolev spaces without
symmetries.
