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Extreme scenarios: the tightest possible constraints on the power spectrum due to primordial black holes

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posted on 2023-06-09, 12:08 authored by Philippa Cole, Christian ByrnesChristian Byrnes
Observational constraints on the abundance of primordial black holes (PBHs) constrain the allowed amplitude of the primordial power spectrum on both the smallest and the largest ranges of scales, covering over 20 decades from 1 - 10^20=Mpc. Despite tight constraints on the allowed fraction of PBHs at their time of formation near horizon entry in the early Universe, the corresponding constraints on the primordial power spectrum are quite weak, typically PR . 10<~2 assuming Gaussian perturbations. Motivated by recent claims that the evaporation of just one PBH would destabilise the Higgs vacuum and collapse the Universe, we calculate the constraints which follow from assuming there are zero PBHs within the observable Universe. Even if evaporating PBHs do not collapse the Universe, this scenario represents the ultimate limit of observational constraints. Constraints can be extended on to smaller scales right down to the horizon scale at the end of in ation, but where power spectrum constraints already exist they do not tighten significantly, even though the constraint on PBH abundance can decrease by up to 46 orders of magnitude. This shows that no future improvement in observational constraints can ever lead to a significant tightening in constraints on in ation (via the power spectrum amplitude). The power spectrum constraints are weak because an order unity perturbation is required in order to overcome pressure forces. We therefore consider an early matter dominated era, during which exponentially more PBHs form for the same initial conditions. We show this leads to far tighter constraints, which approach PR . 10^-9, albeit over a smaller range of scales and are very sensitive to when the early matter dominated era ends. Finally, we show that an extended early matter era is incompatible with the argument that an evaporating PBH would destroy the Universe, unless the power spectrum amplitude decreases by up to ten orders of magnitude.

Funding

STFC DTP 2015; G1687; STFC-SCIENCE AND TECHNOLOGY FACILITIES COUNCIL; ST/N504452/1

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of Cosmology and Astroparticle Physics

ISSN

1475-7516

Publisher

IOP Publishing

Issue

02

Page range

019 1-19

Department affiliated with

  • Physics and Astronomy Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-02-14

First Open Access (FOA) Date

2019-02-12

First Compliant Deposit (FCD) Date

2018-02-14

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