We discuss cosmological perturbation theory at third order, deriving the gauge transformation rules for metric and matter perturbations, and constructing third order gauge invariant quantities. We present the Einstein tensor components, the evolution equations for a perfect fluid, and the Klein-Gordon equation at third order, including scalar, vector and tensor perturbations. In doing so, we also give all second order tensor components and evolution equations in full, exhilarating generality.
A roadmap to cosmological parameter analysis with third-order shear statistics III: Efficient estimation of third-order shear correlation functions and an application to the KiDS-1000 data
I begin by briefly discussing the first two cosmological paradigms, the hot big-bang model and $Λ$CDM. In discussing the third paradigm, I focus on the issues it must address, what its aspirations should be, and how it might be initiated. I end with a brief history of my collaborations with Frank Wilczek.
A roadmap to cosmological parameter analysis with third-order shear statistics IV. Analytic cross-covariance between second- and third-order aperture masses
Using the covariant formalism, we derive the equations of motion for adiabatic and entropy perturbations at third order in perturbation theory for cosmological models involving two scalar fields. We use these equations to calculate the trispectrum of ekpyrotic and cyclic models in which the density perturbations are generated via the entropic mechanism. In these models, the conversion of entropy into curvature perturbations occurs just before the big bang, either during the ekpyrotic phase or during the subsequent kinetic energy dominated phase. In both cases, we find that the non-linearity pa…
We study the third order solutions of the cosmological density perturbations in the Horndeski's most general scalar-tensor theory under the condition that the Vainshtein mechanism is at work. In this work, we thoroughly investigate the independence property of the functions describing the nonlinear mode-couplings, which is also useful for models within the general relativity. Then, we find that the solutions of the density contrast and the velocity divergence up to the third order ones are characterized by 6 parameters. Furthermore, the 1-loop order power spectra obtained with the third order …
We study the correlations of the shear signal between triplets of sources in the Canada-France-Hawaii Lensing Survey (CFHTLenS) to probe cosmological parameters via the matter bispectrum. In contrast to previous studies, we adopted a non-Gaussian model of the data likelihood which is supported by our simulations of the survey. We find that for state-of-the-art surveys, similar to CFHTLenS, a Gaussian likelihood analysis is a reasonable approximation, albeit small differences in the parameter constraints are already visible. For future surveys we expect that a Gaussian model becomes inaccurate.…
Early energy injection to the Cosmic Microwave Background (CMB) from dissipation of acoustic waves generates deviations from the blackbody spectrum not only at second-order but also at third-order in cosmological perturbations. We compute this new spectral distortion $\mathcal κ$ based on third-order cosmological perturbation theory and show that $κ$ arises as a result of mode coupling between spectral distortions and temperature perturbations. The ensemble average of $κ$ can be directly sourced by (integrated) primordial non-Gaussianity. In particular, we roughly estimate the signal as $κ=f^{…
The multi-messenger observation of GW170817 enabled the first historic measurement of the Hubble constant via a standard siren, so-called in analogy to standard candles that enabled the measurement of the luminosity distance versus redshift relationship at small redshift. In the next decades, third-generation observatories are expected to detect hundreds to thousand of gravitational wave events from compact binary coalescences with potentially a joint electromagnetic counterpart. In the present work, we show how future standard siren detections can be used within the framework of Bayesian mode…
The cosmological background of higher order vector modes can be generated by the first order scalar perturbations. We investigate the second order and the third order vector modes systematically. The explicit expressions of two point functions $\langle V^{(n),λ}V^{(n),λ'} \rangle$$\left(n=2,3\right)$ and power spectra corresponded are presented. In the case of a monochromatic primordial power spectrum, the second order vector modes do not exist. However, the third order vector modes can be generated by a monochromatic primordial power spectrum. And it is found that the third order vector modes…
Higher-order, non-Gaussian aspects of the large-scale structure carry valuable information on structure formation and cosmology, which is complementary to second-order statistics. In this work we measure second- and third-order weak-lensing aperture-mass moments from CFHTLenS and combine those with CMB anisotropy probes. The third moment is measured with a significance of $2σ$. The combined constraint on $Σ_8 = σ_8 (Ω_{\rm m}/0.27)^α$ is improved by 10%, in comparison to the second-order only, and the allowed ranges for $Ω_{\rm m}$ and $σ_8$ are substantially reduced. Including general triangl…
Synergy between CSST and third-generation gravitational-wave detectors: Inferring cosmological parameters using cross-correlation of dark sirens and galaxies
Northeastern University（东北大学）；University of Western Australia（西澳大学）；The University of Tokyo（东京大学）；Hainan University（海南大学）
We have derived fourth-order perturbative equations in Lagrangian perturbation theory for a cosmological dust fluid. These equations are derived under the supposition of Newtonian cosmology in the Friedmann-Lemaître-Robertson-Walker Universe model. Even if we consider the longitudinal mode in the first-order perturbation, the transverse mode appears in the third-order perturbation. Furthermore, in this case, six longitudinal-mode equations and four transverse-mode equations appear in the fourth-order perturbation. The application of the fourth-order perturbation leads to a precise prediction o…
We consider the Goode-Wainwright representation of the Szekeres cosmological models and calculate the Taylor expansion of the luminosity distance in order to study the effects of the inhomogeneities on cosmographic parameters. Without making a particular choice for the arbitrary functions defining the metric, we Taylor expand up to the second order in redshift for Family I and up to the third order for Family II Szekeres metrics under the hypotesis, based on observation, that local structure formation is over. In a conservative fashion, we also allow for the existence of a non null cosmologica…
We study the initial conditions for cosmological $N$-body simulations for precision cosmology. In general, Zel'dovich approximation has been applied for the initial conditions of $N$-body simulations for a long time. These initial conditions provide incorrect higher-order growth. These error caused by setting up the initial conditions by perturbation theory is called transients. We investigated the impact of transient on non-Gaussianity of density field by performing cosmological $N$-body simulations with initial conditions based on first-, second-, and third-order Lagrangian perturbation theo…
The next generation of large scale surveys will not only measure cosmological parameters within the framework of General Relativity, but will also allow for precision tests of the framework itself. At the order of linear perturbations, departures from the growth in the LCDM model can be quantified in terms of two functions of time and Fourier number k. We argue that in local theories of gravity, in the quasi-static approximation, these functions must be ratios of polynomials in k, with the numerator of one function being equal to the denominator of the other. Moreover, the polynomials are even…
KiDS-Legacy: Joint analysis of second- and third-order cosmic shear
Universität Innsbruck（因斯布鲁克大学）；Universität Bonn（波恩大学）；University of Waterloo（滑铁卢大学）；Newcastle University（纽卡斯尔大学）；University of California, Santa Cruz（加州大学圣克鲁兹分校）；Polish Academy of Sciences（波兰科学院）；Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology（巴塞罗那高等物理研究所，巴塞罗那科学与技术学院）；University of Edinburgh（爱丁堡大学）；Ruhr University Bochum（鲁尔大学波鸿）；Leiden University（莱顿大学）
Inflationary predictions for the power spectrum of the curvature perturbation have been verified to an excellent degree, leaving many models compatible with observations. In this thesis we studied third-order correlations, that might allow one to further distinguish between inflationary models. From all the possible extensions of the standard inflationary model, we chose to study two-field models with canonical kinetic terms and flat field space. The new feature is the presence of the so-called isocurvature perturbation. Its interplay with the adiabatic perturbation outside the horizon gives b…
We explain the motivation and main results of our work in reference arXiv:0906.0530 [hep-th]. Using the covariant formalism, we derive the equations of motion for adiabatic and entropy perturbations at third order in perturbation theory for cosmological models involving two scalar fields, and use these equations to calculate the trispectrum of ekpyrotic and cyclic models. The non-linearity parameters $f_{NL}$ and $g_{NL}$ are found to combine to leave a very distinct observational imprint.
The next generation of detectors will detect gravitational waves from binary neutron stars at cosmological distances, for which around a thousand electromagnetic follow-ups may be observed per year. So far, most work devoted to the expected cosmological impact of these standard sirens employed them only as distance indicators. Only recently their use as tracers of clustering, similar to what already proposed for supernovae, has been studied. Focusing on the expected specifications of the Einstein Telescope (ET), we forecast here the performance on cosmological parameters of future standard sir…
Pushing spectral siren cosmology into the third-generation era: a blinded mock data challenge
Università di Bologna（博洛尼亚大学）；INFN - Sezione di Bologna（意大利国家核物理研究所博洛尼分部）；INAF - Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（意大利国家天体物理研究所博洛尼亚天文与空间科学观测站）；Aix-Marseille Université（艾克斯-马赛大学）；Université de Toulon（土伦大学）；CNRS, CPT（法国国家科学研究中心， cpt 中心）；INFN, Sezione di Roma（意大利国家核物理研究所罗马分部）；“Sapienza” Universitá di Roma（罗马大学）；CNRS/IN2P3, CPPM（法国国家科学研究中心/法国粒子与核物理研究所，马赛质子与核物理中心）
We investigate aspects of axion as a coherently oscillating massive classical scalar field by analyzing third order perturbations in Einstein's gravity in the axion-comoving gauge. The axion fluid has its characteristic pressure term leading to an axion Jeans scale which is cosmologically negligible for a canonical axion mass. Our classically derived axion pressure term in Einstein's gravity is identical to the one derived in the non-relativistic quantum mechanical context in the literature. We show that except for the axion pressure term, the axion fluid equations are exactly the same as the …
The Marked Power Spectrum as a Practical Bispectrum Measure for Galaxy Redshift Surveys
University of California, Berkeley（加州大学伯克利分校）；Berkeley Center for Cosmological Physics, UC Berkeley（加州大学伯克利分校宇宙学物理中心）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
With 3rd-order statistics of gravitational shear it will be possible to extract valuable cosmological information from ongoing and future weak lensing surveys which is not contained in standard 2nd-order statistics, due to the non-Gaussianity of the shear field. Aperture mass statistics are an appropriate choice for 3rd-order statistics due to their simple form and their ability to separate E- and B-modes of the shear. However, it has been demonstrated that 2nd-order aperture mass statistics suffer from E-/B-mode mixing because it is impossible to reliably estimate the shapes of close pairs of…
Perturbative quantum gravity in the framework of the Schwinger-Keldysh formalism is applied to compute lowest-order corrections to the actual expansion of the Universe described in terms of the spatially flat Friedman-Lematre-Robertson-Walker solution. The classical metric is approximated by a third order polynomial perturbation around the Minkowski metric. It is shown that the quantum contribution to the classical expansion, although extremely small, has damping properties (quantum friction), i.e. it slows down the expansion.
In this paper we start from the original formulation of the galileon model with the original choice for couplings to gravity. Within this framework we find that there is still a subset of possible Lagrangians that give selfaccelerating solutions with stable spherically symmetric solutions. This is a certain constrained subset of the third order galileon which has not been explored before. We develop and explore the background cosmological evolution of this model drawing intuition from other even more restricted galileon models. The numerical results confirm the presence of selfacceleration, bu…
Since the gravitational waves were detected by LIGO and Virgo, it has been promising that lots of information about the primordial Universe could be learned by further observations on stochastic gravitational waves background. The studies on gravitational waves induced by primordial curvature perturbations are of great interest. The aim of this paper is to investigate the third order induced gravitational waves. Based on the theory of cosmological perturbations, the first order scalar induces the second order scalar, vector and tensor perturbations. At the next iteration, the first order scala…
We present fully nonlinear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. For each fluid component we ignore the anisotropic stress. The multiple component nature, however, introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and th…
Multi-messenger standard-siren cosmology for third-generation gravitational-wave detectors: forecasts considering observations of gamma-ray bursts and kilonovae
Liaoning Key Laboratory of Cosmology and Astrophysics, College of Sciences, Northeastern University（东北大学理学院辽宁宇宙学与天体物理重点实验室）；MOE Key Laboratory of Data Analytics and Optimization for Smart Industry, Northeastern University（东北大学工信部智能工业数据优化与分析重点实验室）；National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Northeastern University（东北大学国家工业智能与系统优化前沿科学中心）
A parametric reconstruction of the jerk parameter, the third order derivative of the scale factor expressed in a dimensionless way, has been discussed. Observational constraints on the model parameters have been obtained by Maximum Likelihood Analysis of the models using Supernova Distance Modulus data (SNe), Observational Hubble Data (OHD), Baryon Acoustic Oscillation (BAO) data and CMB shift parameter data (CMBShift). The present value of the jerk parameter has been kept open to start with, but the plots of various cosmological parameter like deceleration parameter $q(z)$, jerk parameter $j(…
The idea of the global gravitational effect as the source of cosmological redshift was considered by de Sitter (1916, 1917), Eddington (1923), Tolman (1929) and Bondi (1947). Also Hubble (1929) called the discovered distance-redshift relation as "De Sitter effect". For homogeneous matter distribution cosmological gravitational redshift is proportional to square of distance: z_grav ~ r^2. However for a fractal matter distribution having the fractal dimension D=2 the global gravitational redshift is the linear function of distance: z_grav ~ r, which gives possibility for interpretation of the Hu…
We investigate the cosmological predictions of several $f(T)$ models, with up to two parameters, at both the background and the perturbation levels. Using current cosmological observations (geometric supernovae type Ia, cosmic microwave background and baryonic acoustic oscillation and dynamical growth data) we impose constraints on the distortion parameter, which quantifies the deviation of these models from the concordance $Λ$ cosmology at the background level. In addition we constrain the growth index $γ$ predicted in the context of these models using the latest perturbation growth data in t…
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [arXiv:1512.02539] to non-canonical scalar field and obtain a new definition of speed of sound in phase-space. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion,…
We probe the pure Einstein's gravity contributions to the second-order density power spectrum. In the small-scale, we discover that the Einstein's gravity contribution is negligibly small. This guarantees that Newton's gravity is sufficient to handle the baryon acoustic oscillation scale. In the large scale, however, we discover that the Einstein's gravity contribution to the second-order power spectrum dominates the linear-order power spectrum. Thus, pure Einstein gravity contribution appearing in the third-order perturbation leads to an infrared divergence in the power spectrum.
In this work, we present MHDEnzo, the extension of the cosmological code Enzo to include the effects magnetic fields through the ideal MHD approximation. We use a higher order Godunov Riemann solver for the computation of interface fluxes. We use two constrained transport methods to compute the electric field from those interface fluxes, which simultaneously advances the induction equation and maintains the divergence of the magnetic field. A third order divergence free reconstruction technique is used to interpolate the magnetic fields in the block structured AMR framework already extant in E…
We study the effect of the cubic torus topology of the Universe on scalar cosmological perturbations which define the gravitational potential. We obtain three alternative forms of the solution for both the gravitational potential produced by point-like masses, and the corresponding force. The first solution includes the expansion of delta-functions into Fourier series, exploiting periodic boundary conditions. The second one is composed of summed solutions of the Helmholtz equation for the original mass and its images. Each of these summed solutions is the Yukawa potential. In the third formula…
Cosmological inflation is the dominating paradigm to account for observations of the Cosmic Microwave Background (CMB). In this thesis, we study the phenomenology of a class of particularly well motivated models of inflation, known under the generic name of hybrid models. They are characterised by a transition from a valley to a hilltop shaped potential. In particular, we study three limiting regimes of the simplest realisation, hybrid inflation, constraining its parameter space using observational bounds on the spectral index and the non-gaussianity of the primordial perturbations. We find th…
We compute the third order gauge invariant action for scalar-graviton interactions in the Jordan frame. We demonstrate that the gauge invariant action for scalar and tensor perturbations on one physical hypersurface only differs from that on another physical hypersurface via terms proportional to the equation of motion and boundary terms, such that the evolution of non-Gaussianity may be called unique. Moreover, we demonstrate that the gauge invariant curvature perturbation and graviton on uniform field hypersurfaces in the Jordan frame are equal to their counterparts in the Einstein frame. Th…
We show that the evolution of interacting massive particles in the de Sitter bulk can be understood at leading order as a series of resonant decay and production events. From this perspective, we classify the cosmological collider signals into local and nonlocal categories with drastically different physical origins. This further allows us to derive a cutting rule for efficiently extracting these cosmological collider signals in an analytical fashion. Our cutting rule is a practical way for extracting cosmological collider signals in model building, and can be readily implemented as symbolic c…
The space of inflationary models is vast, containing wide varieties of mechanisms, symmetries, and spectra of particles. Consequently, the space of observational signatures is similarly complex. Hence, it is natural to look for boundaries of the space of models and their signatures. In this paper, we explore the possible symmetries associated with the primordial cosmological perturbations and their correlators in the asymptotic future. Assuming the observed homogeneity, isotropy and (approximate) scale invariance, we prove three main results. First, correlation functions of scalar metric fluct…
We study cosmological perturbations in a non-local higher-derivative model of gravity introduced by Biswas, Mazumdar and Siegel. We extend previous work, which had focused on classical scalar perturbations around a cosine hyperbolic bounce solution, in three ways. First, we point out the existence of a Starobinsky solution in this model, which is more attractive from a phenomenological point of view (even though it has no bounce). Second, we study classical vector and tensor perturbations. Third, we show how to quantize scalar and tensor perturbations in a de Sitter phase (for choices of param…
