In this paper, therefore, we explore the possibility that the universe is slightly open with Ω0 ≈ . In this case a glimpse of preinflation fluctuations could just now be entering the horizon before the universe becomes totally dark-energy dominated and flat. Our goal, therefore, is to determine what constraints might be placed on inhomogeneities and curvature content in the preinflation universe based upon current cosmological observations. | PHYSICAL REVIEW D 92 123514 2015 Constraints on preinflation fluctuations in a nearly flat open ΛCDM cosmology G. J. Mathews 1 2 . Suh 1 N. Q. Lan 3 and T. Kajino2 4 1 University of Notre Dame Center for Astrophysics Notre Dame Indiana 46556 USA 2 National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka Tokyo 181-8588 Japan 3 Department of Physics Hanoi National University of Education 136 Xuan Thuy Cau Giay Hanoi 100000 Vietnam 4 Department of Astronomy Graduate School of Science The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-0033 Japan Received 30 May 2014 revised manuscript received 26 June 2015 published 11 December 2015 We analyze constraints on parameters characterizing the preinflating universe in an open inflation model with a present slightly open ΛCDM universe. We employ an analytic model to show that for a broad class of inflation-generating effective potentials the simple requirement that some fraction of the observed dipole moment represents a preinflation isocurvature fluctuation allows one to set upper and lower limits on the magnitude and wavelength scale of preinflation fluctuations in the inflaton field and the curvature of the preinflation universe as a function of the fraction of the total initial energy density in the inflaton field as inflation begins. We estimate that if the preinflation contribution to the current cosmic microwave background CMB dipole is near the upper limit set by the Planck Collaboration then the current constraints on ΛCDM cosmological parameters allow for the possibility of a significantly open Ωi preinflating universe for a broad range of the fraction of the total energy in the inflaton field at the onset of inflation. This limit to Ωi is even smaller if a larger dark-flow tilt is allowed. DOI PACS numbers I. INTRODUCTION In this paper therefore we explore the possibility There is now a general consensus that cosmological that the .
