Even if massive ($10\,M_\odot \lesssim M \lesssim 10^4 M_\odot$) primordial black holes (PBHs) can only account for a small fraction of the dark matter (DM) in the universe, they may still be responsible for a sizable fraction of the coalescence events measured by LIGO/Virgo, and/or act as progenitors of the supermassive black holes (SMBHs) observed already at high redshift ($z\gtrsim 6$). In presence of a dominant, non-PBH DM component, the bounds set by CMB via an altered ionization history are modified. We revisit the cosmological accretion of a DM halo around PBHs via toy models and dedicated numerical simulations, deriving updated CMB bounds which also take into account the last Planck data release. We prove that these constraints dominate over other constraints available in the literature at masses $M\gtrsim 20-50\,M_\odot$ (depending on uncertainty in accretion physics), reaching the level $f_{\rm PBH}<3\times 10^{-9}$ around $M\sim 10^{4}\,M_\odot$. These tight bounds are nonetheless consistent with the hypothesis of a primordial origin of the SMBH massive seeds.
Primordial magnetic fields (PMFs) create a large squeezed-type non-Gaussianity in tensor perturbation, which generates non-Gaussian temperature fluctuations in the cosmic microwave background (CMB). We for the first time derive an observational constraint on such a tensor non-Gaussianity from observed CMB maps. Analyzing temperature maps of the WMAP 7-year data, we find that such a tensor non-Gaussianity is consistent with zero. This gives an upper bound on PMF strength smoothed on $1 ~ {\rm Mpc}$ as $B_{1 ~ \rm Mpc} < 3.1 ~{\rm nG}$ at $95%$ C.L.
It is shown that small-scale magnetic fields present before recombination induce baryonic density inhomogeneities of appreciable magnitude. The presence of such inhomogeneities changes the ionization history of the Universe, which in turn decreases the angular scale of the Doppler peaks and increases Silk damping by photon diffusion. This unique signature could be used to (dis)prove the existence of primordial magnetic fields of strength as small as B~10^(-11) Gauss by upcoming cosmic microwave background observations.
A claimed detection of cosmological tensor perturbations from inflation via B-mode polarization of the cosmic microwave background requires distinguishing other possible B-mode sources. One such potential source of confusion is primordial magnetic fields. For sufficiently low-amplitude B-mode signals, the microwave background temperature and polarization power spectra from power-law tensor perturbations and from a power-law primordial magnetic field are indistinguishable. However, we show that such a magnetic field will induce a small-scale Faraday rotation which is detectable using four-point…
We investigate photon signatures of general decaying dark-matter particles in halos of primordial black holes. We derive the halo-profile density and the total decay rate for these combined dark-matter scenarios. For the case of axion-like particles of masses below $\mathcal{O}( 1 )\,$keV, we find strong bounds on the decay constant which are several orders of magnitude stronger than the strongest existing bounds, for all halo masses above $\mathcal{O}( 10^{-5} )$ solar masses. Using future X-ray measurements, it will be possible to push these bounds on such combined dark-matter scenarios even…
Primordial magnetic fields will generate non-Gaussian signals in the cosmic microwave background (CMB) as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. We compute a new measure of magnetic non-Gaussianity, the CMB trispectrum, on large angular scales, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approximately a few times 10^{-29} and 10^{-19}, respectively. Observational limits on CMB non-Gaussianity from WMAP data…
Standard Clocks in the primordial epoch leave a special type of features in the primordial perturbations, which can be used to directly measure the scale factor of the primordial universe as a function of time a(t), thus discriminating between inflation and alternatives. We have started to search for such signals in the Planck 2013 data using the key predictions of the Standard Clock. In this Letter, we summarize the key predictions of the Standard Clock and present an interesting candidate example in Planck 2013 data. Motivated by this candidate, we construct and compute full Standard Clock m…
We constrain the primordial gravitational waves from cosmic microwave background (CMB) and stochastic gravitational wave background (SGWB) observations. SGWB provides the latest way to explore the early universe and the cosmological evolution which can be reflected by primordial gravitational waves. We not only combine LIGO observations with CMB to measure primordial gravitational waves, but also forecast the potential abilities of the LISA detector and PTA projects. In the $Λ$CDM+$r$+$n_t$ model, the standard six parameters change slightly from SGWB observations. While the constraints on tens…
The cosmic microwave background (CMB) observation by the Planck satellite precisely determines primordial curvature fluctuations on larger scales than $\mathcal O(1)\,\mathrm{Mpc}$, while the small-scale curvature fluctuation is still less constrained. The constraint on small-scale fluctuations is highly improved if we assume the standard thermal relic dark matter scenario. When small-scale fluctuations are large enough, dense regions collapse to form small halos even in a redshift $z\gtrsim10^3$, which is called ultracompact minihalos. These minihalos enhance the annihilation of the dark matt…
We discuss early structure formation of small scales sourced by primordial black holes (PBHs) which constitute a small part of present cold dark matter component. We calculate the mass function and power spectrum of haloes originated from the Poisson fluctuations of PBH number and show that the number of small haloes is significantly modified in the presence of PBHs even if their fraction accounts for only $10^{-4}$--$10^{-3}$ of total dark matter abundance. We then compute the subsequent 21cm signature from those haloes. We find that PBHs can provide major contributions at high redshifts with…
Cosmic microwave background observations are most commonly analyzed by estimating the power spectrum. In the limit where the CMB statistics are perfectly Gaussian, this extracts all the information, but the CMB also contains detectable non-Gaussian contributions from secondary, and possibly primordial, sources. We review possible sources of CMB non-Gaussianity and describe statistical techniques which are optimized for measuring them, complementing the power spectrum analysis. The machinery of $N$-point correlation functions provides a unifying framework for optimal estimation of primordial no…
We derive a formula for the halo/galaxy bispectrum on the basis of the integrated Perturbation Theory (iPT). In addition to the gravity-induced non-Gaussianity, we consider the non-Gaussianity of the primordial curvature perturbations, and investigate in detail the effect of such primordial non-Gaussianity on the large-scale halo/galaxy bispectrum. In iPT, the effects of primordial non-Gaussianity are wholly encapsulated in the linear (primordial) polyspectra, and we systematically calculate the contributions to the large-scale behaviors arising from the three types of primordial bispectrum (l…
The most direct probe of non-Gaussian initial conditions has come from bispectrum measurements of temperature fluctuations in the Cosmic Microwave Background and of the matter and galaxy distribution at large scales. Such bispectrum estimators are expected to continue to provide the best constraints on the non-Gaussian parameters in future observations. We review and compare the theoretical and observational problems, current results and future prospects for the detection of a non-vanishing primordial component in the bispectrum of the Cosmic Microwave Background and large-scale structure, and…
We study the impact of primordial non-Gaussianity on the density profile of dark matter halos by using the semi-analytical model introduced recently by Dalal {\it et al.} which relates the peaks of the initial linear density field to the final density profile of dark matter halos. Models with primordial non-Gaussianity typically produce an initial density field that differs from that produced in Gaussian models. We use the path-integral formulation of excursion set theory to calculate the non-Gaussian corrections to the peak profile and derive the statistics of the peaks of non-Gaussian densit…
The General Relativity affirms that any field is a source of gravitational field, thus one should affirm that the energy of Cosmic Microwave Background (CMB) generated primordial gravitational waves. The present article shows that a gravitational wave with dimensionless amplitude $\sim 10^{-5}$ and large wave length $\sim 10$ megaparsecs shifts temperature of CMB radiation about of a part in $10^{5}$.
We perform three-dimensional simulations of structure formation in the early Universe, when boosting the primordial power spectrum on approximately kpc scales. We demonstrate that our simulations are capable of producing power-law profiles close to the steep $ρ\propto r^{-9/4}$ halo profiles that are commonly assumed to be a good approximation to ultracompact minihalos (UCMHs). However, we show that for more realistic initial conditions in which halos are neither perfectly symmetric nor isolated, the steep power-law profile is disrupted and we find that the Navarro-Frenk-White profile is a bet…
A lower bound on primordial power spectrum from halo substructure
University of Amsterdam（阿姆斯特丹大学）；Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo（东京大学宇宙起源研究科）；Yokohama National University（横滨国立大学）；RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论数学科学部）；Institute for Theoretical Physics, Kanazawa University（金泽大学理论物理研究所）；Saga University（佐贺大学）
A cosmic lepton asymmetry $η_{\text{l}}=(n_{\text{l}}-n_{\bar{\text{l}}})/n_γ$ affects the primordial helium abundance and the expansion rate of the early Universe. Both of these effects have an impact on the anisotropies of the cosmic microwave background (CMB). We derive constraints on the neutrino chemical potentials from the Planck 2015 data, assuming equal lepton flavour asymmetries and negligible neutrino masses. We find $ξ=-0.002 ^{+0.114}_{-0.111}$ (95\% CL) for the chemical potentials, which corresponds to $ -0.085 \leq η_{\text{l}} \leq 0.084$. Our constraints on the lepton asymmetry…
We evaluate the angular bispectrum of the CMB temperature anisotropy at large angular scale due to a stochastic background of primordial magnetic fields. The shape of non-Gaussianity depends on the spectral index of the magnetic field power spectrum and is peaked in the squeezed configuration for a scale-invariant magnetic spectrum. By using the large angular part of the bispectrum generated by magnetic fields, the present bounds on non-Gaussianity set a limit on the amplitude of the primordial magnetic field of the order of 10 nGauss for the scale-invariant case and 20 nGauss for the other sp…
We calculate the cosmic microwave background bispectrum of vector modes induced from primordial magnetic fields. We take into account the full angular dependence of the bispectrum and discuss the amplitude and also the shape of the bispectrum in $\ell$ space. In the squeezed limit as $\ell_1 = \ell_2 \gg \ell_3$, we estimate a typical values of the normalized reduced bispectrum as $\ell_1(\ell_1 + 1)\ell_3(\ell_3+1)|b_{\ell_1\ell_2\ell_3}| \sim 2 \times 10^{-19}$, for the strength of the primordial magnetic field smoothed on $1 {\rm Mpc}$ scale $B_{1 \rm Mpc} = 4.7 \rm nG$ assuming a nearly sc…
We utilize Young's algorithm to model the adiabatic compression of the dark matter haloes of galaxies in the THINGS survey to determine the relationship between the halo fit to the rotation curve and the corresponding primordial halo prior to compression. Young's algorithm conserves radial action and angular momentum, resulting in less halo compression than more widely utilized approximations. We find that estimates of the parameters of the NFW haloes fit to the current dark matter distribution systematically overestimate the concentration and underestimate the virial velocity of the correspon…
Study of primordial non-Gaussianity $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ with the cross-correlations between the scalar-induced gravitational waves and the cosmic microwave background
We explore the effect of a cubic correction gnl*phi^3 on the mass function and bias of dark matter haloes extracted from a series of large N-body simulations and compare it to theoretical predictions. Such cubic terms can be motivated in scenarios like the curvaton model, in which a large cubic correction can be produced while simultaneously keeping the quadratic fnl*phi^2 correction small. The deviation from the Gaussian halo mass function is in reasonable agreement with the theoretical predictions. The scale-dependent bias correction Delta b_kappa(k,gnl) measured from the auto- and cross-pow…
We investigate constraints on Lorentz invariance violation in the neutrino sector from a joint analysis of big bang nucleosynthesis and the cosmic microwave background. The effect of Lorentz invariance violation during the epoch of big bang nucleosynthesis changes the predicted helium-4 abundance, which influences the power spectrum of the cosmic microwave background at the recombination epoch. In combination with the latest measurement of the primordial helium-4 abundance, the Planck 2015 data of the cosmic microwave background anisotropies give a strong constraint on the deformation paramete…
Using $N$-body simulations of cosmological large-scale structure formation, for the first time, we show that the anisotropic primordial non-Gaussianity (PNG) causes a scale-dependent modification, given by $1/k^2$ at small $k$ limit, in the three-dimensional power spectra of halo shapes (intrinsic alignments), whilst the conventional power spectrum of halo number density field remains unaffected. We discuss that wide-area imaging and spectrocopic surveys observing the same region of the sky allow us to constrain the quadrupole PNG coefficient $f_{\rm NL}^{s=2}$ at a precision comparable with o…
We study the halo mass function in the presence of the kurtosis type of primordial non-Gaussianity. The kurtosis corresponds to the trispectrum as defined in Fourier space. The primordial trispectrum is commonly characterized by two parameters, $τ_{\rm NL}$ and $g_{\rm NL}$. As applications of the derived non-Gaussian mass function, we consider the effect on the abundance of void structure, the effect on early star formation and on formation of the most massive object at high redshift. We show that by comparing the effects of primordial non-Gaussianity on cluster abundance with that on void ab…
The high-mass end of the halo mass function is a sensitive probe of primordial non-Gaussianity (NG). In a recent study [9] we have computed the NG halo mass function in the context of the Excursion Set theory and shown that the primordial NG imprint is coupled to that induced by the non-linear collapse of dark matter halos. We also found an excellent agreement with N-body simulation results. Here, we perform a more accurate computation which accounts for the interval validity of the bispectrum expansion to next-to-leading order and extend the calculation to the case of a non-vanishing primordi…
We constrain the spectral running by combining cosmic microwave background (CMB) data, baryon acoustic oscillation (BAO) data and the constraint from primordial black holes (PBHs). We find that the constraint from PBHs has a significant impact on the running of running of scalar spectral index, and a power-law scalar power spectrum without running is consistent with observational data once the constraint from PBHs is taken into account. In addition, from the constraints on the slow-roll parameters, the derived tensor spectral index in the single-field slow-roll inflation model is quite small, …
In the last few decades, advances in observational cosmology have given us a standard model of cosmology. We know the content of the universe to within a few percent. With more ambitious experiments on the way, we hope to move beyond the knowledge of what the universe is made of, to why the universe is the way it is. In this review paper we focus on primordial non-Gaussianity as a probe of the physics of the dynamics of the universe at the very earliest moments. We discuss 1) theoretical predictions from inflationary models and their observational consequences in the cosmic microwave backgroun…
This is a summary of presentations delivered at the OC1 parallel session "Primordial Gravitational Waves and the CMB" of the 12th Marcel Grossmann meeting in Paris, July 2009. The reports and discussions demonstrated significant progress that was achieved in theory and observations. It appears that the existing data provide some indications of the presence of gravitational wave contribution to the CMB anisotropies, while ongoing and planned observational efforts are likely to convert these indications into more confident statements about the actual detection.
Modeling the nonlinearity of the halo bispectrum remains a major challenge in modern cosmology, in particular for ongoing and upcoming large-scale structure observations that are performed to study the inflationary physics. The "power spectrum response" offers a solution for bispectrum in the so-called squeezed limit, in which one wavenumber is much smaller than the other two. As a first step, we demonstrate that the halo squeezed-limit bispectrum computed from the second-order standard perturbation theory agrees precisely with the responses of linear halo power spectrum to large-scale density…
This lecture is a sketch of the physics of the cosmic microwave background. The observed anisotropy can be divided into four main contributions: variations in the temperature and gravitational potential of the primordial plasma, Doppler effect from its motion, and a net red/blueshift the photons accumulate from traveling through evolving gravitational potentials on their way from the primordial plasma to here. These variations are due to primordial perturbations, probably caused by quantum fluctuations in the very early universe. The ongoing Planck satellite mission to observe the cosmic micro…
Circular ("V-mode") polarization is expected to be vanishing in the CMB, since it is not produced in Thomson scattering. However, considering that the conventional CMB anisotropies are generated via an early universe mechanism such as inflation or a bouncing scenario, it is possible that circular polarization could be primordially produced and survive to the surface of last scattering. We study this in detail, and find a large class of inflationary models that produce a nearly scale invariant spectrum of scalar V-mode anisotropies. We study the inflationary production and subsequent evolution …
We present the first cosmological simulations of primordial magnetic fields derived from the constraints by the Cosmic Microwave Background observations, based on the fields' gravitational effect on cosmological perturbations. We evolved different primordial magnetic field models with the {\enzo} code and compared their observable signatures (and relative differences) in galaxy clusters, filaments and voids. The differences in synchrotron radio powers and Faraday Rotation measure from galaxy clusters are generally too small to be detected, whereas differences present in filaments will be testa…
We investigate the effect of equilateral-type primordial trispectrum on the halo/galaxy bispectrum. We consider three types of equilateral primordial trispectra which are generated by quartic operators naturally appeared in the effective field theory of inflation and can be characterized by three non-linearity parameters, $g_{\rm NL} ^{\dotσ^4}$, $g_{\rm NL} ^{\dotσ^2 (\partial σ)^2}$, and $g_{\rm NL} ^{(\partial σ)^4}$. Recently, constraints on these parameters have been investigated from CMB observations by using WMAP9 data. In order to consider the halo/galaxy bispectrum with the equilatera…
Primordial magnetic fields (PMFs), being present before the epoch of cosmic recombination, induce small-scale baryonic density fluctuations. These inhomogeneities lead to an inhomogeneous recombination process that alters the peaks and heights of the large-scale anisotropies of the cosmic microwave backround (CMB) radiation. Utilizing numerical compressible MHD calculations and a Monte Carlo Markov chain analysis, which compares calculated CMB anisotropies with those observed by the \textit{WMAP} and \textit{Planck} satellites, we derive limits on the magnitude of putative PMFs. We find that t…
A wide range of multifield inflationary models generate non-Gaussian initial conditions in which the initial adiabatic fluctuation is of the form (zeta_G + g_{NL} zeta_G^3). We study halo clustering in these models using two different analytic methods: the peak-background split framework, and brute force calculation in a barrier crossing model, obtaining agreement between the two. We find a simple, theoretically motivated expression for halo bias which agrees with N-body simulations and can be used to constrain g_{NL} from observations. We discuss practical caveats to constraining g_{NL} using…
If primordial black holes (PBHs) form directly from inhomogeneities in the early Universe, then the number in the mass range $10^5 -10^{12}M_{\odot}$ is severely constrained by upper limits to the $μ$ distortion in the cosmic microwave background (CMB). This is because inhomogeneities on these scales will be dissipated by Silk damping in the redshift interval $5\times 10^4\lesssim z\lesssim2\times 10^6$. If the primordial fluctuations on a given mass scale have a Gaussian distribution and PBHs form on the high-$σ$ tail, as in the simplest scenarios, then the $μ$ constraints exclude PBHs in thi…
Primordial non-Gaussianity can lead to a scale-dependent bias in the density of collapsed halos relative to the underlying matter density. The galaxy power spectrum already provides constraints on local-type primordial non-Gaussianity complementary those from the cosmic microwave background (CMB), while the bispectrum contains additional shape information and has the potential to outperform CMB constraints in future. We develop the bias model for the halo density contrast in the presence of local-type primordial non-Gaussianity, deriving a bivariate expansion up to second order in terms of the…
A primordial vector mode and its associated magnetic field generation are investigated. Firstly, we put an observational constraint on the amount of the primordial vector mode from the seven-year WMAP data. The constraint is found as $r_v \lesssim -\frac{r}{40}+0.012$, where $r_v$ and $r$ are the amounts of vector and tensor perturbation amplitudes with respect to the scalar one, respectively. Secondly, we calculate the spectrum of magnetic fields inevitably created from the primordial vector mode, given the constraint on $r_v$. It is found that the maximum amount of magnetic fields generated …
Primordial dark matter (DM) haloes are the smallest gravitationally bound DM structures from which the first stars, black holes, and galaxies form and grow in the early universe. However, their structures are sensitive to the free streaming scale of DM, which in turn depends on the nature of DM particles. In this work, we test the hypothesis that the slope of the central cusps in primordial DM haloes near the free streaming scale depends on the nature of merging process. By combining and analysing data from a cosmological simulation with the cutoff in the small-scale matter power spectrum as w…
The presence of primordial magnetic fields increases the minimum halo mass in which star formation is possible at high redshifts. Estimates of the dynamical mass of ultra-faint dwarf galaxies (UFDs) within their half-light radius constrain their virialized halo mass before their infall into the Milky Way. The inferred halo mass and formation redshift of the UFDs place upper bounds on the primordial comoving magnetic field, $B_0$. We derive an upper limit of $0.50\pm 0.086$ ($0.31\pm 0.04$) nG on $B_0~$ assuming the average formation redshift of the UFD host halos is $z_{\rm form}=$ 10 (20), re…
We argue that primordial dark matter halos could be generated during radiation domination by long range attractive forces stronger than gravity. In this paper we derive the conditions under which these structures could dominate the dark matter content of the Universe while passing microlensing constraints and cosmic microwave background energy injection bounds. The dark matter particles would be clumped in objects in the solar mass range with typical sizes of the order of the solar system. Consequences for direct dark matter searches are important.
We develop the halo model of large-scale structure as an accurate tool for probing primordial non-Gaussianity. In this study we focus on understanding the matter clustering at several redshifts. The primordial non-Gaussianity is modeled as a quadratic correction to the local Gaussian potential, and is characterized by the parameter f_NL. In our formulation of the halo model we pay special attention to the effect of halo exclusion, and show that this can potentially solve the long standing problem of excess power on large scales in this model. The model depends on the mass function, clustering …
The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight constraints on non-Gaussian processes in the early Universe and allow inference of the dynamics driving inflation. We present a tree level derivation of the halo bispectrum arising from non-linear clustering, non-linear biasing and primordial non-Gaussianity. A diagrammatic description is developed to provide an intuitive understanding of the contributing terms and…
One of the major targets for next-generation cosmic microwave background (CMB) experiments is the detection of the primordial B-mode signal. Planning is under way for Stage-IV experiments that are projected to have instrumental noise small enough to make lensing and foregrounds the dominant source of uncertainty for estimating the tensor-to-scalar ratio $r$ from polarization maps. This makes delensing a crucial part of future CMB polarization science. In this paper we present a likelihood method for estimating the tensor-to-scalar ratio $r$ from CMB polarization observations, which combines th…
If a primordial magnetic field in the universe has non-zero helicity, the violation of parity symmetry results in non-zero correlations between cosmic microwave background temperature and B-mode polarization. In this paper we derive approximations to the relevant microwave background power spectra arising from a helical magnetic field. Using the cross-power spectrum between temperature and B-mode polarization from the WMAP nine-year data, we set a 95\% confidence level upper limit on the helicity amplitude to be 10 nG$^2$ Gpc for helicity spectral index $n_H = -1.9$, for a cosmological magneti…
Since the first limit on the (local) primordial non-Gaussianity parameter, fNL, was obtained from COBE data in 2002, observations of the CMB have been playing a central role in constraining the amplitudes of various forms of non-Gaussianity in primordial fluctuations. The current 68% limit from the 7-year WMAP data is fNL=32+/-21, and the Planck satellite is expected to reduce the uncertainty by a factor of four in a few years from now. If fNL>>1 is found by Planck with high statistical significance, all single-field models of inflation would be ruled out. Moreover, if the Planck satellite fin…
Standard big bang cosmology predicts a cosmic neutrino background at $T_ν\simeq 1.95~$K. Given the current neutrino oscillation measurements, we know most neutrinos move at large, but non-relativistic, velocities. Therefore, dark matter haloes moving in the sea of primordial neutrinos form a neutrino wake behind them, which would slow them down, due to the effect of {\it dynamical friction}. In this paper, we quantify this effect for realistic haloes, in the context of the halo model of structure formation, and show that it scales as $m_ν^4$ $\times$ relative velocity, and monotonically grows …
