arXiv subjects

Wenjuan Fang

Publications and source records attributed to Wenjuan Fang.

At least 19 recordsLinked to original sources

arXiv2025

An updated constraint on the Effective Field Theory of Dark Energy

The Effective Field Theory of Dark Energy (EFTofDE) provides a systematic and model-independent framework to study dark energy (DE) and modified gravity (MG) with one additional scalar degree of freedom. It can describe the known models such as Quintessence, k-essence, DGP, $f(R)$, and Horndeski theories. In this work, we update constraints on EFTofDE by utilizing the most up-to-date public data including the BAO (DESI DR2), CMB (Planck 2018 \& ACT DR6), SNIa (DESY5), weak lensing (DESY3) and full-shape galaxy power (BOSS DR12). We find with the $Λ$CDM background, general relativity (GR) is favored by the data, while with the $w0wa$CDM background, slight modification to GR is favored, but still consistent with GR within $1.5σ$. We also find the significance level for dynamical DE is greatly reduced within EFTofDE compared to within GR, indicating the degeneracy between dynamical DE and MG.

astro-ph.CO↗

arXiv2025

Constraining neutrino mass with the CSST galaxy clusters

With the advent of next-generation surveys, constraints on cosmological parameters are anticipated to become more stringent, particularly for the total neutrino mass. This study forecasts such constraints utilizing galaxy clusters from the Chinese Space Station Telescope (CSST). Employing Fisher matrix techniques, we derive the constraint $σ(M_ν)$ from cluster number counts, cluster power spectrum, and their combination. The investigation covers both the standard cosmological model with massive neutrinos $νΛ$CDM and the inclusion of dynamic dark energy in the $νw_0 w_a$CDM model, revealing a minor impact of dark energy on neutrino mass constraints. We examine the largest source of systematic arising from the mass-observable relation uncertainties and find that, with perfect knowledge of the scaling relation parameters, CSST clusters have the potential to enhance precision, tightening constraints to $\sim0.03$ eV. We also study the effects of the maximum redshift $z_{max}$ and other uncertainties, including those in redshift, halo mass function, and bias. Furthermore, we emphasize the significance of accounting for the growth-induced scale-dependent bias (GISDB) effect, which we find can tighten the final constraint by a factor of $1.2$ - $2.2$.

astro-ph.CO↗

arXiv2025

Cosmological constraints from the Minkowski functionals of the BOSS CMASS galaxy sample

For the first time, we develop a simulation-based model for the Minkowski functionals (MFs) of large-scale structure, which allows us to extract the full information available from the MFs (including both the Gaussian and non-Gaussian part), and apply it to the BOSS DR12 CMASS galaxy sample. Our model is based on high-fidelity mock galaxy catalogs constructed from the \textsc{Abacus}\textsc{Summit} simulations using the halo occupation distribution (HOD) framework, which include the redshift-space distortions and Alcock-Paczynski distortions, incorporate survey realism, including survey geometry and veto masks, and account for angular plus radial selection effects. The cosmological and HOD parameter dependence of the MFs is captured with a neural network emulator trained from the galaxy mocks with various cosmological and HOD parameters. To benchmark the constraining power of the MFs, we also train an emulator for the galaxy 2-point correlation function (2PCF) using the same pipeline. Having validated our approach through successful parameter recovery tests on both internal and external mocks, including non-HOD forward models of the halo-galaxy connection, we apply our forward model to analyze the CMASS data in the redshift range $0.45<z<0.58$. We find the MFs provide stronger constraints on the cosmological parameters than the 2PCF. The combination of the two gives $ω_{\rm cdm}=0.1172^{+0.0020}_{-0.0023}$, $σ_8=0.783\pm 0.026$, and $n_s=0.966^{+0.019}_{-0.015}$, which are tighter by a factor of 2.0, 1.9, and 1.6 than the 2PCF alone. The derived constraint $fσ_8=0.453 \pm 0.016$ is also improved by a factor of 1.9, compared to the 2PCF, and agrees well with Planck 2018 predictions and other results from a series of studies in the literature.

astro-ph.CO↗

arXiv2025

Probing massive neutrinos and modified gravity with redshift-space morphologies and anisotropies of large-scale structure

Strong degeneracy exists between some modified gravity (MG) models and massive neutrinos because the enhanced structure growth produced by modified gravity can be suppressed due to the free-streaming massive neutrinos. Previous works showed this degeneracy can be broken with non-Gaussian or velocity information. Therefore in this work, we focus on the large-scale structure (LSS) in redshift space and investigate for the first time the possibility of using the non-Gaussian information and velocity information captured by the 3D scalar Minkowski functionals (MFs) and the 3D Minkowski tensors (MTs) to break this degeneracy. Based on the Quijote and Quijote-MG simulations, we find the imprints on redshift space LSS left by the Hu-Sawicki $f(R)$ gravity can be discriminated from those left by massive neutrinos with these statistics. With the Fisher information formalism, we first show how the MTs extract information with their perpendicular and parallel elements for both low- and high-density regions; then we compare constraints from the power spectrum monopole and MFs in real space with those in redshift space, and investigate how the constraining power is further improved with anisotropies captured by the quadrupole and hexadecapole of the power spectrum and the MTs; finally, we combine the power spectrum multipoles with MFs plus MTs and find the constraints from the power spectrum multipoles on $Ω_{\mathrm{m}}, h, σ_8$, $M_ν$, and $f_{R_0}$ can be improved, because they are complemented with non-Gaussian information, by a factor of 3.4, 3.0, 3.3, 3.3, and 1.9 on small scales ($k_{\rm{max}}=0.5~h\rm{Mpc}^{-1},\ R_G=5~h^{-1}\rm{Mpc}$), and 2.8, 2.2, 3.4, 3.4, and 1.5 on large scales ($k_{\rm{max}}=0.25~h\rm{Mpc}^{-1},\ R_G=10~h^{-1}\rm{Mpc}$).

astro-ph.CO↗

arXiv2025

Forecasts on Anisotropic Cosmic Birefringence Constraints for CMB Experiment in the Northern Hemisphere

The study of cosmic birefringence through Cosmic Microwave Background (CMB) experiments is a key research area in cosmology and particle physics, providing a critical test for Lorentz and CPT symmetries. This paper focuses on an upcoming CMB experiment in the mid-latitude of the Northern Hemisphere, and investigates the potential to detect anisotropies in cosmic birefringence. Applying a quadratic estimator on simulated polarization data, we reconstruct the power spectrum of anisotropic cosmic birefringence successfully and estimate constraints on the amplitude of the spectrum, $A_{\mathrm{CB}}$, assuming scale invariance. The forecast is based on a wide-scan observation strategy during winter, yielding an effective sky coverage of approximately 23.6%. We consider two noise scenarios corresponding to the short-term and long-term phases of the experiment. Our results show that with a small aperture telescope operating at 95/150GHz, the $2σ$ upper bound for $A_{\mathrm{CB}}$ can reach 0.017 under the low noise scenario when adopting the method of merging multi-frequency data in map domain, and merging multi-frequency data in spectrum domain tightens the limit by about 10%.A large-aperture telescope with the same bands is found to be more effective, tightening the $2σ$ upper limit to 0.0062.

astro-ph.CO↗

arXiv2024

Intrinsic mass-richness relation of clusters from THE THREE HUNDRED hydrodynamic simulations

The main systematics in cluster cosmology is the uncertainty in the mass-observable relation. In this paper, we focus on the most direct cluster observable in optical surveys, i.e. richness, and constrain the intrinsic mass-richness (MR) relation of clusters in THE THREE HUNDRED hydrodynamic simulations with two runs: GIZMO-SIMBA and GADGET-X. We find that modeling the richness at fixed halo mass with a skewed Gaussian distribution yields a simpler and smaller scatter compared to the commonly used log-normal distribution. Additionally, we observe that baryon models have a significant impact on the scatter, while exhibiting no influence on the mass dependence and a slight effect on the amplitude in the MR relation. We select member galaxies based on both stellar mass $M_\star$ and absolute magnitude $\mathscr{M}$. We demonstrate that the MR relation obtained from these two selections can be converted to each other by using the $M_\star-\mathscr{M}$ relation. Finally, we provide a 7-parameter fitting result comprehensively capturing the dependence of the MR relation on both stellar mass cutoff and redshift.

astro-ph.CO↗

arXiv2024

Minkowski Functionals of Large-Scale Structure as a Probe of Modified Gravity

In this study, we explore the potential of utilizing the four Minkowski functionals, which can fully describe the morphological properties of the large-scale structures, as a robust tool for investigating the modified gravity, particularly on non-linear and quasi-linear scales. With the assistance of the N-body simulation, we employ the Minkowski functionals to probe the Hu-Sawicki f(R) gravity model. The focus is on understanding the morphorlogical properties extracted by the Minkowski functionals and their sensitivity to modified gravity. Our analysis involves a comprehensive examination of the cosmic variance arising from finite simulation volumes. By systematically varying smoothing scales and redshifts, we quantify the information encoded in the Minkowski functionals measured from the dark-matter density field. The goal is to assess the capacity of the Minkowksi functionals to constrain the model and explore potential improvements through their combination. Additionally, we investigate the impact of using biased tracers such as dark matter halos and the halo occupation distribution galaxies on the modified gravity signatures within the Minkowksi functionals of the LSS. Furthermore, we evaluate the influence of the redshift space distortion on the observed results. In summary, our study suggests that the Minkowski functionals of the large-scale structures hold promise as a stringent tool for constraining modified gravity and offer valuable insights into the morphological features of the cosmic web.

astro-ph.CO↗

arXiv2023

Probing massive neutrinos with the Minkowski functionals of the galaxy distribution

The characteristic signatures of massive neutrinos on large-scale structure (LSS), if fully captured, can be used to put a stringent constraint on their mass sum, $M_ν$. Previous work utilizing N-body simulations has shown the Minkowski functionals (MFs) of LSS can reveal the imprints of massive neutrinos on LSS, provide important complementary information to two-point statistics and significantly improve constraints on $M_ν$. In this work, we take a step forward and apply the statistics to the biased tracers of LSS, i.e. the galaxies, and in redshift space. We perform a Fisher matrix analysis and quantify the constraining power of the MFs by using the Molino mock galaxy catalogs, which are constructed based on the halo occupation distribution (HOD) framework with parameters for the SDSS $M_r < -21.5$ and -22 galaxy samples. We find the MFs give tighter constraints on all of the cosmological parameters that we consider than the power spectrum. The constraints on $Ω_{\mathrm{m}}, Ω_{\mathrm{b}}, h, n_s, σ_8$, and $M_ν$ from the MFs are better by a factor of 1.9, 2.9, 3.7, 4.2, 2.5, and 5.7, respectively, after marginalizing over the HOD parameters. Specifically, for $M_ν$, we obtain a 1$σ$ constraint of 0.059 eV with the MFs alone for a volume of only $\left(1 h^{-1} \mathrm{Gpc}\right)^3$.

astro-ph.CO↗

arXiv2023

Sciences with the 2.5-meter Wide Field Survey Telescope (WFST)

The Wide Field Survey Telescope (WFST) is a dedicated photometric surveying facility being built jointly by the University of Science and Technology of China and the Purple Mountain Observatory. It is equipped with a 2.5-meter diameter primary mirror, an active optics system, and a mosaic CCD camera with 0.73 gigapixels on the primary focal plane for high-quality image capture over an FOV of 6.5-square-degree. It is anticipated that WFST will be set up at the Lenghu site in the summer of 2023 and begin to observe the northern sky in four optical bands (u, g, r, and i) with a range of cadences, from hourly/daily in the Deep High-Cadence Survey (DHS) program to semiweekly in the Wide-Field Survey (WFS) program, three months later. During a photometric night, a nominal 30 s exposure in the WFS program will reach a depth of 22.27, 23.32, 22.84, and 22.31 (AB magnitudes) in these four bands, respectively, allowing for the detection of a tremendous amount of transients in the low-z universe and a systematic investigation of the variability of Galactic and extragalactic objects. In the DHS program, intranight 90 s exposures as deep as 23 (u) and 24 mag (g), in combination with target of opportunity follow-ups, will provide a unique opportunity to explore energetic transients in demand for high sensitivities, including the electromagnetic counterparts of gravitational wave events, supernovae within a few hours of their explosions, tidal disruption events and fast, luminous optical transients even beyond a redshift of unity. In addition, the final 6-year co-added images, anticipated to reach g=25.8 mag in WFS or 1.5 mags deeper in DHS, will be of fundamental importance to general Galactic and extragalactic science. The highly uniform legacy surveys of WFST will serve as an indispensable complement to those of LSST that monitor the southern sky.

astro-ph.IM↗

arXiv2023

Constraints on dark energy from the CSST galaxy clusters

We study the potential of the galaxy cluster sample expected from the China Space Station Telescope (CSST) survey to constrain dark energy properties. By modelling the distribution of observed cluster mass for a given true mass to be log-normal and adopting a selection threshold in the observed mass $M_{200m} \geq 0.836 \times 10^{14} h^{-1}M_{\odot}$, we find about $4.1 \times 10^{5}$ clusters in the redshift range $0 \leq z \leq 1.5$ can be detected by the CSST. We construct the Fisher matrix for the cluster number counts from CSST, and forecast constraints on dark energy parameters for models with constant ($w_0$CDM) and time dependent ($w_0w_a$CDM) equation of state. In the self-calibration scheme, the dark energy equation of state parameter $w_0$ of $w_0$CDM model can be constrained to $Δw_0 = 0.036$. If $w_a$ is added as a free parameter, we obtain $Δw_0 = 0.077$ and $Δw_a = 0.39$ for the $w_0w_a$CDM model, with a Figure of Merit for ($w_0,w_a$) to be 68.99. Should we had perfect knowledge of the observable-mass scaling relation (``known SR" scheme), we would obtain $Δw_0 = 0.012$ for $w_0$CDM model, $Δw_0 = 0.062$ and $Δw_a = 0.24$ for $w_0w_a$CDM model. The dark energy Figure of Merit of ($w_0,w_a$) increases to 343.25. By extending the maximum redshift of the clusters from $z_{max} \sim 1.5$ to $z_{max} \sim 2$, the dark energy Figure of Merit for ($w_0,w_a$) increases to 89.72 (self-calibration scheme) and 610.97 (``known SR" scheme), improved by a factor of $\sim 1.30$ and $\sim 1.78$, respectively. We find that the impact of clusters' redshift uncertainty on the dark energy constraints is negligible as long as the redshift error of clusters is smaller than 0.01, achievable by CSST. We also find that the bias in logarithm mass must be calibrated to be $0.30$ or better to avoid significant dark energy parameter bias.

astro-ph.CO↗

arXiv2022

The ALPINE-ALMA [CII] survey: The infrared-radio correlation and AGN fraction of star-forming galaxies at z $\sim$ 4.4-5.9

We present the radio properties of 66 spectroscopically-confirmed normal star-forming galaxies (SFGs) at $4.4<z<5.9$ in the COSMOS field that were [C II] detected in the Atacama Large Millimeter Array (ALMA) Large Program to INvestigate [C II] at Early times (ALPINE). We separate these galaxies ("CII-detected-all") into lower redshift ("CII-detected-lz", $\langle z\rangle=4.5$) and higher redshift ("CII-detected-hz", $\langle z\rangle=5.6$) sub-samples and stack multi-wavelength imaging for each sub-sample from X-ray to radio bands. A radio signal is detected in the stacked 3 GHz image of CII-detected-all and -lz samples at $\gtrsim3σ$. We find that the infrared-radio correlation of our sample, quantified by $q_{\mathrm{TIR}}$, is lower than the local relation for normal SFGs at $\sim$3$σ$ significance level, and is instead broadly consistent with that of bright sub-mm galaxies at $2<z<5$. Neither of these samples show evidence of dominant AGN activity in their stacked Spectral Energy Distributions (SEDs), rest-frame UV spectra, or X-ray images. Although we cannot rule out the possible effect of the assumed spectral index and the applied infrared SED templates as at least partially causing these differences, the lower obscured fraction of star formation than at lower redshift can alleviate the tension between our stacked $q_{\mathrm{TIR}}$s and that of local normal SFGs. It is possible that the dust buildup, which primarily governs the IR emission in addition to older stellar populations, has not had enough time to occur fully in these galaxies, whereas the radio emission can respond on a more rapid timescale. Therefore, we might expect a lower $q_{\mathrm{TIR}}$ to be a general property of high-redshift SFGs.

astro-ph.GA↗

arXiv2022

Probing massive neutrinos with the Minkowski functionals of large-scale structure

Massive neutrinos suppress the growth of structure under their free-streaming scales. The effect is most prominent on small scales where the widely-used two-point statistics can no longer capture the full information. In this work, we study the signatures massive neutrinos leave on large-scale structure (LSS) as revealed by its morphological properties, which are fully described by $4$ Minkowski functionals (MFs), and quantify the constraints on the summed neutrino mass $M_ν$ from the MFs, by using publicly available N-body simulations. We find the MFs provide important complementary information, and give tighter constraints on $M_ν$ than the power spectrum. Specifically, depending on whether massive neutrinos are included in the density field (the `m' field) or not (the `cb' field), we find the constraint on $M_ν$ from the MFs with a smoothing scale of $R_G=5 h^{-1}$Mpc is $48$ or $4$ times better than that from the power spectrum. When the MFs are combined with the power spectrum, they can improve the constraint on $M_ν$ from the latter by a factor of 63 for the `m' field and 5 for the `cb' field. Notably, when the `m' field is used, the constraint on $M_ν$ from the MFs can reach $0.0177$eV with a volume of $1(h^{-1}\rm Gpc)^3$, while the combination of the MFs and power spectrum can tighten this constraint to be $0.0133$eV, a $4.5σ$ significance on detecting the minimum sum of the neutrino masses. For the `m' field, we also find the $σ_8$ and $M_ν$ degeneracy is broken with the MFs, leading to stronger constraints on all 6 cosmological parameters considered in this work than the power spectrum.

astro-ph.CO↗

arXiv2022

The effects of peculiar velocities on the morphological properties of large-scale structure

It is known that the large-scale structure (LSS) mapped by a galaxy redshift survey is subject to distortions by galaxies' peculiar velocities. Besides the signatures generated in common N-point statistics, such as the anisotropy in the galaxy 2-point correlation function, the peculiar velocities also induce distinct features in LSS's morphological properties, which are fully described by four Minkowski functionals (MFs), i.e., the volume, surface area, integrated mean curvature and Euler characteristic (or genus). In this work, by using large suite of N-body simulations, we present and analyze these important features in the MFs of LSS on both (quasi-)linear and non-linear scales, with a focus on the latter. We also find the MFs can give competitive constraints on cosmological parameters compared to the power spectrum, probablly due to the non-linear information contained. For galaxy number density similar to the DESI BGS galaxies, the constraint on $σ_8$ from the MFs with one smoothing scale can be better by $\sim 50\%$ than from the power spectrum. These findings are important for the cosmological applications of MFs of LSS, and probablly open up a new avenue for studying the peculiar velocity field itself.

astro-ph.CO↗

arXiv2021

Future prospects on constraining neutrino cosmology with the Ali CMB Polarization Telescope

We forecast the constraints on the parameters of neutrino physics with the constructions of Cosmic Microwave Background (CMB) temperature, E-mode polarization and lensing spectra for the ground-based Ali Cosmic Microwave Background Polarization Telescope (AliCPT). To implement the forecast calculations, we perform numerical simulations which show that AliCPT would yield the result $σ(N_{\mathrm{eff}})=0.42$ and $σ(M_ν)=0.18$ for the first year observation. Moreover, we investigate how the instrumental parameters, such as noise level, full width at half maxima (FWHM), and sky coverage can affect the constraints on these two parameters. Our forecasting results find that a large aperture telescope with a large sky survey strategy would significant improve the current constraints.

astro-ph.CO↗

arXiv2021

Fast scalar quadratic maximum likelihood estimators for the CMB B-mode power spectrum

Constructing a fast and efficient estimator for the B-mode power spectrum of cosmic microwave background (CMB) is of critical importance for CMB science. For a general CMB survey, the Quadratic Maximum Likelihood (QML) estimator for CMB polarization has been proved to be the optimal estimator with minimal uncertainties, but it is computationally very expensive. In this article, we propose two new QML methods for B-mode power spectrum estimation. We use the Smith-Zaldarriaga approach to prepare pure-B mode map, and E-mode recycling method to obtain a leakage free B-mode map. We then use the scalar QML estimator to analyze the scalar pure-B map (QML-SZ) or B-mode map (QML-TC). The QML-SZ and QML-TC estimators have similar error bars as the standard QML estimators but their computational cost is nearly one order of magnitude smaller. The basic idea is that one can construct the pure B-mode CMB map by using the E-B separation method proposed by Smith-Zaldarriaga (SZ) or the one considering the template cleaning (TC) technique, then apply QML estimator to these scalar fields. By simulating potential observations of space-based and ground-based detectors, we test the reliability of these estimators by comparing them with the corresponding results of the traditional QML estimator and the pure B-mode pseudo-Cl estimator.

astro-ph.CO↗

arXiv2021

Multi-messenger Detection Rates and distributions of Binary Neutron Star Mergers and Their Cosmological Implications

The gravitational-wave (GW) events, produced by the coalescence of binary neutron-stars (BNS), can be treated as the standard sirens to probe the expansion history of the Universe, if their redshifts could be determined from the electromagnetic observations. For the high-redshift ($z\gtrsim 0.1$) events, the short $γ$-ray bursts (sGRBs) and the afterglows are always considered as the primary electromagnetic counterparts. In this paper, by investigating various models of sGRBs and afterglows, we discuss the rates and distributions of BNS mergers' multi-messenger observations with GW detectors in second-generation (2G), 2.5G, 3G era with the detectable sGRBs and the afterglows. For instance, for Cosmic Explorer GW detector, the rate is about (300-3500) per year with GECAM-like detector for $γ$-ray emissions and LSST/WFST detector for optical afterglows. In addition, we find these events have the redshifts $z\lesssim 2$ and the inclination angles $ι\lesssim 20^{\circ}$. These results justify the rough estimation in previous works. Considering these events as standard sirens to constrain the equation-of-state parameters of dark energy $w_{0}$ and $w_{a}$, we obtain the potential constraints of $Δw_{0}\simeq 0.02-0.05$ and $Δw_{a}\simeq 0.1-0.4$.

astro-ph.HE↗

arXiv2021

Implications of the Environments of Radio-detected AGN in a Complex Protostructure at z$\sim$3.3

Radio Active Galactic Nuclei (RAGNs) are mainly found in dense structures (i.e., clusters/groups) at redshifts of z$<$2 and are commonly used to detect protoclusters at higher redshift. Here, we attempt to study the host and environmental properties of two relatively faint ($\mathrm L_\mathrm{1.4GHz} \sim10^{25}$ W Hz$^{-1}$) RAGNs in a known protocluster at z=3.3 in the PCl J0227-0421 field, detected using the latest radio observation obtained as part of the Observations of Redshift Evolution in Large-Scale Environments (ORELSE) Survey. Using new spectroscopic observations obtained from Keck/MOSFIRE as part of the Charting Cluster Construction with the VIMOS Ultra-Deep Survey (VUDS) and ORELSE (C3VO) survey and previous spectroscopic data obtained as part of the VIMOS-VLT Deep Survey (VVDS) and VUDS, we revise the three-dimensional overdensity field around this protocluster. The protocluster is embedded in a large scale overdensity protostructure. This protostructure has an estimated total mass of $\sim$2.6$\times10^{15} M_\odot$ and contains several overdensity peaks. Both RAGNs are hosted by very bright and massive galaxies, while their hosts show extreme differences color, indicating that they have different ages and are in different evolutionary stages. Furthermore, we find that they are not in the most locally dense parts of the protostructure, but are fairly close to the centers of their parent overdensity peaks. We propose a scenario where merging might already have happened in both cases, which lowered the local density of their surrounding area and boosted their stellar mass. This work is the first time that two RAGNs at low luminosity have been found and studied within a high redshift protostructure.

astro-ph.GA↗

arXiv2021

Geometrical constraints on curvature from galaxy-lensing cross-correlations

Accurate constraints on curvature provide a powerful probe of inflation. However, curvature constraints based on specific assumptions of dark energy may lead to unreliable conclusions when used to test inflation models. To avoid this, it is important to obtain constraints that are independent on assumptions for dark energy. In this paper, we investigate such constraints on curvature from the geometrical probe constructed from galaxy-lensing cross-correlations. We study comprehensively the cross-correlations of galaxy with magnification, measured from type Ia supernovae's brightnesses ("$gκ^{\rm SN}$"), with shear ("$gκ^{\rm g}$"), and with CMB lensing ("$gκ^{\rm CMB}$"). We find for the LSST and Stage IV CMB surveys, "$gκ^{\rm SN}$" , "$gκ^{\rm g}$" and "$gκ^{\rm CMB}$" can be detected with signal-to-noise ratio $S/N=104,\ 2291,\ 1842$ respectively. When combined with supernovae Hubble diagram ("SN") to constrain curvature, we find galaxy-lensing cross-correlation becomes increasingly important with more degrees of freedom allowed in dark energy. Without any priors, we obtain error on $Ω_K$ of $0.723$ from "SN + $gκ^{\rm SN}$", $0.0417$ from "SN + $gκ^{\rm g}$", and $0.04$ from "SN + $gκ^{\rm g}$ + $gκ^{\rm CMB}$" for the LSST and Stage IV CMB surveys. The last one is more competitive than a Stage IV BAO survey ("BAO"). When galaxy-lensing cross-correlations are added to the combined probe of "SN + BAO + CMB", where "CMB" stands for Planck measurement for the CMB acoustic scale, we obtain constraint on $Ω_K$ of $0.0013$, which is a factor of 7 improvement from "SN + BAO + CMB". We study improvements in these results from increasing the high redshift extension of supernovae.

astro-ph.CO↗