本研究考察经典希格斯暴胀模型，该模型采用具有一个凹陷的修正希格斯势。我们检验了这一修正对曲率扰动产生、随机引力波产生以及原初黑洞（PBHs）潜在形成的影响。与经典模型不同，修正势允许增强的功率谱，并使 PBHs 存在于 $1.5\ imes10^{20}$ g 至 $9.72\ imes10^{32}$ g 的宽质量范围内。我们识别出与暴胀约束相符、并有可能对观测到的暗物质含量作出显著贡献的参数空间区域。此外，本研究探讨了所得参数空间与宇宙学约束的一致性，并讨论了其在解释观测到的引力波信号超出（尤其是 NANOGrav 实验中的超出）方面的意义。总体而言，本研究强调了经典希格斯暴胀模型中修正希格斯势的相关性，阐明了 PBHs 的形成、暗物质的本质以及其与引力波观测之间的联系。
英文摘要：
This study investigates the classical Higgs inflation model with a modified Higgs potential featuring a dip. We examine the implications of this modification on the generation of curvature perturbations, stochastic gravitational wave production, and the potential formation of primordial black holes (PBHs). Unlike the classical model, the modified potential allows for enhanced power spectra and the existence of PBHs within a wide mass range $1.5\times10^{20}$ g -- $9.72\times10^{32}$ g. We identify parameter space regions that align with inflationary constraints and have the potential to contribute significantly to the observed dark matter content. Additionally, the study explores the consistency of the obtained parameter space with cosmological constraints and discusses the implications for explaining the observed excess in gravitational wave signals, particularly in the NANOGrav experiment. Overall, this investigation highlights the relevance of the modified Higgs potential in the classical Higgs inflation model, shedding light on the formation of PBHs, the nature of dark matter, and the connection to gravitational wave observations.
We discuss a possible connection between the recent NANOGrav results and the primordial black holes (PBHs) for the LIGO-Virgo events. In particular, we focus on the axion-like curvaton model, which provides a sizable amount of PBHs and GWs induced by scalar perturbations around the NANOGrav frequency range. The inevitable non-Gaussianity of this model suppresses the induced GWs associated with PBHs for the LIGO-Virgo events to be compatible with the NANOGrav results. We show that the axion-like curvaton model can account for PBHs for the LIGO-Virgo events and the NANOGrav results simultaneousl…
The NANOGrav collaboration for the pulsar timing array (PTA) observation recently announced evidence of an isotropic stochastic process, which may be the first detection of the stochastic gravitational-wave (GW) background. We discuss the possibility that the signal is caused by the second-order GWs associated with the formation of solar-mass primordial black holes (PBHs). This possibility can be tested by future interferometer-type GW observations targeting the stochastic GWs from merger events of solar-mass PBHs as well as by updates of PTA observations.
The recent report of NANOGrav is gathering attention since its signal can be explained by the stochastic gravitational waves (GWs) with $Ω_{\rm GW}\sim 10^{-9}$ at $f\sim 10^{-8}$Hz. The PBH formation scenario is one of the candidates for the NANOGrav signal, which can simultaneously explain the observed $30 M_\odot$ black holes in the binary merger events in LIGO-Virgo collaboration. We focus on the type II axion-like curvaton model of the PBH formation. In type II model the complex field whose phase part is the axion rolls down from the origin of the potential. It is found that type II model…
The NANOGrav pulsar timing array experiment reported evidence for a stochastic common-spectrum process affecting pulsar timing residuals in its 12.5-year dataset, which might be interpreted as the first detection of a stochastic gravitational wave background (SGWB). I examine whether the NANOGrav signal might be explained by an inflationary SGWB, focusing on the implications for the tensor spectral index $n_T$ and the tensor-to-scalar ratio $r$. Explaining NANOGrav while complying with upper limits on $r$ from BICEP2/Keck Array and Planck requires $r \gtrsim {\cal O}(10^{-6})$ in conjunction w…
Protected by an approximate shift symmetry, axions are well motivated candidates for driving cosmic inflation. Their generic coupling to the Chern-Simons term of any gauge theory gives rise to a wide range of potentially observable signatures, including equilateral non-Gaussianites in the CMB, chiral gravitational waves in the range of direct gravitational wave detectors and primordial black holes (PBHs). In this paper we revisit these predictions for axion inflation models non-minimally coupled to gravity. Contrary to the case of minimally coupled models which typically predict scale-invarian…
Releasing the 12.5-year pulsar timing array data, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported the evidence for a stochastic common-spectrum which would herald the detection of a stochastic gravitational wave background (SGWB) for the first time. We investigate if the signal could be generated from the end of a $\sim 10$ MeV but still phenomenologically viable double-field inflation when the field configuration settles to its true vacuum. During the double-field inflation at such scales, bubbles of true vacuum that can collapse to LIGO mass …
We explore the inflationary dynamics leading to formation of closed domain walls in course of evolution of an axion like particle (ALP) field whose Peccei-Quinn-like phase transition occurred well before inflationary epoch. Evolving after inflation, the domain walls may leave their imprint in stochastic gravitational waves background, in the frequency range accessible for the pulsar timing array measurements. We derive the characteristic strain power spectrum produced by the distribution of the closed domain walls and relate it with the recently reported NANOGrav signal excess. We found that t…
We discuss the possibility of explaining the recent NANOGrav results by inflationary gravitational waves (IGWs) with a blue-tilted primordial spectrum. Although such IGWs can account for the NANOGrav signal without contradicting the upper bound on the tensor-to-scalar ratio at the cosmic microwave background scale, the predicted spectrum is in strong tension with the upper bound on the amplitude of the stochastic gravitational wave background by big-bang nucleosynthesis (BBN) and the second LIGO-Virgo observation run. However, the thermal history of the Universe, such as reheating and late-tim…
We study the formation of primordial black holes (PBHs) in the early Universe during a period of slow reheating after inflation. We demonstrate how the PBH formation mechanism may change even before the end of the matter-dominated phase and calculate the expected PBH mass function. We find that there is a threshold for the variance of the density contrast, $σ_c \simeq 0.05$, below which the transition occurs even before reheating, with this having important consequences for the PBH mass function. We also show that there is a maximum cut-off for the PBH mass at around $100\,M_{\odot}$, below wh…
We investigate the cosmology of mini Primordial Black Holes (PBHs) produced by large density perturbations. The mini PBHs evaporate promptly in the early universe and we assume that a stable remnant is left behind. The PBHs remnants can constitute the entire dark matter of the universe for a wide range of remnant masses. We build inflationary models, in the framework of $α$-attractors utilizing exponential functions, in which the PBHs are produced during matter, radiation and kination domination eras. The advantage of these inflationary models is that the spectral index takes values favorable …
We propose a novel scenario to produce abundant primordial black holes (PBHs) in new inflation which is a second phase of a double inflation in the supergravity frame work. In our model, some preinflation phase before the new inflation is assumed and it would be responsible for the primordial curvature perturbations on the cosmic microwave background scale, while the new inflation produces only the small scale perturbations. Our new inflation model has linear, quadratic, and cubic terms in its potential and PBH production corresponds with its flat inflection point. The linear term can be inter…
Primordial Black Holes (PBH) could be the cold dark matter of the universe. They could have arisen from large (order one) curvature fluctuations produced during inflation that reentered the horizon in the radiation era. At reentry, these fluctuations source gravitational waves (GW) via second order anisotropic stresses. These GW, together with those (possibly) sourced during inflation by the same mechanism responsible for the large curvature fluctuations, constitute a primordial stochastic GW background (SGWB) that unavoidably accompanies the PBH formation. We study how the amplitude and the r…
The primordial black hole (PBH) formation is studied in light of the inflating curvaton. The typical scale of the PBH formation is determined by curvaton inflation, which may generate PBH with $10^{14}\mathrm{g}\le M_\mathrm{PBH}\le 10^{38}\mathrm{g}$ when curvaton inflation gives the number of e-foldings $5\leq N_2\leq 38$. The non-Gaussianity of the inflating curvaton does not prevent the PBH formation.
Recent population studies have searched for a subpopulation of primordial black holes (PBHs) in the gravitational-wave (GW) events so far detected by LIGO/Virgo/KAGRA (LVK), in most cases adopting a phenomenological PBH mass distribution. When deriving such population from first principles in the standard scenario, however, the equation of state of the Universe at the time of PBH formation may strongly affect the PBH abundance and mass distribution, which ultimately depend on the power spectrum of cosmological perturbations. Here we improve on previous population studies on several aspects: (i…
Primordial Black Holes (PBHs) serve as a unique probe to the physics of the early Universe, particularly inflation. In light of this, we study the formation of PBHs by the collapse of overdense perturbations generated during a model of warm inflation. For our model, we find that the primordial curvature power spectrum is red-tilted (spectral index $n_s<1$) at the large scale (small $k$) and is consistent with the $n_s-r$ values allowed from the CMB observations. Along with that, it has a blue-tilt ($n_s>1$) for the small PBH scales (large $k$), with a sufficiently large amplitude of the primor…
Primordial black hole (PBH) abundance limits constrain the primordial power spectrum, and hence models of inflation, on scales far smaller than those probed by cosmological observations. Single field inflation models which are compatible with all cosmological data can have large enough perturbations on small scales to overproduce PBHs, and hence be excluded. The standard formulae for the amplitude of perturbations do not hold for modes that exit the horizon close to the end of inflation however. We use a modified flow analysis to identify models of inflation where the amplitude of perturbation…
Most of the inflationary scenarios that try to explain the origin of Primordial Black Holes (PBHs) from the enhancements of the power spectrum to values of order one, at the relevant scales, run into clashes with the Effective Field Theory (EFT) criteria or fail to enhance the power spectrum to such large amplitudes. In this paper, we unravel a mechanism for enhancing the power spectrum during inflation that does not use the flattening of the potential or reduction of the sound speed of scalar perturbations. The mechanism is based on this observation in the formalism of Extended EFT of inflati…
We construct an analytically solvable simplified model that captures the essential features for primordial black hole (PBH) production in most models of single-field inflation. The construction makes use of the Wands duality between the constant-roll (or slow-roll) and the preceding ultra-slow-roll phases and can be realized by a simple inflaton potential of two joined parabolas. Within this framework, it is possible to formulate explicit inflationary scenarios consistent with the CMB observations and copious production of PBHs of arbitrary mass. We quantify the variability of the shape of the…
We explicitly construct a double-field inflationary model, which satisfies the latest Planck constraints at the cosmic microwave background (CMB) scales and produces the whole dark matter energy density as primordial black holes (PBHs), in the mass range $10^{-17}~M_{\odot}\lesssim M_{{}_{\rm PBH}}\lesssim 10^{-13}~M_{\odot}$. The PBHs can be produced after the end of slow-roll inflation from the bubbles of true vacuum that nucleate during the course of inflation. Obtaining PBHs in this mass range enforces the scale of inflation to be extremely low, $10^{-7} \lesssim H \lesssim 10^{-3} ~{\rm G…
NANOGrav 15-year gravitational-wave signals from binary supermassive black-holes seeded by primordial black holes, and implications for the origins of Little Red Dots
Graduate University for Advanced Studies (SOKENDAI)（高等研究院）；High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；National Astronomical Observatory of Japan（日本国立天文台）；University of Tokyo（东京大学）；The University of Tokyo（东京大学）
Primordial Black Hole (PBH) is one of the leading non-particle candidates for dark matter (DM). Although several observations severely constrain the amount of PBHs, it is recently pointed out that there is an uncertainty on the microlensing constraints below $\sim 10^{-10} M_\odot$ which was ignored originally but may weaken the constraints significantly. In this paper, facing this uncertainty, we investigate the possibility that PBHs can make up all DM in a broad mass spectrum. Moreover, we propose a concrete inflation model which can simultaneously produce PBHs for all DM in a broad mass spe…
For the first time, the running of the running of the spectral index $β_s$ has been measured by Planck. This parameter is crucial for dark matter Primordial Black Holes (PBHs) formation. We study the PBHs formation in inflation potentials with superimposed periodic oscillations. We show that the value of $β_s$ suggested by the recent cosmic microwave background data is easily explained in these models. As a by-product, we also show that the nonproduction of (long--lived) PBHs puts a stronger upper bound on $β_s$.
In this paper, we show that if passive fluctuations are considered, primordial black holes (PBHs) can be easily produced in the framework of single-field, slow-roll inflation models. The formation of PBHs is due to the blue spectrum of passive fluctuations and an enhancement of the spectral range which exits horizon near the end of inflation. Therefore the PBHs are light with masses $\lesssim 10^{15}g$ depending on the number of e-folds when the scale of our observable universe leaves horizon. These PBHs are likely to have evaporated and cannot be a candidate for dark matter but they may still…
Primordial black holes (PBHs) are one of the candidates to explain the gravitational wave (GW) signals observed by the LIGO detectors. Among several phenomena in the early Universe, cosmic inflation is a major example to generate PBHs from large primordial density perturbations. In this paper, we discuss the possibility to interpret the observed GW events as mergers of PBHs which are produced by cosmic inflation. The primordial curvature perturbation should be large enough to produce a sizable amount of PBHs and thus we have several other probes to test this scenario. We point out that the cur…
We study a double inflation model (a hybrid inflation + a new inflation) in supergravity and discuss the formation of primordial black holes (PBHs) with mass \sim 10^{-20}-10^{5}M_{\odot}. We find that in a wide range of parameter space, we obtain PBHs which amount to Ω\simeq 1, i.e., PBH dark matter. Also, we find a set of inflation parameters which produces PBHs evaporating now. Those PBHs may be responsible for antiproton fluxes observed by the BESS experiment.
Primordial black holes (PBHs) can constitute the predominant fraction of dark matter (DM) if PBHs reside in the currently unconstrained "sublunar" mass range. PBHs originating from scalar perturbations generated during inflation can naturally appear with a broad spectrum in a class of models. The resulting stochastic gravitational wave (GW) background generated from such PBH production can account for the recently reported North American Nanohertz Observatory for Gravitational Waves (NANOGrav) pulsar timing array data signal, and will be testable in future GW observations by interferometer-typ…
We interpret the recent NANOGrav results in terms of a stochastic gravitational wave background from metastable cosmic strings. The observed amplitude of a stochastic signal can be translated into a range for the cosmic string tension and the mass of magnetic monopoles arising in theories of grand unification. In a sizable part of the parameter space, this interpretation predicts a large stochastic gravitational wave signal in the frequency band of ground-based interferometers, which can be probed in the very near future. We confront these results with predictions from successful inflation, le…
We consider the process of primordial black hole (PBH) formation originated from primordial curvature perturbations produced during waterfall transition (with tachyonic instability), at the end of hybrid inflation. It is known that in such inflation models, rather large values of curvature perturbation amplitudes can be reached, which can potentially cause a significant PBH production in the early Universe. The probability distributions of density perturbation amplitudes in this case can be strongly non-Gaussian, which requires a special treatment. We calculated PBH abundances and PBH mass spe…
We present a novel mechanism for the production of primordial black holes (PBHs). The mechanism is based on a period of thermal inflation followed by fast-roll inflation due to tachyonic mass of order the Hubble scale. Large perturbations are generated at the end of the thermal inflation as the thermal inflaton potential turns from convex to concave. These perturbations can lead to copious production of PBHs when the relevant scales re-enter horizon. We show that such PBHs can naturally account for the observed dark matter in the Universe when the mass of the thermal inflaton is about $10^6\,$…
We study possibilities to explain the whole dark matter abundance by primordial black holes (PBHs) or to explain the merger rate of binary black holes estimated from the gravitational wave detections by LIGO/Virgo. We assume that the PBHs are originated in a radiation- or matter-dominated era from large primordial curvature perturbation generated by inflation. We take a simple model-independent approach considering inflation with large running spectral indices which are parametrized by $n_\text{s}, α_\text{s}$, and $β_\text{s}$ consistent with the observational bounds. The merger rate is fitte…
We investigate whether an Early-Universe stochastic gravitational-wave background (SGWB) can account for the common spectrum process reported by NANOGrav, while also being consistent with current and projected CMB measurements of extra radiation. We compute the contribution of effective number of relativistic species, $ΔN_{eff}$, for a number of Early-Universe models proposed to explain the pulsar timing array (PTA) spectrum. We demonstrate that models predicting $ΔN_{eff}$ above the CMB limit would be firmly excluded, implying that the NANOGrav signal in tension with these bounds must instead…
Lattice study of primordial black hole formation in bumpy axion inflation
Kavli IPMU (WPI), UTIAS, University of Tokyo（东京大学）；ICRR, University of Tokyo（东京大学）；Physics Division, Faculty of Science, Kanagawa University（神奈川大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所）；Department of Physics, Tohoku University（东北大学）
