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Steepest growth of the power spectrum and primordial black holes

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posted on 2023-06-09, 18:17 authored by Christian ByrnesChristian Byrnes, Philippa Cole, Subodh P Patil
We derive analytic bounds on the shape of the primordial power spectrum in the context of single-field inflation. In particular, the steepest possible growth has a spectral index of ns - 1 = 4 once transients have died down. Its primary implication is that any constraint on the power spectrum at a particular scale can be extrapolated to an upper bound over an extended range of scales. This is important for models which generate relics due to an enhanced amplitude of the primordial scalar perturbations, such as primordial black holes. In order to generate them, the power spectrum needs to grow many orders of magnitude larger than its observed value on CMB scales—typically achieved through a phase of ultra slow-roll inflation—and is thus subject to additional constraints at small scales. We plot all relevant constraints including CMB spectral distortions and gravitational waves sourced by scalar perturbations at second order. We show how this limits the allowed mass of PBHs, especially for the large masses of interest following recent detections by LIGO and prospects for constraining them further with future observations. We show that any transition from approximately constant epsilon slow-roll inflation to a phase where the power spectrum rapidly rises necessarily implies an intervening dip in power. We also show how to reconstruct a potential that can reproduce an arbitrary time-varying epsilon, offering a complementary perspective on how ultra slow-roll can be achieved.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of Cosmology and Astroparticle Physics

ISSN

1475-7516

Publisher

IOP Publishing

Issue

06

Volume

2019

Page range

1-40

Article number

a028

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Astronomy Centre Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2019-07-03

First Open Access (FOA) Date

2020-06-12

First Compliant Deposit (FCD) Date

2019-07-02

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