Title: Is quantum diffusion actually important during inflation? How to not overproduce Primordial Black Holes.
Abstract: The early universe offers a unique opportunity to study the interplay between gravity and quantum effects. A period of accelerated expansion in the early universe – known as inflation – can seed the density perturbations that will form large-scale structure from initially small, quantum fluctuations. These quantum fluctuations can backreact on the field driving inflation – the inflaton – as they are stretched by the accelerated expansion. For modes observed in the CMB the perturbations are very small and the quantum diffusion (or backreaction) must also be very small. In this regime the standard slow-roll (SR) approximation is still very good. However larger density perturbations which could potentially collapse to form Primordial Black Holes (PBHs) are also of interest and in the SR approximation a negligible amount are formed. One method to enhance the number of PBHs formed is to therefore consider the Ultra Slow-Roll (USR) regime characterised by a plateau in the inflaton potential where the quantum diffusion is the dominant effect on the inflaton.
In this talk we demonstrate that previous calculations incorrectly compute the amount of PBHs formed as they fail to take into account the Hamilton-Jacobi constraint which restricts the inflaton momenta to lie on the same integral curve everywhere in the universe. We derive analytic formulae for the mass fraction, $\beta$, of PBHs formed due to the inflaton entering a USR region and plot the dependence of $\beta$ on the inflaton’s momenta as it enters the plateau and the width of the plateau itself. This allows us to put new constraints on how wide a plateau region could be without overproducing PBHs. In particular, we note that PBH abundance constraints are violated before the inflaton enters the quantum diffusion dominated regime. This tells us therefore that even in the extreme case where enough PBHs are formed to be all the dark matter, a semi-classical description is sufficient for many observables of interest.
This talk is based on the paper:
“Inflation is always semi-classical: Diffusion domination overproduces Primordial Black Holes”
JCAP12(2021)027 arXiv: 2107.05317