Yet, if this were correct, and the Universe had achieved arbitrarily high temperatures in the past, there would be a number of clear signatures of this we could observe today. There would be temperature fluctuations in the Big Bang’s leftover glow that would have tremendously large amplitudes. The fluctuations that we see would be limited by the speed of light; they would only appear on scales of the cosmic horizon and smaller. There would be leftover, high-energy cosmic relics from earlier times, like magnetic monopoles.

And yet, the temperature fluctuations are only 1-part-in-30,000, thousands of times smaller than a singular Big Bang predicts. Super-horizon fluctuations are real, robustly confirmed by both WMAP and Planck. And the constraints on magnetic monopoles and other ultra-high-energy relics are incredibly tight. These missing signatures have a huge implication: the Universe never reached these arbitrarily large temperatures.