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تسجيل مستخدم جديدPrimordial Black Holes from Inflation and Quantum Diffusion
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Primordial black holes as dark matter may be generated in single-field models of inflation thanks to the enhancement at small scales of the comoving curvature perturbation. This mechanism requires leaving the slow-roll phase to enter a non-attractor phase during which the inflaton travels across a plateau and its velocity drops down exponentially. We argue that quantum diffusion has a significant impact on the primordial black hole mass fraction making the classical standard prediction not trustable.
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We report on a novel phenomenon of the resonance effect of primordial density perturbations arisen from a sound speed parameter with an oscillatory behavior, which can generically lead to the formation of primordial black holes in the early Universe.
For a general inflaton field, it can seed primordial density fluctuations and their propagation is governed by a parameter of sound speed square. Once if this parameter achieves an oscillatory feature for a while during inflation, a significant non-perturbative resonance effect on the inflaton field fluctuations takes place around a critical length scale, which results in significant peaks in the primordial power spectrum. By virtue of this robust mechanism, primordial black holes with specific mass function can be produced with a sufficient abundance for dark matter in sizable parameter ranges.
We present a new realization of the resonant production of primordial black holes as well as gravitational waves in a two-stage inflation model consisting of a scalar field phi with an axion-monodromy-like periodic structure in the potential that gov
erns the first stage and another field chi with a hilltop-like potential that dominates the second stage. The parametric resonance seeded by the periodic structure at the first stage amplifies the perturbations of both fields inside the Hubble radius. While the evolution of the background trajectory experiences a turn as the oscillatory barrier height increases, the amplified perturbations of chi remain as they are and contribute to the final curvature perturbation. It turns out that the primordial power spectrum displays a significant resonant peak on small scales, which can lead to an abundant production of primordial black holes. Furthermore, gravitational waves are also generated from the resonantly enhanced field perturbations during inflation, the amplitude of which may be constrained by future gravitational wave interferometers.
It has been shown that black holes would have formed in the early Universe if, on any given scale, the spectral amplitude of the Cosmic Microwave Background (CMB) exceeds 10^(-4). This value is within the bounds allowed by astrophysical phenomena for
the small scale spectrum of the CMB, corresponding to scales which exit the horizon at the end of slow-roll inflation. Previous work by Kohri et. al. (2007) showed that for black holes to form from a single field model of inflation, the slope of the potential at the end of inflation must be flatter than it was at horizon exit. In this work we show that a phenomenological Hilltop model of inflation, satisfying the Kohri et. al. criteria, could lead to the production of black holes, if the power of the inflaton self-interaction is less than or equal to 3, with a reasonable number or e-folds. We extend our analysis to the running mass model, and confirm that this model results in the production of black holes, and by using the latest WMAP year 5 bounds on the running of the spectral index, and the black hole constraint we update the results of Leach et. al. (2000) excluding more of parameter space.
The next generation of space-borne gravitational wave detectors may detect gravitational waves from extreme mass-ratio inspirals with primordial black holes. To produce primordial black holes which contribute a non-negligible abundance of dark matter
and are consistent with the observations, a large enhancement in the primordial curvature power spectrum is needed. For a single field slow-roll inflation, the enhancement requires a very flat potential for the inflaton, and this will increase the number of $e$-folds. To avoid the problem, an ultra-slow-roll inflation at the near inflection point is required. We elaborate the conditions to successfully produce primordial black hole dark matter from single field inflation and propose a toy model with polynomial potential to realize the big enhancement of the curvature power spectrum at small scales while maintaining the consistency with the observations at large scales. The power spectrum for the second order gravitational waves generated by the large density perturbations at small scales is consistent with the current pulsar timing array observations.
Primordial black holes (PBHs) cannot be produced abundantly enough to be the dark matter in canonical single-field inflation under slow roll. This conclusion is robust to local non-Gaussian correlations between long- and short-wavelength curvature mo
des, which we show have no effect in slow roll on local primordial black hole abundances. For the prototypical model which evades this no go, ultra-slow roll (USR), these squeezed non-Gaussian correlations have at most an order unity effect on the variance of PBH-producing curvature fluctuations for models that would otherwise fail to form sufficient PBHs. Moreover, the transition out of USR, which is necessary for a successful model, suppresses even this small enhancement unless it causes a large increase in the inflaton kinetic energy in a fraction of an e-fold, which we call a large and fast transition. Along the way we apply the in-in formalism, the delta N formalism, and gauge transformations to compute non-Gaussianities and illuminate different aspects of the physical origin of these results. Local non-Gaussianity in the squeezed limit does not weaken the Gaussian conclusion that PBHs as dark matter in canonical single-field inflation require a complicated and fine-tuned potential shape with an epoch where slow roll is transiently violated.
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