Venue: Maths 103
Even in the “precision era” of cosmology, measurements of the cosmic microwave background and large scale structure only cover around three orders of magnitude in length scales. However, another 30 orders of magnitude in length scales must also have exited the horizon during inflation, but these smaller scales remain unobserved. Primordial Black Holes (PBHs) can form in the early universe from the collapse of large density fluctuations. Tight observational limits on their abundance provide the best upper limit on the size of the primordial fluctuations on small scales, with PBHs only forming from extremely large and rare density fluctuations. The number of PBHs formed is therefore highly sensitive to small changes in the tail of the fluctuations probability density function, which probes non-Gaussianity.
We study how local non-Gaussianity of arbitrary size (parameterised by fNL and gNL) changes the PBH abundance and the resulting constraints on the amplitude of the fluctuations on very small scales. Intriguingly, even non-linearity parameters of order unity have a significant impact on the PBH abundance. The sign of the non-Gaussianity is particularly important, with the constraint on the allowed fluctuation amplitude tightening by an order of magnitude as fNL changes from just -0.5 to +0.5. If PBHs are observed in the future then negative fNL on these scales would be ruled out, regardless of the amplitude of the fluctuations.