  We find the best-fit cosmological parameters for a scenario of inflation with
only the sufficient amount of accelerated expansion for the $\lambda\phi^4$
potential. While for the simplest scenario of chaotic inflation all observable
primordial fluctuations cross the Hubble horizon during the slow-roll epoch,
for the scenario of just-enough inflation the slow-roll conditions are violated
at the largest length scales. Performing a numerical mode-by-mode integration
for the perturbations on the largest scales and comparing the predicted
anisotropies of the cosmic microwave background to results from the WMAP 7-yr
data analysis, we find the initial conditions in agreement with current
cosmological data. In contrast to the simplest chaotic model for the quartic
potential, the just-enough inflation scenario is not ruled out. Although this
scenario naturally gives rise to a modification of the first multipoles, for a
quartic potential it cannot explain the lack of power at the largest angular
scales.
