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Steepest growth of the power spectrum and primordial black holes · Around

2018

Steepest growth of the power spectrum and primordial black holes

Byrnes, Christian T., Cole, Philippa S., Patil, Subodh P.

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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 $n_s - 1 = 4$ 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.

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