We study non-Gaussianity generated by adiabatic and isocurvature primordial perturbations. We first obtain, in a very general setting, the non-linear perturbations, up to third order, for an arbitrary number of cosmological fluids, going through one or several decay transitions. We then apply this formalism to the mixed curvaton and inflaton model, allowing for several decay channels. We compute the various contributions to the bispectrum and trispectrum resulting from adiabatic and isocurvature perturbations, which are correlated in general. By investigating some hybrid decay scenario, we show that significant non-Gaussianity of adiabatic and isocurvature types can be generated without conflicting with the present isocurvature constraints from the power spectrum. In particular, we find cases where non-Gaussianity of isocurvature origin can dominate its adiabatic counterpart, both in the bispectrum and in the trispectrum.
Non-Gaussianity may exist in the CDM isocurvature perturbation. We provide general expressions for the bispectrum and trispectrum of both adiabatic and isocurvature pertubations. We apply our result to the QCD axion case, and found a consistency relation between the coefficients of the bispectrum and trispectrum : tau_{NL}^(iso)~10^3 [f_{NL}^(iso)]^{4/3}, if the axion is dominantly produced by quantum fluctuation. Thus future observations of the trispectrum, as well as the bispectrum, will be important for understanding the origin of the CDM and baryon asymmetry.
We calculate the primordial trispectrum of curvature perturbation in quasi-single field inflation, with general sound speeds for both the inflaton and the massive scalar. Special attention is paid to various soft limits of the trispectrum, where the shape function shows characteristic oscillatory pattern (known as the quantum primordial standard clock signal) as a function of the momentum ratio. Our calculation is greatly simplified by using the "mixed propagator" developed under a diagrammatic representation of the in-in formalism.
We make an complementary investigation of the primordial trispectrum from exchanging intermediate scalar modes in multi-field inflation models with generalized kinetic terms. Together with the calculation of irreducible contributions to the primordial trispectrum in Ref.[103], we give the full leading-order primordial trispectrum in generalized multi-field models.
We explain the motivation and main idea of our work in reference arXiv:0907.2476 [hep-th]. We present a simple model of multifield Dirac-Born-Infeld inflation whose bispectrum exhibits a linear combination of the equilateral and local shapes, which are usually considered as separate possibilities. We also point out the presence of a particularly interesting component of the primordial trispectrum.
We compute all N-point primordial curvature correlation functions from inflation at tree-level up to N of order ten or more depending on the choice of parameters. This is achieved for resonant inflationary models in which the inflaton potential has a periodic modulation on top of a slow-roll flat term. These models find a natural UV completion in string theory implementation of axion monodromy. Key to the success of our computation is the observation that gravitational interactions among the perturbations can be neglected, which we argue is justified for any model of inflation with parametrica…
We study the scale dependent bias of the halo power spectrum arising from primordial non-Gaussianity. We present an analytic result of the halo bias including up to the trispectrum contributions. We find the scale dependent bias opens a new possibility of probing the relation between the non-linearity parameters $\fnl$ and $\tnl$.
We present trispectrum estimation methods which can be applied to general non-separable primordial and CMB trispectra. We present a general optimal estimator for the connected part of the trispectrum, for which we derive a quadratic term to incorporate the effects of inhomogeneous noise and masking. We describe a general algorithm for creating simulated maps with given arbitrary (and independent) power spectra, bispectra and trispectra. We propose a universal definition of the trispectrum parameter $T_{NL}$, so that the integrated bispectrum on the observational domain can be consistently comp…
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…
It has been pointed out that hypermagnetic helicity decay at the electroweak symmetry breaking may have produced the observed baryon asymmetry of the Universe through the chiral anomaly in the standard model of particle physics. Although fully helical magnetic field that can adequately produce the observed baryon asymmetry is not strong enough to explain the origin of the intergalactic magnetic field inferred by the Fermi satellite, the mixture of helical and nonhelical primordial magnetic fields may explain both baryogenesis and the intergalactic magnetic fields simultaneously. We first show …
Cosmic magnetic fields are observed to be coherent on large scales and could have a primordial origin. Non-Gaussian signals in the cosmic microwave background (CMB) are generated by primordial magnetic fields as the magnetic stresses and temperature anisotropy they induce depend quadratically on the magnetic field. We compute the CMB scalar trispectrum on large angular scales, for nearly scale-invariant magnetic fields, 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 approxim…
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…
In single-field inflationary models with a low sound speed, the orthogonal shape of the primordial bispectrum arises due to partial cancellations between equilateral-type shapes. This fact allows for a speed of sound c_s as low as about 0.01, which is actually weakly preferred by WMAP data. For such values, the trispectrum, scaling like 1/c_s^4, is of order 10^8 and is therefore comparable to, and greater than, the 1 sigma observational bound t_NL^eq=(-3.11 +- 7.5)*10^6. Hence, the trispectrum is already constraining inflationary mechanisms candidates for generating an orthogonal bispectrum at…
We investigate primordial non-Gaussianity and dark matter isocurvature fluctuations in the modulated reheating and the curvaton scenarios. In these scenarios, large non-Gaussianity can be generated, on the other hand, depending on how dark matter is produced, too large isocurvature fluctuations can also arise, which is inconsistent with current observations. In this paper, we study this issue in a mixed scenario where the curvature fluctuations can also be produced from the inflaton fluctuations as well as those from a light scalar field such as the modulus and the curvaton. We show that primo…
We investigate the primordial trispectra of the general multifield DBI inflationary model. In contrast with the single field model, the entropic modes can source the curvature perturbations on the super horizon scales, so we calculate the contributions from the interaction of four entropic modes mediating one adiabatic mode to the trispectra, at the large transfer limit ($T_{RS}\gg1$). We obtained the general form of the 4-point correlation functions, plotted the shape diagrams in two specific momenta configurations, "equilateral configuration" and "specialized configuration". Our figures show…
Angular bispectrum and trispectrum of scalar-induced gravitational waves: all contributions from primordial non-Gaussianity $f_\mathrm{NL}$ and $g_\mathrm{NL}$
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…
Motivated by the interest in models of the early universe where statistical isotropy is broken and can be revealed in cosmological observations, we consider an SU(2) theory of gauge interactions in a single scalar field inflationary scenario. We calculate the trispectrum of curvature perturbations, as a natural follow up to a previous paper of ours, where we studied the bispectrum in the same kind of models. The choice of a non-Abelian set-up turns out to be very convenient: on one hand, gauge boson self-interactions can be very interesting being responsible for extra non-trivial terms (natura…
The new Planck constraints on the local bispectrum parameter fnl are about 10^5 times tighter than the current constraints on the trispectrum parameter gnl, which means that the allowed numerical values of the second and third order terms in the perturbative expansion of the curvature perturbation are comparable. We show that a consequence of this is that if gnl is large enough to be detectable, then it will induce a large variation between the observable value of fnl and its value in a larger inflated volume. Even if there were only a few extra efoldings between the beginning of inflation and…
We compute the connected four point correlation function (the trispectrum in Fourier space) of cosmological density perturbations at one-loop order in Standard Perturbation Theory (SPT) and the Effective Field Theory of Large Scale Structure (EFT of LSS). This paper is a companion to our earlier work on the non-Gaussian covariance of the matter power spectrum, which corresponds to a particular wavenumber configuration of the trispectrum. In the present calculation, we highlight and clarify some of the subtle aspects of the EFT framework that arise at third order in perturbation theory for gene…
Non-Gaussianity of the primordial density perturbations provides an important measure to constrain models of inflation. At cubic order the non-Gaussianity is captured by two parameters $τ_{\rm NL}$ and $g_{\rm NL}$ that determine the amplitude of the density perturbation trispectrum. Here we report measurements of the kurtosis power spectra of the cosmic microwave background (CMB) temperature as mapped by Planck by making use of correlations between square temperature-square temperature and cubic temperature-temperature anisotropies. In combination with noise simulations, we find the best join…
We investigate tomography of 21-cm brightness temperature fluctuations during the Dark Ages as a probe for constraining primordial non-Gaussianity. We expand the 21- cm brightness temperature up to cubic order in perturbation theory and improve previous models of the signal by including the effect of the free electron fraction. Using modified standard perturbation theory methods that include baryonic pressure effects we derive an improved secondary bispectrum and for the first time derive the secondary trispectrum of 21-cm brightness temperature fluctuations. We then forecast the amount of inf…
Isocurvature Constraints on Dark Matter from Evaporated Primordial Black Holes
Università degli Studi di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Università degli Studi Roma Tre（罗马第三大学）；INFN Sezione di Roma Tre（意大利国家核物理研究所罗马第三分部）；Universität Zürich（苏黎世大学）；ETH Zürich（苏黎世联邦理工学院）
Planck isocurvature constraint on primordial black holes lighter than a kiloton
School of Physics, Korea Institute for Advanced Study（韩国高等科学研究院物理学院）；Department of Science Education, Ewha Womans University（梨花女子大学科学教育系）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Department of Astronomy and Astrophysics and Institute for Gravitation and the Cosmos, The Pennsylvania State University（宾夕法尼亚州立大学天文学与天体物理学系及引力与宇宙研究所）；Cosmology, Gravity and Astroparticle Physics Group, Center for Theoretical Physics of the Universe, Institute for Basic Science（基础科学研究院宇宙理论物理中心宇宙学、引力和高能粒子物理组）；Department of Science Education, Gwangju National University of Education（光州国立教育大学科学教育系）；Department of Physics Education & Research Institute of Natural Science, Gyeongsang National University（庆尚国立大学物理教育系及自然科学研究所）
We show that primordial black holes can be produced from the collapse of large isocurvature perturbations of the cold dark matter. We develop a novel procedure to compute the resulting black hole abundance by studying matched perturbations of matter-only universes, and we use our procedure to translate observational constraints on black hole abundances into model-independent constraints on cold dark matter isocurvature perturbations over a wide range of scales. The constraint on the typical amplitude of the primordial perturbations weakens slightly slower than linearly on small scales.
In this thesis, we show how the structure of the landscape potential of the primordial Universe may be probed through the primordial density perturbations responsible for the origin of the cosmic microwave background anisotropies and the large-scale structure of our Universe. Isocurvature fields may have fluctuated across the barriers separating local minima of the landscape potential during inflation. We analyze how this process could have impacted the evolution of the primordial curvature perturbations. If the typical distance separating consecutive minima of the landscape potential and the …
We study one-loop corrections to the two-point correlation function of tensor perturbations in primordial cosmology induced by massless spectator matter fields. Using the Schwinger-Keldysh formalism in cosmological perturbation theory, we employ dimensional regularization and cutoff regularization to study the finite quantum corrections at one-loop arising from isocurvature fields of the massless scalar, fermion and abelian gauge field which are freely propagating on the FRW spacetime. For all cases, we find a logarithmic running of the form $\frac{C}{q^3} \, \frac{H^4}{M^4_p} \log \left( \fra…
We investigate whether non-adiabatic perturbations from inflation could produce an asymmetric distribution of temperature anisotropies on large angular scales in the cosmic microwave background (CMB). We use a generalised non-linear $δN$ formalism to calculate the non-Gaussianity of the primordial density and isocurvature perturbations due to the presence of non-adiabatic, but approximately scale-invariant field fluctuations during multi-field inflation. This local-type non-Gaussianity leads to a correlation between very long wavelength inhomogeneities, larger than our observable horizon, and …
In this paper, we show how the structure of the landscape potential of the primordial Universe may be probed through the properties of the primordial density perturbations responsible for the origin of the cosmic microwave background anisotropies and the large-scale structure of our Universe. Isocurvature fields -fields orthogonal to the inflationary trajectory- may have fluctuated across the barriers separating local minima of the landscape potential during inflation. We analyze how this process could have impacted the evolution of the primordial curvature perturbations. If the typical distan…
We present posterior likelihoods and Bayesian model selection analysis for generalized cosmological models where the primordial perturbations include correlated adiabatic and cold dark matter isocurvature components. We perform nested sampling with flat and, for the first time, curved spatial geometries of the Universe, using data from the cosmic microwave background (CMB) anisotropies, the Union supernovae (SN) sample and a combined measurement of the integrated Sachs-Wolfe (ISW) effect. The CMB alone favors a 3% (positively correlated) isocurvature contribution in both the flat and curved ca…
Primordial non-Gaussianity generated in an inflationary model where inflation is preceded by a radiation era is discussed. It is shown that both bispectrum and trispectrum non-Gaussianities are enhanced due to the presence of pre-inflationary radiation era. One distinguishing feature of such a scenario is that the trispectrum non-Gaussianity is larger than the bispectrum one.
We study non-Gaussian properties of the isocurvature perturbations in the dark radiation, which consists of the active neutrinos and extra light species, if exist. We first derive expressions for the bispectra of primordial perturbations which are mixtures of curvature and dark radiation isocurvature perturbations. We also discuss CMB bispectra produced in our model and forecast CMB constraints on the nonlinearity parameters based on the Fisher matrix analysis. Some concrete particle physics motivated models are presented in which large isocurvature perturbations in extra light species and/or …
We study the $TTμ$ bispectrum, generated by correlations between Cosmic Microwave Background temperature (T) anisotropies and chemical potential ($μ$) distortions, and we analyze its dependence on primordial local trispectrum parameters $g_{\rm NL}$ and $τ_{\rm NL}$. We cross-check our results by comparing the full bispectrum calculation with the expectations from a general physical argument, based on predicting the shape of $μ$-T correlations from the couplings between short and long perturbation modes induced by primordial non-Gaussianity. We show that $both$ $g_{\rm NL}$ and $τ_{\rm NL}$-pa…
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…
We calculate the shape correlations between trispectra in various equilateral non-Gaussian models, including DBI inflation, ghost inflation and Lifshitz scalars, using the full trispectrum as well as the reduced trispectum. We find that most theoretical models are distinguishable from the shapes of primordial trispectra except for several exceptions where it is difficult to discriminate between the models, such as single field DBI inflation and a Lifshitz scalar model. We introduce an estimator for the amplitude of the trispectrum, $g_{\rm NL} ^{equil}$ and relate it to model parameters in var…
The kinetic Sunyaev Zel'dovich effect is a secondary CMB temperature anisotropy that provides a powerful probe of the radial-velocity field of matter distributed across the Universe. This velocity field is reconstructed by combining high-resolution CMB measurements with galaxy survey data, and it provides an unbiased tracer of matter perturbations in the linear regime. In this paper, we show how this measurement can be used to probe primordial non-Gaussianity of the local type, particularly focusing on the trispectrum amplitude $τ_{\rm NL}$, as may arise in a simple two-field inflation model t…
We numerically study the primordial black hole (PBH) formation by an isocurvature perturbation of a massless scalar field on super Hubble scales in the radiation-dominated universe. As a first step we perform simulations of spherically symmetric configurations. For the initial condition, we employ the spatial gradient expansion and provide the general form of the growing mode solutions valid up through the second order in this expansion. The initial scalar field profile is assumed to be Gaussian with a characteristic comoving wavenumber $k$; $\sim\exp(-k^2R^2)$, where $R$ is the radial coordin…
We study the non-Gaussian features in single-field slow-roll inflationary scenario where inflation is preceded by a radiation era. In such a scenario both bispectrum and trispectrum non-Gaussianities are enhanced. Interestingly, the trispectrum in this scenario does not depend up on the slow-roll parameters and thus $τ_{NL}$ is larger than $f_{NL}$ which can be a signature of such a pre-inflationary radiation era.
We explore the correlations between primordial non-Gaussianity and isocurvature perturbation. We sketch the generic relation between the bispectrum of the curvature perturbation and the cross-correlation power spectrum in the presence of explicit couplings between the inflaton and another light field which gives rise to isocurvature perturbation. Using a concrete model of a Peccei-Quinn type field with generic gravitational couplings, we illustrate explicitly how the primordial bispectrum correlates with the cross-correlation power spectrum. Assuming the resulting fnl ~ O(1), we find that the …
We investigate new shapes of local primordial non-Gaussianities in the CMB. Allowing for a primordial isocurvature mode along with the main adiabatic one, the angular bispectrum is in general a superposition of six distinct shapes: the usual adiabatic term, a purely isocurvature component and four additional components that arise from correlations between the adiabatic and isocurvature modes. We present a class of early Universe models in which various hierarchies between these six components can be obtained, while satisfying the present upper bound on the isocurvature fraction in the power sp…
We investigate the primordial non-Gaussianities from the trispectra in multi-field inflation models, which can be seen as generalization of multi-field $k$-inflation and multi-DBI inflation. We derive the full fourth-order perturbation action for the inflaton fields and evaluate the four-point correlation functions for the perturbations in the limit $\ca \ll 1$ and $\ce \ll1$. There are three types of momentum-dependent shape functions which arise from three types of four-point interaction vertices. The final trispectrum of the curvature perturbation can be expressed in terms of the deformatio…
We use the δN formalism to study the trispectrum T_ζof the primordial curvature perturbation ζwhen the latter is generated by vector field perturbations, considering the tree-level and one-loop contributions. The order of magnitude of the level of non-gaussianity in the trispectrum, τ_{NL}, is calculated in this scenario and related to the order of magnitude of the level of non-gaussianity in the bispectrum, f_{NL}, and the level of statistical anisotropy in the power spectrum, g_ζ. Such consistency relations will put under test this scenario against future observations. Comparison with the ex…
We study the covariance in the angular power spectrum estimates of CMB fluctuations when the primordial fluctuations are non-Gaussian. The non-Gaussian covariance comes from a nonzero connected four-point correlation function -- or the trispectrum in Fourier space -- and can be large when long-wavelength (super-CMB) modes are strongly coupled to short-wavelength modes. The effect of such non-Gaussian covariance can be modeled through additional freedom in the theoretical CMB angular power spectrum and can lead to different inferred values of the standard cosmological parameters relative to tho…
We analytically derive a more accurate formula for the power spectrum of the biased objects with the primordial non-Gaussianity parameterized not only by the non-linearity parameter fNL, but also by gNL and tauNL which characterize the trispectrum of the primordial curvature perturbations. We adopt the integrated perturbation theory which was constructed in Matsubara (2011). We discuss an inequality between fNL and tauNL in the context of the scale-dependent bias, by introducing a stochasticity parameter. We also mention higher order loop corrections into the scale-dependency of the bias param…
We study CMB constraints on non-Gaussianity from isocurvature perturbations of general types. Specifically, we study CDM/neutrino isocurvature perturbations which are uncorrelated or totally correlated with adiabatic ones. Using the data from the WMAP 7-year observation at V and W bands, we obtained optimal constraints on the nonlinearity parameters of adiabatic and isocurvature perturbations. Our result shows that primordial perturbations are consistent with Gaussian ones at around 2 sigma level for above mentioned isocurvature modes.
We compute the impact of the running of higher order density correlation functions on the two point functions of CMB spectral distortions (SD). We show that having some levels of running enhances all of the SDs by few orders of magnitude which might make them easier to detect. Taking a reasonable range for $ |n_{f_{NL}} |\lesssim 1.1$ and with $f_{NL} = 5$ we show that for PIXIE like experiment, the signal to noise ratio, $(S/N)_{i}$, enhances to $\lesssim 4000$ and $\lesssim 10$ for $μT$ and $yT$ toward the upper limit of $n_{f_{NL}}$. In addition, assuming $ |n_{τ_{NL}}|< 1$ and $τ_{NL} = 10…
We investigate the degeneracy of the isocurvature perturbations and the primordial gravitational waves, by using recent observations of the cosmic microwave background (CMB) reported by Planck and BICEP2 collaborations. We show that the tension in the bound on the tensor-to-scalar ratio $r$ between Planck and BICEP2 can be resolved by introducing the anti-correlated isocurvature perturbations. Quantitatively, we find that with the anti-correlated isocurvature perturbations the constraints on $r$ from Planck alone and BICEP2 results can be consistent at 68 % C.L.
The late-time effect of primordial non-Gaussianity offers a window into the physics of inflation and the very early Universe. In this work we study the consequences of a particular class of primordial non-Gaussianity that is fully characterized by initial density fluctuations drawn from a non-Gaussian probability density function, rather than by construction of a particular form for the primordial bispectrum. We numerically generate multiple realisations of cosmological structure and use the late-time matter power spectrum, bispectrum and trispectrum to determine the effect of these modified i…
Primordial black holes (PBHs) are black holes which may have formed very early on during the radiation dominated era in the early universe. We present here a method by which the large scale perturbations in the density of primordial black holes may be used to place tight constraints on non-gaussianity if PBHs account for dark matter (DM). The presence of local-type non-gaussianity is known to have a significant effect on the abundance of primordial black holes, and modal coupling from the observed CMB scale modes can significantly alter the number density of PBHs that form within different reg…
We formulate the two-point correlation function of primordial black holes (PBHs) at their formation time, based on the functional integration approach which has often been used in the context of halo clustering. We find that PBH clustering on super-Hubble scales could never be induced in the case where the initial primordial fluctuations are Gaussian, while it can be enhanced by the so-called local-type trispectrum (four-point correlation function) of the primordial curvature perturbations.
We compute the primordial trispectrum for curvature perturbations produced during cosmic inflation in models with standard kinetic terms, when the initial quantum state is not necessarily the vacuum state. The presence of initial perturbations enhances the trispectrum amplitude for configuration in which one of the momenta, say $k_3$, is much smaller than the others, $k_3 \ll k_{1,2,4}$. For those squeezed configurations the trispectrum acquires the so-called local form, with a scale dependent amplitude that can get values of order $ ε({k_1}/{k_3})^2$. This amplitude can be larger than the pre…
