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Register a new userPrimordial black holes and second order gravitational waves from ultra-slow-roll inflation
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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.
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We numerically calculate the evolution of second order cosmological perturbations for an inflationary scalar field without resorting to the slow-roll approximation or assuming large scales. In contrast to previous approaches we therefore use the full non-slow-roll source term for the second order Klein-Gordon equation which is valid on all scales. The numerical results are consistent with the ones obtained previously where slow-roll is a good approximation. We investigate the effect of localised features in the scalar field potential which break slow-roll for some portion of the evolution. The numerical package solving the second order Klein-Gordon equation has been released under an open source license and is available for download.
Recent observational constraints indicate that primordial black holes (PBHs) with the mass scale $sim 10^{-12}M_{odot}$ can explain most of dark matter in the Universe. To produce this kind of PBHs, we need an enhance in the primordial scalar curvature perturbations to the order of ${mathcal{O}(10^{-2})}$ at the scale $ k sim 10^{12}~rm Mpc^{-1}$. Here, we investigate the production of PBHs and induced gravitational waves (GWs) in the framework of textbf{$k$-inflation}. We solve numerically the Mukhanov-Sasaki equation to obtain the primordial scalar power spectrum. In addition, we estimate the PBHs abundance $f_{text{PBH}}^{text{peak}}$ as well as the energy density parameter $Omega_{rm GW,0}$ of induced GWs. Interestingly enough is that for a special set of model parameters, we estimate the mass scale and the abundance of PBHs as $sim{cal O}(10^{-13})M_{odot}$ and $f_{text{PBH}}^{text{peak}}=0.96$, respectively. This confirms that the mechanism of PBHs production in our inflationary model can justify most of dark matter. Furthermore, we evaluate the GWs energy density parameter and conclude that it behaves like a power-law function $Omega_{rm GW}sim (f/f_c)^n$ where in the infrared limit $fll f_{c}$, the power index reads $n=3-2/ln(f_c/f)$.
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 governs 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.
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.
Primordial black holes (PBHs) from the early Universe have been connected with the nature of dark matter and can significantly affect cosmological history. We show that coincidence dark radiation and density fluctuation gravitational wave signatures associated with evaporation of $lesssim 10^9$ g PBHs can be used to explore and discriminate different formation scenarios of spinning and non-spinning PBHs spanning orders of magnitude in mass-range, which is challenging to do otherwise.
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