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Steepest growth of the power spectrum and primordial black holes
journal contribution
posted on 2023-06-09, 18:17 authored by Christian ByrnesChristian Byrnes, Philippa Cole, Subodh P PatilWe 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 PhysicsISSN
1475-7516Publisher
IOP PublishingExternal DOI
Issue
06Volume
2019Page range
1-40Article number
a028Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Astronomy Centre Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2019-07-03First Open Access (FOA) Date
2020-06-12First Compliant Deposit (FCD) Date
2019-07-02Usage metrics
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