Observing the temperature of the Big Bang through large scale structure

It is widely accepted that the Universe underwent a period of thermal equilibrium at very early times. One expects a residue of this primordial state to be imprinted on the large scale structure of space time. In this paper we study the morphology of this thermal residue in a universe whose early dynamics is governed by a scalar field. We calculate the amplitude of fluctuations on large scales and compare it to the imprint of vacuum fluctuations. We then use the observed power spectrum of fluctuations on the cosmic microwave background to place a constraint on the temperature of the Universe before and during inflation. We also present an alternative scenario where the fluctuations are predominantly thermal and near scale-invariant.