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, $p(\mu)$, from the measured SN Ia flux distribution, and applied it to the Pantheon sample. We find that $p(\mu)$ can be reconstructed at a significance better than 2$\sigma$ 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 $p(\mu)$ reconstructed from SNe Ia as an independent cosmological probe.Comment: 7 pages, 5 figures, comments welcom

The effective volume of supernovae samples and sample variance

The source of the tension between local SN Ia based Hubble constant measurements and those from the CMB or BAO+BBN measurements is one of the most interesting unknowns of modern cosmology. Sample variance forms a key component of the error on the local measurements, and will dominate the error budget in the future as more supernovae are observed. Many methods have been proposed to estimate sample variance in many contexts, and we compared results from a number of them in Zhai \& Percival (2022), confirming that sample variance for the Pantheon supernovae sample does not solve the Hubble tension. We now extend this analysis to include a method based on analytically calculating correlations between the radial peculiar velocities of supernovae, comparing this technique with results from numerical simulations, which can be considered a non-linear Monte-Carlo solution that works similarly. We consider the dependence of these errors on the linear power spectrum and how non-linear velocities contribute to the error. Using this technique, and matching sample variance errors, we can define an effective volume for supernovae samples, finding that the Pantheon sample is equivalent to a top-hat sphere of radius $\sim220~h^{-1}$Mpc. We use this link between sample-variance errors to compute $\Delta H_{0}$ for idealised surveys with particular angular distributions of supernovae. For example, a half-sky survey at the Pantheon depth has the potential to suppress the sample variance of $H_{0}$ to $\sim0.1$ km s$^{-1}$Mpc$^{-1}$, a significant improvement compared with the current result. Finally, we consider the strength of large-scale velocity power spectrum required to explain the Hubble tension using sample variance, finding it requires an extreme model well beyond that allowed by other observations.Comment: 9 pages, 4 figures, comments welcom

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 σ₈. 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 ∼10% measurement on σ₈. The SNe Ia from Roman will be powerful in constraining the cosmological model

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 is independent of the galaxy selection. This demonstrates that cosmological inference using small scale clustering measurements is robust to changes in the catalog selection.Comment: 16 pages, 13+2 figures, comments welcom