V. De Luca, G. Franciolini, A. Riotto
We elaborate on the mass function of primordial black holes in the case in which the power spectrum of the curvature perturbation is broad. For the case of a broad and flat spectrum, we argue that such a mass function is peaked at the smallest primordial black mass which can be formed and possesses a tail decaying like $M^{-3/2}$, where $M$ is the mass of the primordial black hole.
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A common mechanism to form primordial black holes in the early universe is by enhancing at small-scales the scalar perturbations generated during inflation. If these fluctuations have a large enough amplitude, they may collapse into primordial black holes upon horizon re-entry. Such primordial black holes may comprise the totality of the dark matter. We offer some considerations about the formation and clustering of primordial black holes when the scalar perturbations are characterised by a broad spectrum. Using the excursion set method, as well as the supreme statistics, we show that the clou…
The Primordial Black Hole Abundance: The Broader, the Better
本文指出，除非曲率扰动功率谱极尖峰，原初黑洞丰度始终由最宽紧致函数轮廓主导，阈值为2/5，这加剧了其与脉冲星计时阵列引力波信号之间的紧张关系。
Broad primordial power spectrum and $μ$-distortion constraints on primordial black holes
针对超大质量原初黑洞形成假说受宇宙微波背景μ畸变严格约束的问题，研究发现宽功率谱在非高斯曲率扰动假设下可弱化该约束，为缓解相关限制提供了可能。
Impact of generalized holonomy corrections on the cosmological primordial power spectra
本文在确保变形约束代数闭合的条件下，自洽研究了广义和乐修正对微扰传播的影响，计算了原初功率谱，证明圈量子宇宙学的主要已知结果对修正细节具有稳健性。
Reconstructing Primordial Black Hole Power Spectra from Gravitational Waves
本文提出一种直接且计算高效的新方法，利用标量诱导引力辐射和现有脉冲星计时阵列数据，在多种原初黑洞形成情景下系统重建原初功率谱。
Emergent cosmological models, together with the Big Bang and bouncing scenarios, are among the possible descriptions of the early Universe. This work aims at clarifying some general features of the primordial tensor power spectrum in this specific framework. In particular, some naive beliefs are corrected. Using a toy model, we investigate the conditions required to produce a scale invariant spectrum and show to which extent this spectrum can exhibit local features sensitive to the details of the scale factor evolution near the transition time.
A mechanism for generating primordial black-hole mass spectra with many spikes is proposed and investigated. This mechanism relies on the choice of non-Bunch-Davies vacua, these leading to oscillatory features in the inflationary power spectrum. This in turn generates oscillations in the primordial black-hole mass function with exponentially enhanced spikes. This ``multimodal'' effect is demonstrated for most of the well-studied models of primordial black-hole formation.
With the recently published Cosmic Microwave Background data from Planck we address the optimized binning of the primordial power spectrum. As an important modification to the usual binning of the primordial spectrum, along with the spectral amplitude of the bins, we allow the position of the bins also to vary. This technique enables us to address the location of the possible broad physical features in the primordial spectrum with relatively smaller number of bins compared to the analysis performed earlier. This approach is in fact a reconstruction method looking for broad features in the prim…
In this paper we constrain the tilt of the spectra of primordial gravitational waves from Background Imaging of Cosmic Extragalactic Polarization (BICEP2) data only. We find $r=0.21_{-0.10}^{+0.04}$ and $n_t=-0.06_{-0.23}^{+0.25}$ (at $68\%$ C.L.) which implies that a scale-invariant primordial gravitational waves spectra is consistent with BICEP2 nicely. Our results provide strong evidence for supporting inflation model, and the alternative models, for example the ekpyrotic model which predicts $n_t=2$, are ruled out at more than $5σ$ significance.
We develop an exact formalism for the computation of the abundance of primordial black holes (PBHs) in the presence of local non-gaussianity (NG) in the curvature perturbation field. For the first time, we include NG going beyond the widely used quadratic and cubic approximations, and consider a completely generic functional form. Adopting threshold statistics of the compaction function, we address the computation of the abundance both for narrow and broad power spectra. While our formulas are generic, we discuss explicit examples of phenomenological relevance considering the physics case of t…
We study the Schwinger effect during inflation and its imprints on the primordial power spectrum and bispectrum. The produced charged particles by Schwinger effect during inflation can leave a unique angular dependence on the primordial spectra.
Exact numerical primordial primordial power spectra are computed and plotted for the for the best-fit Planck 2018 curved universe parameters. It is found that the spectra have generic cut-offs and oscillations within the observable window for the level of curvature allowed by current CMB measurements and provide a better fit to current data. Derivations for the Mukhanov-Sasaki equation for curved universes are presented and analysed, and theoretical implications for the quantum and classical initial conditions for inflation are discussed within the curved regime.
There is a growing expectation that the gravitational wave detectors will start probing the stochastic gravitational wave backgrounds in the following years. We explore the spectral shapes of gravitational waves induced to second order by scalar perturbations and presumably have been produced in the early universe. We calculate the gravitational wave spectra generated during radiation and kination eras together with the associated primordial black hole counterpart. We employ power spectra for the primordial curvature perturbation generated by $α$-attractors and nonminimal derivative coupling i…
During the era of primordial nucleosynthesis the background of non-equilibrium antineutrinos is being formed due to decays of neutrons and nuclei of tritium. The spectra of antineutrinos of this background were calculated taking into account the Coulomb interaction between electron and daughter nucleus in $β^-$-decay. The dependence of these spectra on the value of the baryon-to-photon ratio $η$ at the period of primordial nucleosynthesis is investigated. The observations of these antineutrinos will allow us to look directly at the very early Universe and nonequilibrium processes taken place b…
This article is devoted to the study of scalar perturbations in loop quantum cosmology. It aims at clarifying the situation with respect to the way initial conditions are set and to the specific choice of an inflaton potential. Several monomial potentials are studied. Both the dressed metric and deformed algebra approaches are considered. We show that the calculation of the ultraviolet part of the spectrum, which is the physically relevant region for most background trajectories, is reliable, whereas the infrared and intermediate parts do depend on some specific choices that are made explicit.
Effects of heavy fields on primordial spectra of curvature perturbations are discussed in inflationary models with a sudden turning trajectory. When heavy fields are excited after the sudden turn and oscillate around the bottom of the potential, the following two effects are generically induced: deformation of the inflationary background spacetime and conversion interactions between adiabatic and isocurvature perturbations, both of which can affect the primordial density perturbations. In this paper, we calculate primordial spectra in inflationary models with sudden turning potentials taking i…
Probing small-scale primordial power spectra with induced gravitational waves
本研究通过分析诱导引力波探测小尺度原初功率谱，提出TSIGWs作为约束原初扰动的新方法。
We derive a direct correlation between the power spectrum and bispectrum of the primordial curvature perturbation in terms of the Goldstone mode based on the effective field theory approach to inflation. We show examples of correlated bispectra for the parametrized feature models presented by the Planck collaboration. We also discuss the consistency relation and the validity of our explicit correlation between the power spectrum and bispectrum.
We suggest the new feature of primordial gravitational waves sourced by the axion-gauge couplings, whose forms are motivated by the dimensional reduction of the form field in the string theory. In our inflationary model, as an inflaton we adopt two types of axion, dubbed the model-independent axion and the model-dependent axion, which couple with two gauge groups with different sign combination each other. Due to these forms both polarization modes of gauge fields are amplified and enhance both helicies of tensor modes during inflation. We point out the possibility that a primordial blue-tilte…
In this letter, combining peak theory and the numerical analysis of gravitational collapse in the radiation dominated era, we show that the abundance of primordial blacks holes, generated by an enhancement in the inflationary power spectrum, is extremely dependent on the shape of the peak. Given the amplitude of the power spectrum, we show that the density of primordial black holes generated from a narrow peak, is exponentially smaller than in the case of a broad peak. Specifically, for a top-hat profile of the power spectrum in Fourier space, we find that for having primordial black holes com…
Multi-peaked spectra of the primordial gravitational waves are considered as a phenomenologically relevant source of information about the dynamics of sequential phase transitions in the early Universe. In particular, such signatures trace back to specific patterns of the first-order electroweak phase transition in the early Universe occurring in multiple steps. Such phenomena appear to be rather generic in multi-scalar extensions of the Standard Model. In a particularly simple extension of the Higgs sector, we have identified and studied the emergence of sequential long- and short-lasting tra…
We extend the work of Contaldi et al. and derive analytical approximations for primordial power spectra arising from models of inflation which include primordial spatial curvature. These analytical templates are independent of any specific inflationary potential and therefore illustrate and provide insight into the generic effects and predictions of primordial curvature, manifesting as cut-offs and oscillations at low multipoles and agreeing with numerical calculations. We identify through our analytical approximation that the effects of curvature can be mathematically attributed to shifts in …
We investigate the primordial power spectra for general kinetic inflation models that support a period of kinetic dominance in the case of curved universes. We present derivations of the Mukhanov-Sasaki equations with a nonstandard scalar kinetic Lagrangian which manifests itself through the inflationary sound speed $c_s^2$. We extend the analytical approximations exploited in Contaldi et al [1] and Thavanesan et al [2] to general kinetic Lagrangians and show the effect of $k$-inflation on the primordial power spectra for models with curvature. In particular, the interplay between sound speed …
We observationally examine cosmological models based on primordial power spectra with quantized wavevectors. Introducing a linearly quantized power spectrum with $k_0=3.225\times10^{-4}\mathrm{Mpc}^{-1}$ and spacing $Δk = 2.257 \times 10^{-4} \mathrm{Mpc}^{-1}$ provides a better fit to the Planck 2018 observations than the concordance baseline, with $Δχ^2 = -8.55$. Extending the results of Lasenby et al [1], we show that the requirement for perturbations to remain finite beyond the future conformal boundary in a universe containing dark matter and a cosmological constant results in a linearly …
Background-independent one-loop renormalization of tensor and scalar primordial spectra
该研究针对单圈原初谱提出背景独立重整化框架，应用于标量诱导张量谱和标量谱，通过隔离紫外部分并利用WKB行为提取极点吸收到抵消项，得到与模型无关且适用于数值分析的重整化谱表达式。
Certain inflationary models as well as realisations of phase transitions in the early Universe predict the formation of primordial black holes. For most mass ranges, the fraction of matter in the form of primordial black holes is limited by many different observations on various scales. Primordial black holes are assumed to be formed when overdensities that cross the horizon have Schwarzschild radii larger than the horizon. Traditionally it was therefore assumed that primordial black-hole masses were equal to the horizon mass at their time of formation. However, detailed calculations of their …
Spin of Primordial Black Holes from Broad Power Spectrum: Radiation Dominated Universe
本文研究辐射主导时期宽曲率功率谱形成的原初黑洞初始自旋，引入宽度参数并给出不同质量区间的无量纲Kerr参数上限。
The tree order power spectra of primordial inflation depend upon the norm-squared of mode functions which oscillate for early times and then freeze in to constant values. We derive simple differential equations for the power spectra, that avoid the need to numerically simulate the physically irrelevant phases of the mode functions. We also derive asymptotic expansions which should be valid until a few e-foldings before first horizon crossing, thereby avoiding the need to evolve mode functions from the ultraviolet over long periods of inflation.
We provide the power spectrum of small scalar perturbations propagating in an inflationary scenario within loop quantum cosmology. We consider the hybrid quantization approach applied to a Friedmann--Robertson--Walker spacetime with flat spatial sections coupled to a massive scalar field. We study the quantum dynamics of scalar perturbations on an effective background within this hybrid approach. We consider in our study adiabatic states of different orders. For them, we find that the hybrid quantization is in good agreement with the predictions of the dressed metric approach. We also propose …
Disentangling the primordial nature of stochastic gravitational wave backgrounds with CMB spectral distortions
本研究利用CMB谱畸变与引力波的关联，通过更新的窗口函数和约束映射，区分随机引力波背景的原初或天体物理起源，并强调未来CMB光谱仪的关键作用。
Gravitational waves from primordial scalar and tensor perturbations
本文研究辐射主导时期原初标量和张量扰动诱导的二阶引力波，给出功率谱显式表达式，并发现当张标比为0.2时，原初张量扰动可使LISA观测信噪比提高约50%。
GammaPBHPlotter: A public code for calculating the complete Hawking evaporation gamma-ray spectra from primordial black holes
GammaPBHPlotter是一个公开Python代码，用于计算10^14至10^18克原初黑洞的完整霍金蒸发伽马射线谱，涵盖直接发射、次级发射、末态辐射和飞行中湮灭等分量。
CMB Spectral Distortions: A Multimessenger Probe of the Primordial Universe
本文回顾CMB谱畸变研究的关键科学目标，提出结合下一代实验与引力波、21厘米宇宙学等互补探针，可实现对奇异物理场景的模型区分，为原初宇宙研究提供新的多信使探测路径。
The slow-roll inflation for a single scalar field that couples to the Gauss-Bonnet (GB) term represents an important higher-order curvature correction inspired by string theory. With the arrival of the era of precision cosmology, it is expected that the high-order corrections become more and more important. In this paper we study the observational predictions of the slow-roll inflation with the GB term by using the third-order uniform asymptotic approximation method. We calculate explicitly the primordial power spectra, spectral indices, running of the spectral indices for both scalar and tens…
Constraining the impact of standard model phase transitions on primordial black holes
本文研究了早期宇宙标准模型相变对原初黑洞形成的影响，指出状态方程减弱会指数级增强形成率，但利用标准模型增强激发原初黑洞种群面临挑战，且电弱相变无法显著影响总丰度。
Both the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck observations reported the hemispherical asymmetry of the cosmic microwave background (CMB) temperature fluctuation. The hemispherical asymmetry might be stemmed from the primordial statistical anisotropy during the inflationary era of the universe. In this paper, we study possible implications of the primordial power spectra with dipolar anisotropy on the CMB temperature fluctuation and polarizations. We explicitly show that the statistical dipolar anisotropy may induce the off-diagonal (\(\ell'\neq\ell\)) $TT$, $EE$, $BB$, and $T…
We study temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation sourced from primordial cross-bispectra between metric perturbations and vector fields, which are generated from the inflation model where an inflaton and a vector field are coupled. In case the vector field survives after the reheating, both the primordial scalar and tensor fluctuations can be enhanced by the anisotropic stress composed of the vector fields during radiation dominated era. We show that through this enhancement the primordial cross-bispectra generate not only CMB bispectra but …
Recently, the Planck 2013 results showed possible evidence for a dipolar power modulation of the CMB temperature fluctuations at low--(\ell) multipoles. This anomaly might imply certain deviations from statistical isotropy. To incorporate the Planck's data into standard cosmological model, we propose an inflation model of the very early universe in an anisotropic spacetime. A generalized Friedmann-Robertson-Walker (FRW) metric is presented in the Randers-Finsler spacetime. We obtain the primordial power spectrum of the scalar perturbation with direction dependence, such as the dipolar modulati…
A broad range of single field models of inflation are analyzed in light of all relevant recent cosmological data, checking whether they can lead to the formation of long-lived Primordial Black Holes (PBHs). To that end we calculate the spectral index of the power spectrum of primordial perturbations as well as its first and second derivatives. PBH formation is possible only if the spectral index increases significantly at small scales, i.e. large wave number $k$. Since current data indicate that the first derivative $α_S$ of the spectral index $n_S(k_0)$ is negative at the pivot scale $k_0$, P…
Lukewarm inflation, primordial black holes and gravitational waves
本研究提出次级微温暴胀可稀释热遗留物并增强小尺度扰动功率谱，产生近乎恒定的引力波背景和亚太阳质量原初黑洞，可解释NANOGrav信号并兼容暗物质组成。
Evidences for the primordial black holes (PBH) presence in the early Universe renew permanently. New limits on their mass spectrum challenge existing models of PBH formation. One of the known model is based on the closed walls collapse after the inflationary epoch. Its intrinsic feature is multiple production of small mass PBH which might contradict observations in the nearest future. We show that the mechanism of walls collapse can be applied to produce substantially different PBH mass spectra if one takes into account the classical motion of scalar fields together with their quantum fluctuat…
We consider two different definitions for loop corrections to the primordial power spectra. One of these is to simply correct the mode functions in the tree order relations using the linearized effective field equations. The second definition involves the spatial Fourier transform of the 2-point correlator. Although the two definitions agree at tree order, we show that they disagree at one loop using the Schwinger-Keldysh formalism, so there are at least two plausible ways of loop correcting the tree order result. We discuss the advantages and disadvantages of each.
We study the power spectra of f(R) inflation using a new technique in which the norm-squared of the mode functions is evolved. Our technique results in excellent analytic approximations for how the spectra depend upon the function $f(R)$. Although the spectra are numerically the same in the Jordan and Einstein frames for the same wave number $k$, they depend upon the geometries of these frames in quite different ways. For example, the power spectra in the two frames are different functions of the number of e-foldings until end of inflation. We discuss how future data on reheating can be used t…
Measurements of 21 cm line fluctuations from minihalos have been discussed as a powerful probe of a wide range of cosmological models. However, previous studies have taken into account only the pixel variance, where contributions from different scales are integrated. In order to sort out information from different scales, we formulate the angular power spectrum of 21 cm line fluctuations from minihalos at different redshifts, which can enhance the constraining power enormously. By adopting this formalism, we investigate expected constraints on parameters characterizing the primordial power spe…
We study the effect of sudden transitions in the effective Planck mass during inflation on primordial power spectra. Specifically, we consider models in which this variation results from the non-minimal coupling of a Brans-Dicke type scalar field. We find that the scalar power spectra develop features at the scales corresponding to those leaving the horizon during the transition. In addition, we observe that the tensor perturbations are largely unaffected, so long as the variation of the Planck mass is below the percent level. Otherwise, the tensor power spectra exhibit damped oscillations ove…
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…
We calculate the spectral distortions from Hawking evaporation of primordial black holes before the epoch of recombination, taking into account emission of all standard model particles, including quark and gluons, and evolving the resulting particle cascades in the expanding Universe. We show that the constraints on the abundance of primordial black holes are stronger by more than an order of magnitude compared to the previous calculations which take only the primary photon emission into account. We also show that the shapes of the spectral distortions is different from the $y$ or $i$-type dis…
We study the spectral tilt of primordial perturbations in Horava-Lifshitz cosmology. The uniform approximation, which is a generalization of the familiar Wentzel-Kramers-Brillouin (WKB) method, is employed to compute the spectral index both numerically and analytically in a closed form. We clarify how the spectral index depends on the inflation model and parameters in the modified dispersion relation.
We investigate constraints on power spectra of the primordial curvature and tensor perturbations with priors based on single-field slow-roll inflation models. We stochastically draw the Hubble slow-roll parameters and generate the primordial power spectra using the inflationary flow equations. Using data from recent observations of CMB and several measurements of geometrical distances in the late Universe, Bayesian parameter estimation and model selection are performed for models that have separate priors on the slow-roll parameters. The same analysis is also performed adopting the standard pa…
We expound ten principles in an attempt to clarify the debate over infrared loop corrections to the primordial scalar and tensor power spectra from inflation. Among other things we note that existing proposals for nonlinear extensions of the scalar fluctuation field $ζ$ introduce new ultraviolet divergences which no one understands how to renormalize. Loop corrections and higher correlators of these putative observables would also be enhanced by inverse powers of the slow roll parameter $ε$. We propose an extension which should be better behaved.
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 examine the possibility of positive spectral index of the power spectrum of the primordial tensor perturbation produced during inflation in the light of the detection of the B-mode polarization by the BICEP2 collaboration. We find a blue tilt is in general possible when the slow-roll parameter decays rapidly. We present two known examples in which a positive spectral index for the tensor power spectrum can be obtained. We also briefly discuss other consistency tests for further studies on inflationary dynamics.
We have developed a precise dictionary between the spectrum of primordial density fluctuations and the parameters of the effective field theory (EFT) of inflation that determine the primordial power spectrum (PPS). At lowest order the EFT contains two parameters: the slow-roll parameter $ε$, which acts as an order parameter, and the speed of sound $c_s$. Applying second-order perturbation theory, we provide maps from the PPS to the EFT parameters that are precise up to the cube of the fractional change in the PPS $(Δ\mathcal{P}/\mathcal{P})^3$, or less than $1\%$ for spectral features that mod…
The holographic space-time model of inflation and its predictions for the CMB primordial spectra
本文基于模哈密顿量涨落关系推广，计算HST暴胀模型原初标量与张量功率谱的精确归一化，表明其无跨普朗克问题且预测与现有CMB数据及张量-标量比观测相符。
Primordial black holes (PBHs) with a wide mass distribution imprinted by the thermal history of the Universe, which naturally produces a high peak at the solar mass scale, could explain the gravitational-wave events seen by LIGO/Virgo and up to the totality of the dark matter. We show that compared to monochromatic or log-normal mass functions, the gravitational wave backgrounds (GWBs) from early PBH binaries and from late binaries in clusters are strongly enhanced at low frequency and could even explain the NANOGrav observations. This enhancement comes from binaries with very low mass ratios,…
We investigate the power spectrum of the distortion of Cosmic Microwave Background (CMB) due to the decay of the primordial magnetic fields. It is known that there are two-types of the CMB distortions, so-called μ- and y-types and we find that the signal of the y-type distortion becomes larger than that of the μ-type one. We also discuss cross power spectra between the CMB distortions and the CMB temperature anisotropy, which are naturally generated due to the existence of the primordial magnetic fields. We find that such cross power spectra have small amplitudes compared with the auto-power s…
We study the effect of supergravity corrections due to a linear and a bilinear term in the Kähler potential, in the context of a supersymmetric hybrid inflation model. By appropriate choice of the parameters associated to these terms, we are able to satisfy the main cosmological constraints for the spectral index $n_s$ and the tensor-to-scalar ratio $r$. In addition, this model predicts primordial black hole abundance enough to account for the whole dark matter of the Universe and gravitational wave spectra within the reach of future detection experiments. The predictions of the model can be m…
The existence of the cosmological particle horizon as the maximum measurable length $l_{max}$ in the universe leads to a generalization of the quantum uncertainty principle (GUP) to the form $Δx Δp \geq \frac{\hbar}{2}\frac{1}{1-αΔx^2} $, where $α\equiv l_{max}^{-2}$. The effects of this GUP on simple quantum mechanical systems has been shown recently by one of the authors\cite{Perivolaropoulos:2017rgq} to be extremely small (beyond current measurements) due to the extremely large scale of the current particle horizon. This is not the case in the Early Universe during the quantum generation of…
Current measurements of the temperature and polarization anisotropy power spectra of the Cosmic Microwave Background (CMB) seem to indicate that the naive expectation for the slow-roll hierarchy within the most simple inflationary paradigm may not be respected in nature. We show that a primordial power spectra with localized features could in principle give rise to the observed slow-roll anarchy when fitted to a featureless power spectrum. Future CMB missions have the key to disentangle among the two possible paradigms and firmly establish the slow-roll mechanism as the responsible one for the…
The gravitational waves measured at LIGO are presumed here to come from merging primordial black holes. We ask how these primordial black holes could arise through inflationary models while not conflicting with current experiments. Among the approaches that work, we investigate the opportunity for corroboration through experimental probes of gravitational waves at pulsar timing arrays. We provide examples of theories that are already ruled out, theories that will soon be probed, and theories that will not be tested in the foreseeable future. The models that are most strongly constrained are th…
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