Predictions of just-enough inflation
  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. 
Erandy Ramirez, Dominik J. Schwarz
astro-ph.CO gr-qc hep-th