Abstract
The present universe has small vacuum energy density (cosmological constant) and small spatial curvature. Therefore, before symmetry breaking, it had to have huge positive vacuum energy density, significant curvature, and low entropy. Because the energy positivity condition was not then satisfied, there need not have been an initial singularity (Hot Big Bang). If the universe is spatially open or the initial entropy high enough, then before the elementary particle phase transition, it was indeed an inflecting universe with an initial singularity. But if the universe is spatially closed and of low initial entropy, it needed to be a curvature-dominated bouncing universe, with a minimum size and maximum temperature (Tepid Little Bang). The closure of the present universe will therefore determine whether or not there was an initial singularity.
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