arXiv subjects

Zhongxu Zhai

Publications and source records attributed to Zhongxu Zhai.

At least 37 records · Page 2Linked to original sources

arXiv2023

Aemulus $ν$: Precise Predictions for Matter and Biased Tracer Power Spectra in the Presence of Neutrinos

We present the Aemulus $ν$ simulations: a suite of 150 $(1.05 h^{-1}\rm Gpc)^3$ $N$-body simulations with a mass resolution of $3.51\times 10^{10} \frac{Ω_{cb}}{0.3} ~ h^{-1} M_{\odot}$ in a $wν$CDM cosmological parameter space. The simulations have been explicitly designed to span a broad range in $σ_8$ to facilitate investigations of tension between large scale structure and cosmic microwave background cosmological probes. Neutrinos are treated as a second particle species to ensure accuracy to $0.5\, \rm eV$, the maximum neutrino mass that we have simulated. By employing Zel'dovich control variates, we increase the effective volume of our simulations by factors of $10-10^5$ depending on the statistic in question. As a first application of these simulations, we build new hybrid effective field theory and matter power spectrum surrogate models, demonstrating that they achieve $\le 1\%$ accuracy for $k\le 1\, h\,\rm Mpc^{-1}$ and $0\le z \le 3$, and $\le 2\%$ accuracy for $k\le 4\, h\,\rm Mpc^{-1}$ for the matter power spectrum. We publicly release the trained surrogate models, and estimates of the surrogate model errors in the hope that they will be broadly applicable to a range of cosmological analyses for many years to come.

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arXiv2023

Small scale clustering of BOSS galaxies: dependence on luminosity, color, age, stellar mass, specific star formation rate and other properties

We measure and analyze galaxy clustering and the dependence on luminosity, color, age, stellar mass and specific star formation rate using Baryon Oscillation Spectroscopic Survey (BOSS) galaxies at $0.48<z<0.62$. We fit the monopole and quadrupole moments of the two-point correlation function (2PCF) and its projection on scales of $0.1$ -- $60.2h^{-1}$Mpc, after having split the catalog in a variety of ways. We find that the clustering dependence is consistent with previous well-established results showing the broad trends expected: For example, that brighter, redder, older, more massive and quenched galaxies are more strongly clustered. We also investigate the dependence on additional parameters previously derived from stellar population synthesis model fits to the spectra. We find that galaxy clustering depends on look-back formation time at a low level, while it has little dependence on metallicity. To understand the physics behind these trends, we fit the clustering with a simulation-based emulator to simultaneously model cosmology and galaxy bias using a Halo Occupation Distribution framework. After marginalizing parameters determining the background cosmology, galaxy bias, and a scaling parameter to decouple halo velocity field, we find that the growth rate of large scale structure as determined by the redshift-space distortions is consistent with previous analysis using the full sample, and we do not find evidence that cosmological constraints depend systematically on galaxy selection. This demonstrates that cosmological inference using small scale clustering measurements is robust to changes in the catalog selection.

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arXiv2023

Phenomenological power spectrum models for H$α$ emission line galaxies from the Nancy Grace Roman Space Telescope

The High Latitude Spectroscopic Survey (HLSS) is the reference baseline spectroscopic survey for NASA's Nancy Grace Roman space telescope, measuring redshifts of $\sim 10$M H$α$ emission line galaxies over a $2000$ deg$^2$ footprint at $z=1-2$. In this work, we use a realistic Roman galaxy mock catalogue to explore optimal phenomenological modeling of the measured power spectrum. We consider two methods for modeling the redshift-space distortions (Kaiser squashing and another with a window function on $β$ that selects out the coherent radial infall pairwise velocities, $M_A$ and $M_B$, respectively), two models for the nonlinear impact of baryons that smears the BAO signal (a fixed ratio between the smearing scales in the perpendicular and parallel dimensions and another where these smearing scales are kept as a free parameters, P$_{dw}(k|k_*)$ and P$_{dw}(k|Σ_\perp,Σ_\parallel)$, respectively), and two analytical emulations of nonlinear growth (one employing the halo model and another formulated from simulated galaxy clustering of a semi-analytical model, $F_{HM}$ and $F_{SAM}$, respectively). We find that the best model combination employing $F_{HM}$ is $P_{dw}(k|k_*)*F_{HM}*M_B$, while the best combination employing $F_{SAM}$ is $P_{dw}(k|k_*)*F_{SAM}*M_B$, which leads to unbiased measurements of cosmological parameters. We compare these to the Effective Field Theory of Large-Scale Structure perturbation theory model $P_{EFT}(k|Θ)$, and find that our simple phenomenological models are comparable across the entire redshift range for $k_{max}=0.25$ and $0.3$ $h$/Mpc. We expect the tools that we have developed to be useful in probing dark energy and testing gravity using Roman in an accurate and robust manner.

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arXiv2023

The Aemulus Project V: Cosmological constraint from small-scale clustering of BOSS galaxies

We analyze clustering measurements of BOSS galaxies using a simulation-based emulator of two-point statistics. We focus on the monopole and quadrupole of the redshift-space correlation function, and the projected correlation function, at scales of $0.1\sim60~h^{-1}$Mpc. Although our simulations are based on $w$CDM with general relativity (GR), we include a scaling parameter of the halo velocity field, $γ_f$, defined as the amplitude of the halo velocity field relative to the GR prediction. We divide the BOSS data into three redshift bins. After marginalizing over other cosmological parameters, galaxy bias parameters, and the velocity scaling parameter, we find $fσ_{8}(z=0.25) = 0.413\pm0.031$, $fσ_{8}(z=0.4) = 0.470\pm0.026$ and $fσ_{8}(z=0.55) = 0.396\pm0.022$. Compared with Planck observations using a flat $Λ$CDM model, our results are lower by $1.9σ$, $0.3σ$ and $3.4σ$ respectively. These results are consistent with other recent simulation-based results at non-linear scales, including weak lensing measurements of BOSS LOWZ galaxies, two-point clustering of eBOSS LRGs, and an independent clustering analysis of BOSS LOWZ. All these results are generally consistent with a combination of $γ_f^{1/2}σ_8\approx 0.75$. We note, however, that the BOSS data is well fit assuming GR, i.e. $γ_f=1$. We cannot rule out an unknown systematic error in the galaxy bias model at non-linear scales, but near-future data and modeling will enhance our understanding of the galaxy--halo connection, and provide a strong test of new physics beyond the standard model.

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arXiv2023

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the growth rate of structure from the small-scale clustering of the luminous red galaxy sample

We measure the small-scale clustering of the Data Release 16 extended Baryon Oscillation Spectroscopic Survey Luminous Red Galaxy sample, corrected for fibre-collisions using Pairwise Inverse Probability weights, which give unbiased clustering measurements on all scales. We fit to the monopole and quadrupole moments and to the projected correlation function over the separation range $7-60\,h^{-1}$Mpc with a model based on the Aemulus cosmological emulator to measure the growth rate of cosmic structure, parameterized by $fσ_8$. We obtain a measurement of $fσ_8(z=0.737)=0.408\pm0.038$, which is $1.4σ$ lower than the value expected from 2018 Planck data for a flat $Λ$CDM model, and is more consistent with recent weak-lensing measurements. The level of precision achieved is 1.7 times better than more standard measurements made using only the large-scale modes of the same sample. We also fit to the data using the full range of scales $0.1-60\,h^{-1}$Mpc modelled by the Aemulus cosmological emulator and find a $4.5σ$ tension in the amplitude of the halo velocity field with the Planck+$Λ$CDM model, driven by a mismatch on the non-linear scales. This may not be cosmological in origin, and could be due to a breakdown in the Halo Occupation Distribution model used in the emulator. Finally, we perform a robust analysis of possible sources of systematics, including the effects of redshift uncertainty and incompleteness due to target selection that were not included in previous analyses fitting to clustering measurements on small scales.

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arXiv2023

Isolating the linear signal when making redshift space distortion measurements

Constraints on the linear growth rate, $fσ_8$, using small scale redshift space distortion measurements have a significant statistical advantage over those made on large scales. However, these measurements need to carefully disentangle the linear and non-linear information when interpreting redshift space distortions in terms of $fσ_8$. It is particularly important to do this given that some previous measurements found a significant deviation from the expectation based on the $Λ$CDM model constrained by Planck CMB data. We construct a new emulator-based model for small scale galaxy clustering with scaling parameters for both the linear and non-linear velocities of galaxies, allowing us to isolate the linear growth rate. We train the emulator using simulations from the AbacusCosmos suite, and apply it to data from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) luminous red galaxy sample. We obtain a value of $fσ_8(z=0.737)=0.368\pm0.041$, in 2.3-$σ$ tension with the Planck 2018 $Λ$CDM expectation, and find less dependence on the minimum measurement scale than previous analyses.

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arXiv2022

Sample Variance for Supernovae Distance Measurements and the Hubble tension

Recent local measurements of the Hubble constant made using supernovae have delivered a value that differs by $\sim$5$σ$ (statistical error) from predictions using the Cosmic Microwave Background (CMB), or using Baryon Acoustic Oscillations (BAO) and Big-Bang Nucleosynthesis (BBN) constraints, which are themselves consistent. The effective volume covered by the supernovae is small compared to the other probes, and it is therefore interesting to consider whether sample variance (often also called cosmic variance) is a significant contributor to the offset. We consider four ways of calculating the sample variance: (i) perturbation theory applied to the luminosity distance, which is the most common method considered in the literature; (ii) perturbation of cosmological parameters, as is commonly used to alleviate super-sample covariance in sets of N-body simulations; (iii) a new method based on the variance between perturbed spherical top-hat regions; (iv) using numerical N-body simulations. All give consistent results showing that, for the Pantheon supernova sample, sample variance can only lead to fluctuations in $H_0$ of order $\pm1$ km s$^{-1}$Mpc$^{-1}$ or less. While this is not in itself a new result, the agreement between the methods used adds to its robustness. Furthermore, it is instructive to see how the different methods fit together. We also investigate the internal variance of the $H_{0}$ measurement using SH0ES and Pantheon data. By searching for an offset between measurements in opposite hemispheres, we find that the direction coincident with the CMB dipole has a higher $H_{0}$ measurement than the opposite hemisphere by roughly 4 km s$^{-1}$Mpc$^{-1}$. We compare this with a large number of simulations and find that the size of this asymmetry is statistically likely, but the preference of direction may indicate that further calibration is needed.

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arXiv2021

Illuminating Galaxy Evolution at Cosmic Noon with ISCEA: the Infrared Satellite for Cosmic Evolution Astrophysics

ISCEA (Infrared Satellite for Cosmic Evolution Astrophysics) is a small astrophysics mission whose Science Goal is to discover how galaxies evolved in the cosmic web of dark matter at cosmic noon. Its Science Objective is to determine the history of star formation and its quenching in galaxies as a function of local density and stellar mass when the Universe was 3-5 Gyrs old (1.2 10 Mpc in each of 50 protocluster (cluster and cosmic web) fields at 1.2 < z < 2.1. ISCEA measures the star formation quenching factor in those fields, and galaxy kinematics with a precision < 50 km/s to deduce the 3D spatial distribution in each field. ISCEA will transform our understanding of galaxy evolution at cosmic noon. ISCEA is a small satellite observatory with a 30cm equivalent diameter aperture telescope with a FoV of 0.32 deg^2, and a multi-object spectrograph with a digital micro-mirror device (DMD) as its programmable slit mask. ISCEA will obtain spectra of 1000 galaxies simultaneously at an effective resolving power of R=1000, with 2.8"x2.8" slits, over the NIR wavelength range of 1.1 to 2.0 microns, a regime not accessible from the ground without large gaps in coverage. ISCEA will achieve a pointing accuracy of <= 2" FWHM over 200s. ISCEA will be launched into a Low Earth Orbit, with a prime mission of 2.5 years. ISCEA's space-qualification of DMDs opens a new window for spectroscopy from space, enabling revolutionary advances in astrophysics.

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arXiv2021

The High Latitude Spectroscopic Survey on the Nancy Grace Roman Space Telescope

The Nancy Grace Roman Space Telescope will conduct a High Latitude Spectroscopic Survey (HLSS) over a large volume at high redshift, using the near-IR grism (1.0-1.93 $μ$m, $R=435-865$) and the 0.28 deg$^2$ wide field camera. We present a reference HLSS which maps 2000 deg$^2$ and achieves an emission line flux limit of 10$^{-16}$ erg/s/cm$^2$ at 6.5$σ$, requiring $\sim$0.6 yrs of observing time. We summarize the flowdown of the Roman science objectives to the science and technical requirements of the HLSS. We construct a mock redshift survey over the full HLSS volume by applying a semi-analytic galaxy formation model to a cosmological N-body simulation, and use this mock survey to create pixel-level simulations of 4 deg$^2$ of HLSS grism spectroscopy. We find that the reference HLSS would measure $\sim$ 10 million H$α$ galaxy redshifts that densely map large scale structure at $z=1-2$ and 2 million [OIII] galaxy redshifts that sparsely map structures at $z=2-3$. We forecast the performance of this survey for measurements of the cosmic expansion history with baryon acoustic oscillations and the growth of large scale structure with redshift space distortions. We also study possible deviations from the reference design, and find that a deep HLSS at $f_{\rm line}>7\times10^{-17}$erg/s/cm$^2$ over 4000 deg$^2$ (requiring $\sim$1.5 yrs of observing time) provides the most compelling stand-alone constraints on dark energy from Roman alone. This provides a useful reference for future optimizations. The reference survey, simulated data sets, and forecasts presented here will inform community decisions on the final scope and design of the Roman HLSS.

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arXiv2021

Simulating properties of emission line galaxies from Nancy Grace Roman Space Telescope

We simulate the emission line galaxy properties for the Nancy Grace Roman Space Telescope by creating a 4 deg$^{2}$ galaxy mock catalog using Galacticus, a semi-analytic model (SAM) for galaxy formation and evolution. The simulated galaxy properties include emission line luminosity, equivalent width (EW), broad band photometry, and spectral energy distribution (SED). We compare this mock catalog with the latest observational data from WISP and MOSDEF. We find that our Galacticus model makes predictions consistent with observational data, over a wide redshift range for multiple emission lines. We use this validated galaxy mock catalog to forecast the photometric completeness of H$α$ and [OIII] emission lines as a function of line flux cut and H band magnitdue cut, for both Roman and Euclid-like surveys. Our prediction for the photometric completeness of a Euclid-like survey is in good agreement with previous work based on WISP data. Our predictions for the photometric completeness of possible implementations of the Roman High Latitude Wide Area Spectroscopic Survey (HLWASS) provides key input for the planning of such a survey. We find that at H = 24, a Euclid-like survey to the line flux limit of 2$\times 10^{-16}\,$erg/s/cm$^2$ is 97\% complete, while a Roman HLWASS to the line flux limit of $10^{-16}\,$erg/s/cm$^2$ is only 94.6\% complete (it becomes 98\% complete at H = 25).

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arXiv2021

Linear bias and halo occupation distribution of emission line galaxies from Nancy Grace Roman Space Telescope

We present measurements of the linear galaxy bias of H$α$ and [OIII] emission line galaxies (ELGs) for the High Latitude Spectroscopic Survey (HLSS) of Nancy Grace Roman Space Telescope, using galaxy mocks constructed using semi-analytical model for galaxy formation, {\it Galacticus}, with a large cosmic volume and redshift coverage. We compute the two-point statistics of galaxies in configuration space and measure linear bias within scales of $10\sim50 h^{-1}$Mpc. We adopt different selection algorithms to investigate the impact of the Roman line flux cut, as well as the effect of dust model used to calibrate Galacticus, on the bias measurements. We consider galaxies with H$α$ and [OIII] emissions over the redshift range $1<z<3$, as specified by the current baseline for the Roman HLSS. We find that the linear bias for the H$α$ and [OIII] ELGs can be expressed as a linear function with respect to redshift: $b \simeq 0.88z+0.49$ for H$α$ $(1<z<2)$, and $b \simeq 0.98z+0.49$ for [OIII] $(2<z<3)$. We have also measured the Halo Occupation Distributions of these H$α$ and [OIII] emission line galaxies to understand their distribution within dark matter halos. Our results provide key input to enable the reliable forecast of dark energy and cosmology constraints from Roman.

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arXiv2020

Clustering in the Simulated H$α$ Galaxy Redshift Survey from Nancy Grace Roman Space Telescope

We present a realistic 2000 deg$^{2}$ H$α$ galaxy mock catalog with $1<z<2$ for the Nancy Grace Roman Space Telescope galaxy redshift survey, the High Latitude Spectroscopic Survey (HLSS), created using Galacticus, a semi-analytical galaxy formation model, and high resolution cosmological N-body simulations. Galaxy clustering can probe dark energy and test gravity via baryon acoustic oscillation (BAO) and redshift space distortion (RSD) measurements. Using our realistic mock as the simulated Roman HLSS data, and a covariance matrix computed using a large set of approximate mocks created using EZmock, we investigate the expected precision and accuracy of the BAO and RSD measurements using the same analysis techniques used in analyzing real data. We find that the Roman H$α$ galaxy survey alone can measure the angular diameter distance with 2\% uncertainty, the Hubble parameter with 3-6\% uncertainty, and the linear growth parameter with 7\% uncertainty, in each of four redshift bins. Our realistic forecast illustrates the power of the Roman galaxy survey in probing the nature of dark energy and testing gravity.

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arXiv2020

Forecasting Cosmological Constraints from the Weak Lensing Magnification of Type Ia Supernovae Measured by the Nancy Grace Roman Space Telescope

The weak lensing magnification of Type Ia Supernovae (SNe Ia) is sensitive to the clustering of matter, and provides an independent cosmological probe complementary to SN Ia distance measurements. The Nancy Grace Roman Space Telescope is uniquely sensitive to this measurement as it can discover high redshift SNe Ia and measure them with high precision. We present a methodology for reconstructing the probability distribution of the weak lensing magnification $μ$ of SNe Ia, $p(μ)$, from observational data, and using it to constrain cosmological parameters. We find that the reconstructed $p(μ)$ can be fitted accurately by a stretched Gaussian distribution, and used to measure the variance of $μ$, $ξ_μ$, which can be compared to theoretical predictions in a likelihood analysis. Applying our methodology to a set of realistically simulated SNe Ia expected from the Roman Space Telescope, we find that using the weak lensing magnification of the SNe Ia constrains a combination of matter density $Ω_m$ and matter clustering amplitude $σ_8$. SN Ia distances alone lead to a better than 1\% measurement of $Ω_m$. The combination of SN Ia weak lensing magnification and distance measurements result in a $\sim$ 10\% measurement on $σ_8$. The SNe Ia from Roman will be powerful in constraining the cosmological model.

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arXiv2020

CMB distance priors revisited: effects of dark energy dynamics, spatial curvature, primordial power spectrum, and neutrino parameters

As a physical and sufficient compression of the full CMB data, the CMB distance priors, or shift parameters, have been widely used and provide a convenient way to include CMB data when obtaining cosmological constraints. In this paper, we revisit this data vector and examine its stability under different cosmological models. We find that the CMB distance priors are an accurate substitute for the full CMB data when probing dark energy dynamics. This is true when the primordial power spectrum model is directly generalized from the power spectrum of the model used in the derivation of the distance priors from the CMB data. We discover a difference when a non-flat model with the untilted primordial inflation power spectrum is used to measure the distance priors. This power spectrum is a radical change from the more conventional tilted primordial power spectrum and violates fundamental assumptions for the reliability of the CMB shift parameters. We also investigate the performance of CMB distance priors when the sum of neutrino masses $\sum m_ν$ and the effective number of relativistic species $N_{\text{eff}}$ are allowed to vary. Our findings are consistent with earlier results: the neutrino parameters can change the measurement of the sound horizon from CMB data, and thus the CMB distance priors. We find that when the neutrino model is allowed to vary, the cold dark matter density $ω_{c}$ and $N_{\text{eff}}$ need to be included in the set of parameters that summarize CMB data, in order to reproduce the constraints from the full CMB data. We present an updated and expanded set of CMB distance priors which can reproduce constraints from the full CMB data within $1σ$, and are applicable to models with massive neutrinos, as well as non-standard cosmologies.

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arXiv2019

Prediction of H$α$ and [OIII] Emission Line Galaxy Number Counts for Future Galaxy Redshift Surveys

We perform a simulation with Galacticus, a semi-analytical galaxy formation model, to predict the number counts of H$α$ and [OIII] emitting galaxies. With a state-of-the-art N-body simulation, UNIT, we first calibrate Galacticus with the current observation of H$α$ luminosity function. The resulting model coupled with a dust attenuation model, can reproduce the current observations, including the H$α$ luminosity function from HiZELS and number density from WISP. We extrapolate the model prediction to higher redshift and the result is found to be consistent with previous investigations. We then use the same galaxy formation model to predict the number counts for [OIII] emitting galaxies. The result provides further validation of our galaxy formation model and dust model. We present number counts of H$α$ and [OIII] emission line galaxies for three different line flux limits: $5\times10^{-17}$erg/s/cm$^{2}$, $1\times10^{-16}$erg/s/cm$^{2}$ (6.5$σ$ nominal depth for WFIRST GRS), and $2\times10^{-16}$erg/s/cm$^{2}$ (3.5$σ$ depth of Euclid GRS). At redshift $2<z<3$, our model predicts that WFIRST can observe hundreds of [OIII] emission line galaxies per square degree with a line flux limit of $1\times10^{-16}$erg/s/cm$^{2}$. This will provide accurate measurement of large scale structure to probe dark energy over a huge cosmic volume to an unprecedented high redshift. Finally, we compare the flux ratio of H$α$/[OIII] within the redshift range of $0<z<3$. Our results show the known trend of increasing H$α$/[O III] flux ratio with H$α$ flux at low redshift, which becomes a weaker trend at higher redshifts.

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arXiv2019

The Aemulus Project IV: Emulating Halo Bias

Models of the spatial distribution of dark matter halos must achieve new levels of precision and accuracy in order to satisfy the requirements of upcoming experiments. In this work, we present a halo bias emulator for modeling the clustering of halos on large scales. It incorporates the cosmological dependence of the bias beyond the mapping of halo mass to peak height. The emulator makes substantial improvements in accuracy compared to the widely used Tinker et al. (2010) model. Halos in this work are defined using an overdensity criteria of 200 relative to the mean background density. Halo catalogs are produced for 40 N-body simulations as part of the Aemulus project at snapshots from z=3 to z=0. The emulator is trained over the mass range $6\times10^{12}-7\times10^{15}\ h^{-1}M_{\odot}$. Using an additional suite of 35 simulations, we determine that the precision of the emulator is redshift dependent, achieving sub-percent levels for a majority of the redshift range. Two additional simulation suites are used to test the ability of the emulator to extrapolate to higher and lower masses. Our high-resolution simulation suite is used to develop an extrapolation scheme in which the emulator asymptotes to the Tinker et al. (2010) model at low mass, achieving ~3% accuracy down to $10^{11}\ h^{-1}M_{\odot}$. Finally, we present a method to propagate emulator modeling uncertainty into an error budget. Our emulator is made publicly available at \url{https://github.com/AemulusProject/bias_emulator}.

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arXiv2019

Reconstructing the weak lensing magnification distribution of Type Ia supernovae

Weak lensing of Type Ia supernovae (SNe Ia) is a systematic uncertainty in the use of SNe Ia as standard candles, as well as an independent cosmological probe, if the corresponding magnification distribution can be extracted from data. We study the peak brightness distribution of SNe Ia in the Pantheon sample, and find that the high $z$ sub-sample shows distinct weak lensing signatures compared to the low $z$ subsample: a long tail at the bright end due to high magnifications and a shift of the peak brightness toward the faint end, consistent with findings from earlier work. We have developed a technique to reconstruct the weak lensing magnification distribution of SNe Ia, $p(μ)$, from the measured SN Ia flux distribution, and applied it to the Pantheon sample. We find that $p(μ)$ can be reconstructed at a significance better than 2$σ$ for the subsample of SNe Ia at $z>0.7$ (124 SNe Ia), and at a lower significance for the SNe Ia at $z>0.9$ (49 SNe Ia), due to the small number of SNe Ia at high redshifts. The large number of $z>1$ SNe Ia from future surveys will enable the use of $p(μ)$ reconstructed from SNe Ia as an independent cosmological probe.

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arXiv2018

Robust and model-independent cosmological constraints from distance measurements

We present a systematic analysis of the cosmological constraints from the "Pantheon Sample" of 1048 Type Ia Supernovae (SNe Ia) in the redshift range $0.01<z<2.3$ compiled by Scolnic et al. (2018). Applying the flux-averaging method for detecting unknown systematic effects, we find that the "Pantheon" sample has been well calibrated and the bias caused by unknown systematic errors has been minimized. We present the estimate of distances measured from SNe Ia and reconstruct the expansion history of the Universe. The results are in agreement with a simple cosmological constant model and reveals the possible improvements that future SN Ia observations from WFIRST and LSST can target. We have derived distance priors using the CMB data from the Planck 2018 final data release, and combine them with SNe Ia and BAO data, to explore the impact from the systematic errors of SNe Ia on the combined cosmological parameter constraints. Using the combined data set of SNe Ia, BAO, and CMB distance priors, we measure the dark energy density function $X(z)=ρ_X(z)/ρ_X(0)$ as a free function (defined as a cubic spline of its values at $z=0.33, 0.67, 1.0$), along with the cosmological parameters ($Ω_k$, $Ω_m$, $Ω_b$, $H_0$). We find no deviation from a flat Universe dominated by a cosmological constant ($X(z)=1$), and $H_0=68.4\pm 0.9\text{km s}^{-1}\text{Mpc}^{-1}$, straddling the Planck team's measurement of $H_0=67.4\pm 0.5\text{km s}^{-1}\text{Mpc}^{-1}$, and Riess et al. (2018) measurement of $H_0=73.52\pm 1.62\text{km s}^{-1}\text{Mpc}^{-1}$. Adding $H_0=73.52\pm 1.62\text{km s}^{-1}\text{Mpc}^{-1}$ as a prior to the combined data set leads to the time dependence of the dark energy density at $z\sim 0.33$ at 68\% confidence level. Not including the systematic errors on SNe Ia has a similar but larger effect on the dark energy density measurement.

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