If the present universe is slightly open then pre-in ation curvature would appear as a cosmic dark-flow component of the CMB dipole moment. We summarize current cosmological constraints on this cosmic dark ow and analyze the possible constraints on parameters characterizing the pre-in ating universe in an in ation model with a present-day very slightly open ΛCDM cosmology. We employ an analytic model to show that for a broad class of in ation-generating effective potentials, the simple requirement that the observed dipole moment represents the pre-in ation curvature as it enters the horizon allows one to set upper and lower limits on the magnitude and wavelength scale of pre-in ation uctuations in the in aton field and the curvature parameter of the pre-in ation universe, as a function of the fraction of the total initial energy density in the in aton field. We estimate that if the current CMB dipole is a universal dark flow (or if it is near the upper limit set by the Planck Collaboration) then the present constraints on ΛCDM cosmological parameters imply rather small curvature Ωk ~ 0:1 for the pre-in ating universe for a broad range of the fraction of the total energy in the in aton field at the onset of in ation. Such small pre-in ation curvature might be indicative of open-in ation models in which there are two epochs of in ation.

ABSTRACT
1. INTRODUCTION
2. MODEL
3. RESULTS
4. CONCLUSIONS
REFERENCES

• Grant J. Mathews(University of Notre Dame, Center for Astrophysics)
• N. Q. Lan(University of Notre Dame, Center for Astrophysics/Hanoi National University of Education)
• T. Kajino(National Astronomical Observatory of Japan)