We study the optimal use of third order statistics in the analysis of weak lensing by large-scale structure. These higher order statistics have long been advocated as a powerful tool to break measured degeneracies between cosmological parameters. Using ray-tracing simulations, incorporating important survey features such as a realistic depth-dependent redshift distribution, we find that a joint two- and three-point correlation function analysis is a much stronger probe of cosmology than the skewness statistic. We compare different observing strategies, showing that for a limited survey time there is an optimal depth for the measurement of third-order statistics, which balances statistical noise and cosmic variance against signal amplitude. We find that the chosen CFHTLS observing strategy was optimal and forecast that a joint two- and three-point analysis of the completed CFHTLS-Wide will constrain the amplitude of the matter power spectrum $σ_8$ to 10% and the matter density parameter $Ω_m$ to 17%, a factor of ~2.5 improvement on the two-point analysis alone. Our error analysis includes all non-Gaussian terms, finding that the coupling between cosmic variance and shot noise is a non-negligible contribution which should be included in any future analytical error calculations.
Massive neutrinos, due to their free streaming, produce a suppression in the matter power spectrum at intermediate and small scales which could be probed by galaxy clustering and/or weak lensing observables. This effect happens at scales that are also influenced by baryon feedback, i.e. galactic winds or Active Galactic Nuclei (AGN) feedback, which in realistic hydrodynamic simulations has also been shown to produce a suppression of power. Leaving aside, for the moment, the complex issue of galaxy bias, we focus here on matter clustering and tomographic weak lensing, we investigate the possibl…
The light travel time differences in strong gravitational lensing systems allows an independent determination of the Hubble constant. This method has been successfully applied to several lens systems. The formally most precise measurements are, however, in tension with the recent determination of $H_0$ from the Planck satellite for a spatially flat six-parameters $ΛCDM$ cosmology. We reconsider the uncertainties of the method, concerning the mass profile of the lens galaxies, and show that the formal precision relies on the assumption that the mass profile is a perfect power law. Simple analyt…
We study cosmological models with interaction between dark energy (DE) and dark matter (DM). For the interaction term $Q$ in cosmic evolution equations, there is a model-independent degeneracy-breaking (D-B) point when $Q_{1}$ (a part of $Q$) equals to zero, where the interaction can be probed without degeneracy between the constant DE equation of state (EoS).
The small-scale cosmic microwave background (CMB) is dominated by anisotropies from the kinematic Sunyaev-Zeldovich (kSZ) effect, and upcoming experiments will measure it very precisely, but the optical depth degeneracy limits the cosmological information that can be extracted. At the same time, fast radio bursts (FRBs) are an exciting new frontier for astrophysics, but their usefulness as cosmological probes is currently unclear. We show that FRBs are uniquely suited for breaking the kSZ optical depth degeneracy. This opens up new possibilities for constraining cosmology with the kSZ effect, …
Breaking the Mass-sheet Degeneracy in Time-delay Cosmology with Lensed and Unlensed Type Ia Supernovae
College of Physics, Hebei Normal University（河北师范大学物理学院）；Shijiazhuang Key Laboratory of Astronomy and Space Science, Hebei Normal University（河北师范大学石家庄天文与空间科学重点实验室）；School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）
The inversion of gravitational lens systems is hindered by the fact that multiple mass distributions are often equally compatible with the observed properties of the images. Besides using clear examples to illustrate the effect of the so-called monopole and mass sheet degeneracies, this article introduces the most general form of said mass sheet degeneracy. While the well known version of this degeneracy rescales a single source plane, this generalization allows any number of sources to be rescaled. Furthermore, it shows how it is possible to rescale each of those sources with a different scal…
Mass determinations from gravitational lensing shear and the higher order estimator flexion are both subject to the mass sheet degeneracy. Mass sheet degeneracy refers to a transformation that leaves the reduced shear and flexion invariant. In general, this transformation can be approximated by the addition of a constant surface mass density sheet. We propose a new technique to break the mass sheet degeneracy. The method uses mass moments of the shear or flexion fields in combination with convergence information derived from number counts which exploit the magnification bias. The difference be…
We develop a novel statistical strong lensing approach to probe the cosmological parameters by exploiting multiple redshift image systems behind galaxies or galaxy clusters. The method relies on free-form mass inversion of strong lenses and does not need any additional information other than gravitational lensing. Since in free-form lensing the solution space is a high-dimensional convex polytope, we consider Bayesian model comparison analysis to infer the cosmological parameters. The volume of the solution space is taken as a tracer of the probability of the underlying cosmological assumption…
We constrain properties of cluster haloes by performing likelihood analysis using lensing shear and flexion data. We test our analysis using two mock cluster haloes: an isothermal ellipsoid (SIE) model and a more realistic elliptical Navarro-Frenk-White (eNFW) model. For both haloes, we find that flexion is more sensitive to the halo ellipticity than shear. The introduction of flexion information significantly improves the constraints on halo ellipticity, orientation and mass. We also point out that there is a degeneracy between the mass and the ellipticity of SIE models in the lensing signal.
The mass-sheet degeneracy is a well-known problem in gravitational lensing which limits our capability to infer astrophysical lens properties or cosmological parameters from observations. As the number of gravitational wave observations grows, detecting lensed events will become more likely, and to assess how the mass-sheet degeneracy may affect them is crucial. Here we study both analytically and numerically how the lensed waveforms are affected by the mass-sheet degeneracy computing the amplification factor from the diffraction integral. In particular, we differentiate between the geometrica…
The Etherington distance duality relation is well-established for metric theories of gravity, and confirms the duality between the luminosity distance and the angular diameter distance through the conservation of surface brightness. A violation of the Etherington distance duality due to lensing in a non-metric spacetime would lead to fluctuations in surface brightness of galaxies. Likewise, fluctuations of the surface brightness can arise in classical astrophysics as a consequence of intrinsic tidal interaction of galaxies with their environment. Therefore, we study these in two cases in detai…
We study weak gravitational lensing by the cosmic large-scale structure of the 21-cm radiation background in the 3d-weak lensing formalism. The interplay between source distance measured at finite resolution, visibility and lensing terms is analysed in detail and the resulting total covariance $C_{\ell}(k,k')$ is derived. The effect of lensing correlates different multipoles through convolution, breaking the statistical homogeneity of the 21-cm radiation background. This homogeneity breaking can be exploited to reconstruct the lensing field $\hatϕ_{\ell m}(κ)$ and noise lensing reconstruction …
Line intensity mapping is rapidly gaining prominence as a tool to understand galaxy evolution and cosmology at high redshift. However, the standard power spectrum analysis for these surveys suffers from a tight degeneracy between the overall mean line intensity and the bias of the emitting galaxies. We outline a new formalism for the Voxel Intensity Distribution (VID), a one-point statistic which is known to contain information beyond the power spectrum. We use this new calculation to show for the first time that the VID can be used to break this key degeneracy in intensity mapping data.
This paper is the first of a series of papers constraining cosmological parameters with weak lensing peak statistics using $\sim 450~\rm deg^2$ of imaging data from the Kilo Degree Survey (KiDS-450). We measure high signal-to-noise ratio (SNR: $ν$) weak lensing convergence peaks in the range of $3<ν<5$, and employ theoretical models to derive expected values. These models are validated using a suite of simulations. We take into account two major systematic effects, the boost factor and the effect of baryons on the mass-concentration relation of dark matter haloes. In addition, we investigate t…
An arguable aspect of the modified gravity theories is that many of them present the so-called degeneracy problem. For instance, the cosmological evolution, gravitational collapse and the main features of standard black-hole configurations, can be mimicked by many of those theories. In this communication we revise briefly the appropriate observable quantities to be measured in order to discard alternative theories to LCDM, such as the observed growth of scalar perturbations with Sloan data and the CMB tensor perturbations evolution.
We make a number of comments regarding modeling degeneracies in strong lensing measurements of the Hubble parameter $H_0$. The first point concerns the impact of weak lensing associated with different segments of the line of sight. We show that external convergence terms associated with the lens-source and observer-lens segments need to be included in cosmographic modeling, in addition to the usual observer-source term, to avoid systematic bias in the inferred value of $H_0$. Specifically, we show how an incomplete account of some line of sight terms biases stellar kinematics as well as ray tr…
We aim to constrain mass-varying neutrino models using large scale structure observations and produce forecast for the Euclid survey. We investigate two models with different scalar field potential and both positive and negative coupling parameters β. These parameters correspond to growing or decreasing neutrino mass, respectively. We explore couplings up to |β|<5. In the case of the exponential potential, we find an upper limit on $Ω_νh^2$<0.004 at 2-$σ$ level. In the case of the inverse power law potential the null coupling can be excluded with more than 2-σsignificance; the limits on the co…
Redshift space distortion (RSD) is a powerful way of measuring the growth of structure and testing General Relativity, but it is limited by cosmic variance and the degeneracy between galaxy bias b and the growth rate factor f. The cross-correlation of lensing shear with the galaxy density field can in principle measure b in a manner free from cosmic variance limits, breaking the f-b degeneracy and allowing inference of the matter power spectrum from the galaxy survey. We analyze the growth constraints from a realistic tomographic weak lensing photo-z survey combined with a spectroscopic galaxy…
While usually cosmological initial conditions are assumed to be Gaussian, inflationary theories can predict a certain amount of primordial non-Gaussianity which can have an impact on the statistical properties of the lensing observables. In order to evaluate this effect, we build a large set of realistic maps of different lensing quantities starting from light-cones extracted from large dark-matter only N-body simulations with initial conditions corresponding to different levels of primordial local non-Gaussianity strength $f_{\rm NL}$. Considering various statistical quantities (PDF, power sp…
We investigate how the cosmological constraints from SNe Ia are improved by including the effects of weak-lensing convergence. To do so, we introduce the lognormal function as the convergence PDF modeling the lensing scatter of SN Ia magnitude, and apply a sample selection for SNe Ia to avoid strongly lensed samples. Comparing with the contribution of other uncertainties (e.g., the intrinsic magnitude scatter), we find that the lensing effect is dominant at $z > 1$. Then forecasting the parameter constraints for the Wide-Field InfraRed Survey Telescope survey, we show that considering the weak…
We present a full forward-modeled $w$CDM analysis of the KiDS-1000 weak lensing maps using graph-convolutional neural networks (GCNN). Utilizing the $\texttt{CosmoGrid}$, a novel massive simulation suite spanning six different cosmological parameters, we generate almost one million tomographic mock surveys on the sphere. Due to the large data set size and survey area, we perform a spherical analysis while limiting our map resolution to $\texttt{HEALPix}$ $n_\mathrm{side}=512$. We marginalize over systematics such as photometric redshift errors, multiplicative calibration and additive shear bia…
State Key Laboratory of Dark Matter Physics, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院暗物质物理全国重点实验室）；Key Laboratory for Particle Astrophysics and Cosmology (MOE) / Shanghai Key Laboratory for Particle Physics and Cosmology（粒子天体物理学与宇宙学教育部重点实验室/上海粒子物理与宇宙学重点实验室）；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空间天体物理与科学观测站）；INFN – Sezione di Bologna（意大利国家核物理研究所博洛尼部分所）
We study the interacting dark energy model with time varying dark energy equation of state. We examine the stability in the perturbation formalism and the degeneracy among the coupling between dark sectors, the time-dependent dark energy equation of state and dark matter abundance in the cosmic microwave background radiation. Further we discuss the possible ways to break such degeneracy by doing global fitting using the latest observational data and we get a tight constraint on the interaction between dark sectors.
Gravitational lensing offers a competitive method to measure $H_0$ with the goal of 1% precision. A major obstacle comes in the form of lensing degeneracies, such as the mass sheet degeneracy (MSD), which make it possible for a family of density profiles to reproduce the same lensing observables but return different values of $H_0$. The modeling process artificially selects one choice from this family, potentially biasing $H_0$. The effect is more pronounced when the profile of a given lens is not perfectly described by the lens model, which will always be the case to some extent. To explore t…
Combining galaxy cluster and void abundances breaks the degeneracy between mean matter density $Ω_{\rm m}$ and power spectrum normalization $σ_8$. In a first for voids, we constrain $Ω_{\rm m} = 0.21 \pm 0.10$ and $σ_8 = 0.95 \pm 0.21$ for a flat $Λ$CDM universe, using extreme-value statistics on the claimed largest cluster and void. The Planck-consistent results detect dark energy with two objects, independently of other dark energy probes. Cluster-void studies also offer complementarity in scale, density, and non-linearity - of particular interest for testing modified-gravity models.
We explore the Minkowski functionals of weak lensing convergence map to distinguish between $f(R)$ gravity and the general relativity (GR). The mock weak lensing convergence maps are constructed with a set of high-resolution simulations assuming different gravity models. It is shown that the lensing MFs of $f(R)$ gravity can be considerably different from that of GR because of the environmentally dependent enhancement of structure formation. We also investigate the effect of lensing noise on our results, and find that it is likely to distinguish F5, F6 and GR gravity models with a galaxy surve…
The key probes of the growth of large-scale structure are its rate $f$ and amplitude $σ_8$. Redshift space distortions in the galaxy power spectrum allow us to measure only the combination $fσ_8$, which can be used to constrain the standard cosmological model or alternatives. By using measurements of the galaxy-galaxy lensing cross-correlation spectrum or of the galaxy bispectrum, it is possible to break the $fσ_8$ degeneracy and obtain separate estimates of $f$ and $σ_8$ from the same galaxy sample. Currently there are only a handful of such separate measurements, but even this allows for imp…
There are many possibilities of scenarios in the early universe, which can give rise to the same observational signals due to the degeneracy among each other, caused by equivalence under the conformal transformations. In order to break the degeneracy, in this paper we take into account the so-called "frame-invariant variables" proposed by A. Ijjas and P. J. Steinhardt in \cite{Ijjas:2015zma}. We discuss how the different scenarios will distribute in different parametric space constructed from those variables, waiting for the judgement of real observations in the future. Several concrete models…
Uncertain feedback processes in galaxies affect the distribution of matter, currently limiting the power of weak lensing surveys. If we can identify cosmological statistics that are robust against these uncertainties, or constrain these effects by other means, then we can enhance the power of current and upcoming observations from weak lensing surveys such as DES, Euclid, the Rubin Observatory, and the Roman Space Telescope. In this work, we investigate the potential of the electron density auto-power spectrum as a robust probe of cosmology and baryonic feedback. We use a suite of (magneto-)hy…
Weak gravitational lensing has become a common tool to constrain the cosmological model. The majority of the methods to derive constraints on cosmological parameters use second-order statistics of the cosmic shear. Despite their success, second-order statistics are not optimal and degeneracies between some parameters remain. Tighter constraints can be obtained if second-order statistics are combined with a statistic that is efficient to capture non-Gaussianity. In this paper, we search for such a statistical tool and we show that there is additional information to be extracted from statistical…
The integrated Sachs-Wolfe (ISW) effect and its non-linear extension Rees-Sciama (RS) effect provide us the information of the time evolution of gravitational potential. The cross-correlation between the cosmic microwave background (CMB) and the large scale structure (LSS) is known as a promising way to extract the ISW (RS) effect. It is known that the RS effect shows the unique behavior by changing the anti-correlated cross correlation between the CMB and the mass tracer into the positively correlated cross correlation compared to the linear ISW effect. We show that the dependence of this fli…
In a recent work, Baldi et al. highlighted the issue of cosmic degeneracies, consisting in the fact that the standard statistics of the large-scale structure might not be sufficient to conclusively test cosmological models beyond $Λ$CDM when multiple extensions of the standard scenario coexist in nature. In particular, it was shown that the characteristic features of an $f(R)$ Modified Gravity theory and of massive neutrinos with an appreciable total mass $Σ_{i}m_{ν_{i}}$ are suppressed in most of the basic large-scale structure observables for a specific combination of the main parameters of …
We examine the dark energy and matter densities allowed by precision measurements of distances out to various redshifts, in the presence of spatial curvature and (near) arbitrary behavior of the dark energy equation of state. Degeneracies among the parameters permit a remarkably large variation in their values when using only distance measurements of the late time universe and making no assumptions about the dark energy or curvature. Going beyond distance measurements to a lower limit on the growth of structure bounds the allowed region significantly but still leaves considerable freedom to ma…
We measure the galaxy 2- and 3-point correlation functions at $z=[0.5,0.7]$ and $z=[0.7, 0.9]$, from the final data release of the VIPERS survey (PDR2). We model the two statistics including a nonlinear 1-loop model for the 2-point function and a tree-level model for the 3-point function, and perform a joint likelihood analysis. The entire process and nonlinear corrections are tested and validated through the use of the 153 highly realistic VIPERS mock catalogues, showing that they are robust down to scales as small as 10 $h^{-1} \, \mathrm{Mpc}$. The mocks are also adopted to compute the cova…
We present a numerical analysis supporting the evidence that the redshift evolution of the drifting coefficient of the field cluster mass function is capable of breaking several cosmic degeneracies. This evidence is based on the data from the CoDECS and DUSTGRAIN-pathfinder simulations performed separately for various non-standard cosmologies including coupled dark energy, $f(R)$ gravity and combinations of $f(R)$ gravity with massive neutrinos as well as for the standard $Λ$CDM cosmology. We first numerically determine the field cluster mass functions at various redshifts in the range of $0\l…
Combining galaxy cluster and void abundances is a novel, powerful way to constrain deviations from General Relativity and the $Λ$CDM model. For a flat $w$CDM model with growth of large-scale structure parameterized by the redshift-dependent growth index $γ(z) = γ_0 + γ_1 z/(1+z)$ of linear matter perturbations, combining void and cluster abundances in future surveys with Euclid and the 4-metre Multi-Object Spectroscopic Telescope (4MOST) could improve the Figure of Merit for ($w, γ_0, γ_1$) by a factor of 20 compared to individual abundances. In an ideal case, improvement on current cosmologic…
We investigate the expected cosmological constraints from a combination of weak lensing and large-scale galaxy clustering using realistic redshift distributions. Introducing a systematic bias in the weak lensing redshift distributions (of 0.05 in redshift) produces a $>2σ$ bias in the recovered matter power spectrum amplitude and dark energy equation of state, for preliminary Stage III surveys. We demonstrate that these cosmological errors can be largely removed by marginalising over unknown biases in the assumed weak lensing redshift distributions, if we assume high quality redshift informati…
Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, leads to a negative creation pressure, which can be used to explain the accelerated expansion of the Universe. Recently, it has been shown that the dynamics of expansion of such models can not be distinguished from the concordance $Λ$CDM model, even at higher orders in the evolution of density perturbations, leading at the so called "dark degeneracy". However, depending on the form of the CDM creation rate, the inclusion of spatial curvature leads to a different behavior of CCDM when compared to $Λ$CDM, even at ba…
Weak gravitational lensing is one of the key probes of cosmology. Cosmic shear surveys aimed at measuring the distribution of matter in the universe are currently being carried out (Pan-STARRS) or planned for the coming decade (DES, LSST, EUCLID, WFIRST). Crucial to the success of these surveys is the control of systematics. In this work a new method to constrain one such family of systematics, known as multiplicative bias, is proposed. This method exploits the cross-correlation between weak lensing measurements from galaxy surveys and the ones obtained from high resolution CMB experiments. Th…
We address the problem of determining inflationary characteristics in a model independent way. We start from a recently proposed equation which allows to accurately calculate the value of the inflaton at horizon crossing $ϕ_k$. We then use an equivalent form of this equation to write a formula that relates the number of e-folds from horizon crossing to the pivot scale $N_{ke}+N_{ep}$ with the tensor-to-scalar index $r$, hence a general bound for $N_{ke}+N_{ep}$ follows. $N_{ke}$ is the number of e-folds from the scale factor $a_k$ during inflation to the end of inflation at $a_e$ and $N_{ep}$ …
Future large-scale spectroscopic astronomical surveys, e.g. Euclid, will enable the compilation of vast new catalogues of clusters and voids in the galaxy distribution. By combining the constraining power of both cluster and void number counts, such surveys could place stringent simultaneous limits on the sum of neutrino masses $M_ν$ and the dark energy equation of state $w(z) = w_0 + w_a z/(1+z)$. For minimal normal-hierarchy neutrino masses, we forecast that Euclid clusters + voids ideally could reach uncertainties $σ(M_ν) \lesssim 15$ meV, $σ(w_0) \lesssim~0.02$, $σ(w_a) \lesssim 0.07$, ind…
General relativity (GR) has been well tested up to solar system scales, but it is much less certain that standard gravity remains an accurate description on the largest, that is, cosmological, scales. Many extensions to GR have been studied that are not yet ruled out by the data, including by that of the recent direct gravitational wave detections. Degeneracies among the standard model ($Λ$CDM) and modified gravity (MG) models, as well as among different MG parameters, must be addressed in order to best exploit information from current and future surveys and to unveil the nature of dark energy…
We identify a scalar-tensor model embedded in the Horndeski action whose cosmological background and linear scalar fluctuations are degenerate with the concordance cosmology. The model admits a self-accelerated background expansion at late times that is stable against perturbations with a sound speed attributed to the new field that is equal to the speed of light. While degenerate in scalar fluctuations, self-acceleration of the model implies a present cosmological tensor mode propagation at < 95% of the speed of light with a damping of the wave amplitude that is > 5% less efficient than in ge…
The clustering of X-ray selected AGN appears to be a valuable tool for extracting cosmological information. Using the recent high-precision angular clustering results of ~30000 XMM-Newton soft (0.5-2 keV) X-ray sources (Ebrero et al. 2009), which have a median redshift of $z\sim 1$, and assuming a flat geometry, a constant in comoving coordinates AGN clustering evolution and the AGN bias evolution model of Basilakos et al. (2008), we manage to break the Omega_m-sigma_8 degeneracy. The resulting cosmological constraints are: Omega_m=0.27 (+0.03 -0.05), w=-0.90 (+0.10 -0.16) and sigma_8=0.74 (+0…
We construct two linear filtering techniques based on weak gravitational lensing to constrain the inner slope $α$ of the density profile of dark-matter halos. Both methods combine all available information into an estimate of this single number. Under idealised assumptions, $α$ is constrained to ~15% if the halo concentration c is known, and to < 30% if not. We argue that the inevitable degeneracy between density-profile slope and halo concentration cannot be lifted under realistic conditions, and show by means of Fisher-matrix methods which linear combination of $α$ and c is best constrained …
We demonstrate the potential of Deep Learning methods for measurements of cosmological parameters from density fields, focusing on the extraction of non-Gaussian information. We consider weak lensing mass maps as our dataset. We aim for our method to be able to distinguish between five models, which were chosen to lie along the $σ_8$ - $Ω_m$ degeneracy, and have nearly the same two-point statistics. We design and implement a Deep Convolutional Neural Network (DCNN) which learns the relation between five cosmological models and the mass maps they generate. We develop a new training strategy whi…
