Steepest growth of the power spectrum and primordial black holes
By C. Byrnes, P. S. Cole, S. Patil. Journal of Cosmology and Astroparticle Physics, 2018
344 citations recorded by the source corpus.
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 ϵ 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 ϵ, offering a complementary perspective on how ultra slow-roll can be achieved.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/7598d0f663439458a948e38a3bd1b9b5362f4ef2
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Citations in the corpus
- Challenges and opportunities of gravitational-wave searches at MHz to GHz frequencies (2020, methodology): “The nondetection of the stochastic GW background can also be used to constrain fluctuations [100, 101].”
- Primordial Black Holes as Dark Matter: Recent Developments (2020, background): “The μ constraint also implies a maximum mass for the PBHs which provide the dark matter if there is some theoretical limit on the steepness of the power spectrum [217].”
- Solar-mass primordial black holes explain NANOGrav hint of gravitational waves (2020, background): “It is interesting that we can indirectly probe physics of inflation by probing the primordial scalar (curvature/density) perturbations inferred from the second-order GWs and PBH abundances [17–22].”
- Primordial black hole formation and abundance: contribution from the non-linear relation between the density and curvature perturbation (2019, background): “For the narrow peak, we will take the peak to be narrow enough such that it can be treated as a Dirac-delta function, Pζ = AsδD(ln(k/k∗)), although note that such a power spectrum is unphysical (for example, [10] describes that the power spectrum cannot be steeper than k4, at least in the context of”
- Generating PBHs and small-scale GWs in two-field models of inflation (2020, background): “This can be achieved in single-field inflation scenarios by using a local feature in the inflaton potential like a rapid change of its amplitude or a break in its first derivative [7–9], an inflection point [10–18] or a tiny bump superimposed on it [19, 20], non-trivial inflaton sound speed [21–23]1”
- Primordial black holes and gravitational waves from parametric amplification of curvature perturbations (2019, background): “This can be achieved through several ways, such as running mass inflationary models [59–61], multiple-field inflationary models [14, 62], ultra-slow-roll inflationary models [63–65] or sound speed resonance [66–68].”