Lensing Power Spectrum Research Articles

Forecasting super-sample covariance in future weak lensing surveys with SuperSCRAM

The observable universe contains density perturbations on scales larger than any finite volume survey. Perturbations on scales larger than a survey can measure degrade its power to constrain cosmological parameters. The dependence of survey observables such as the weak lensing power spectrum on these long-wavelength modes results in super-sample covariance. Accurately forecasting parameter constraints for future surveys requires accurately accounting for the super-sample effects. If super-sample covariance is in fact a major component of the survey error budget, it may be necessary to investigate mitigation strategies that constrain the specific realization of the long-wavelength modes. We present a Fisher matrix based formalism for approximating the magnitude of super-sample covariance and the effectiveness of mitigation strategies for realistic survey geometries. We implement our formalism in the public code SuperSCRAM: Super-Sample Covariance Reduction and Mitigation. We illustrate SuperSCRAM with an example application, where the modes contributing to super-sample covariance in the WFIRST weak lensing survey are constrained by the low-redshift galaxy number counts in the wider LSST footprint. We find that super-sample covariance increases the volume of the error ellipsoid in 7D cosmological parameter space by a factor of 4.5 relative to Gaussian statistical errors only, but our simple mitigation strategy more than halves the contamination, to a factor of 2.0.

Constraining neutrino mass with tomographic weak lensing peak counts

Massive cosmic neutrinos change the structure formation history by suppressing perturbations on small scales. Weak lensing data from galaxy surveys probe the structure evolution and thereby can be used to constrain the total mass of the three active neutrinos. However, much of the information is at small scales where the dynamics are nonlinear. Traditional approaches with second order statistics thus fail to fully extract the information in the lensing field. In this paper, we study constraints on the neutrino mass sum using lensing peak counts, a statistic which captures non-Gaussian information beyond the second order. We use the ray-traced weak lensing mocks from the Cosmological Massive Neutrino Simulations (MassiveNuS), and apply LSST-like noise. We discuss the effects of redshift tomography, multipole cutoff $\ell_{\rm max}$ for the power spectrum, smoothing scale for the peak counts, and constraints from peaks of different heights. We find that combining peak counts with the traditional lensing power spectrum can improve the constraint on neutrino mass sum, $\Omega_m$, and $A_s$ by 39%, 32%, and 60%, respectively, over that from the power spectrum alone.

CMB lensing bispectrum: Assessing analytical predictions against full-sky lensing simulations

Cosmic microwave background (CMB) lensing is an integrated effect whose kernel is greater than half the peak value in the range $1<z<5$. Measuring this effect offers a powerful tool to probe the large-scale structure of the Universe at high redshifts. With the increasing precision of ongoing CMB surveys, other statistics than the lensing power spectrum, in particular the lensing bi-spectrum, will be measured at high statistical significance. This will provide ways to improve the constraints on cosmological models and lift degeneracies. Following on an earlier paper, we test analytical predictions of the CMB lensing bi-spectrum against full-sky lensing simulations, and discuss their validity and limitation in detail. The tree-level prediction of perturbation theory agrees with the simulation only up to $\ell\sim 200$, but the one-loop order allows capturing the simulation results up to $\ell\sim 600$. We also show that analytical predictions based on fitting formulas for the matter bi-spectrum agree reasonably well with simulation results, although the precision of the agreement depends on the configurations and scales considered. For instance, the agreement is at the $10\%$-level for the equilateral configuration at multipoles up to $\ell\sim2000$, but the difference in the squeezed limit raises to more than a factor of two at $\ell\sim2000$. This discrepancy appears to come from limitations in the fitting formula of the matter bi-spectrum. We also find that the analytical prediction for the post-Born correction to the bi-spectrum is in good agreement with the simulation. We conclude by discussing the bi-spectrum prediction in some theories of modified gravity.

Measuring the small-scale matter power spectrum with high-resolution CMB lensing

We present a method to measure the small-scale matter power spectrum using high-resolution measurements of the gravitational lensing of the Cosmic Microwave Background (CMB). To determine whether small-scale structure today is suppressed on scales below 10 kiloparsecs (corresponding to M < 10^9 M_sun), one needs to probe CMB-lensing modes out to L ~ 35,000, requiring a CMB experiment with about 20 arcsecond resolution or better. We show that a CMB survey covering 4,000 square degrees of sky, with an instrumental sensitivity of 0.5 uK-arcmin at 18 arcsecond resolution, could distinguish between cold dark matter and an alternative, such as 1 keV warm dark matter or 10^(-22) eV fuzzy dark matter with about 4-sigma significance. A survey of the same resolution with 0.1 uK-arcmin noise could distinguish between cold dark matter and these alternatives at better than 20-sigma significance; such high-significance measurements may also allow one to distinguish between a suppression of power due to either baryonic effects or the particle nature of dark matter, since each impacts the shape of the lensing power spectrum differently. CMB temperature maps yield higher signal-to-noise than polarization maps in this small-scale regime; thus, systematic effects, such as from extragalactic astrophysical foregrounds, need to be carefully considered. However, these systematic concerns can likely be mitigated with known techniques. Next-generation CMB lensing may thus provide a robust and powerful method of measuring the small-scale matter power spectrum.

Effect of non-Gaussian lensing deflections on CMB lensing measurements

We investigate the impact of non-Gaussian lensing deflections on measurements of the CMB lensing power spectrum. We find that the false assumption of their Gaussianity significantly biases these measurements in current and future experiments at the percent level. The bias is detected by comparing CMB lensing reconstructions from simulated CMB data lensed with Gaussian deflection fields to reconstructions from simulations lensed with fully non-Gaussian deflection fields. The non-Gaussian deflections are produced by ray-tracing through snapshots of an N-body simulation and capture both the non-Gaussianity induced by non-linear structure formation and by multiple correlated deflections. We find that the amplitude of the measured bias is in agreement with analytical predictions by B\"ohm et al. 2016. The bias is largest in temperature-based measurements and we do not find evidence for it in measurements from a combination of polarization fields ($EB,EB$). We argue that the non-Gaussian bias should be even more important for measurements of cross-correlations of CMB lensing with low-redshift tracers of large-scale structure.

Cosmological implications of scale-independent energy-momentum squared gravity: Pseudo nonminimal interactions in dark matter and relativistic relics

In this paper, we introduce a scale-independent energy-momentum squared gravity (EMSG) that allows different gravitational couplings for different types of sources, which may lead to scenarios with many interesting applications/implications in cosmology. In the present study, to begin with, we study a modification of the $\Lambda$ cold dark matter ($\Lambda$CDM) model, where photons and baryons couple to the spacetime as in general relativity, while the cold dark matter and relativistic relics (neutrinos and any other relativistic relics) couple to the spacetime in accordance with EMSG. This scenario induces pseudo nonminimal interactions on these components, leading to modification at both the background and perturbative levels. A consequence of this scenario is that the dimensionless free parameter of the theory may induce direct changes on the effective number of the relativistic species, without the need to introduce new extra species. In order to quantify the observational consequences of the cosmological scenario, we use the cosmic microwave background Planck data (temperature, polarization, and lensing power spectrum) and baryonic acoustic oscillations data. We find that the free model parameter is too small to induce statistically significant corrections on the $\Lambda$CDM model due to EMSG. We deduce that the model presented here is quite rich with promising cosmological applications/implications that deserve further investigations.

Weak-lensing Power Spectrum Reconstruction by Counting Galaxies. II. Improving the ABS Method with the Shift Parameter

Abstract In Paper I of this series, we proposed an analytical method of blind separation (ABS) to extract the cosmic magnification signal in galaxy number distribution and reconstruct the weak-lensing power spectrum. Here, we report a new version of the ABS method with significantly improved performance. This version is characterized by a shift parameter, , with the special case of corresponding to the original ABS method. We have tested this new version, compared it with the previous one, and confirmed its superior performance in all investigated situations. Therefore, it supercedes the previous version. The proof of concept studies presented in this paper demonstrate that it may enable surveys such as LSST and SKA to reconstruct the lensing power spectrum at z ≃ 1 with 1% accuracy. We will test the new ABS method in more realistic simulations to verify its applicability to real data.

Constraints on Cosmological Parameters from the Angular Power Spectrum of a Combined 2500 deg2 SPT-SZ and Planck Gravitational Lensing Map

Abstract We report constraints on cosmological parameters from the angular power spectrum of a cosmic microwave background (CMB) gravitational lensing potential map created using temperature data from 2500 deg2 of South Pole Telescope (SPT) data supplemented with data from Planck in the same sky region, with the statistical power in the combined map primarily from the SPT data. We fit the lensing power spectrum to a model including cold dark matter and a cosmological constant ( ), and to models with single-parameter extensions to . We find constraints that are comparable to and consistent with those found using the full-sky Planck CMB lensing data, e.g., = 0.598 ± 0.024 from the lensing data alone with weak priors placed on other parameters. Combining with primary CMB data, we explore single-parameter extensions to . We find or &lt; 0.70 eV at 95% confidence, in good agreement with results including the lensing potential as measured by Planck. We include two parameters that scale the effect of lensing on the CMB: , which scales the lensing power spectrum in both the lens reconstruction power and in the smearing of the acoustic peaks, and , which scales only the amplitude of the lensing reconstruction power spectrum. We find × = 1.01 ± 0.08 for the lensing map made from combined SPT and Planck data, indicating that the amount of lensing is in excellent agreement with expectations from the observed CMB angular power spectrum when not including the information from smearing of the acoustic peaks.

Tensions between direct measurements of the lens power spectrum from Planck data

We apply a recently developed method to directly measure the gravitational lensing power spectrum from CMB power spectra to the Planck satellite data. This method allows us to analyze the tension between the temperature power spectrum and lens reconstruction in a model independent way. Even when allowing for arbitrary variations in the lensing power spectrum, the tension remains at the 2.4$\sigma$ level. By separating the lensing and unlensed high redshift information in the CMB power spectra, we also show that under $\Lambda$CDM the two are in tension at a similar level whereas the unlensed information is consistent with lensing reconstruction. These anomalies are driven by the smoother acoustic peaks relative to $\Lambda$CDM at $\ell \sim 1250 - 1500$. Both tensions relax slightly when polarization data are considered. This technique also isolates the one aspect of the lensing power spectrum that the Planck CMB power spectra currently constrain and can be straightforwardly generalized to future data when CMB power spectra constrain multiple aspects of lensing which are themselves correlated with lensing reconstruction.

Flat-Sky Pseudo-Cls Analysis for Weak Gravitational Lensing

We investigate the use of estimators of weak lensing power spectra based on a flat-sky implementation of the Pseudo-Cl (PCl) technique, where the masked shear field is transformed without regard for masked regions of sky. This masking mixes power, and E-convergence and B-modes. To study the accuracy of forward-modelling and full-sky power spectrum recovery we consider both large-area survey geometries, and small-scale masking due to stars and a checkerboard model for field-of-view gaps. The power spectrum for the large-area survey geometry is sparsely-sampled and highly oscillatory, which makes modelling problematic. Instead, we derive an overall calibration for large-area mask bias using simulated fields. The effects of small-area star masks can be accurately corrected for, while the checkerboard mask has oscillatory and spiky behaviour which leads to percent biases. Apodisation of the masked fields leads to increased biases and a loss of information. We find that we can construct an unbiased forward-model of the raw PCls, and recover the full-sky convergence power to within a few percent accuracy for both Gaussian and lognormal-distributed shear fields. Propagating this through to cosmological parameters using a Fisher-Matrix formalism, we find we can make unbiased estimates of parameters for surveys up to 1,200 deg$^2$ with 30 galaxies per arcmin$^2$, beyond which the percent biases become larger than the statistical accuracy. This implies a flat-sky PCl analysis is accurate for current surveys but a Euclid-like survey will require higher accuracy.

Searching for signatures of dark matter-dark radiation interaction in observations of large-scale structure

In this paper, we conduct a search in the latest large-scale structure measurements for signatures of the dark matter-dark radiation interaction proposed by Buen-Abad et al. (2015). We show that prior claims of a detection of this interaction rely on a use of the SZ cluster mass function that ignores uncertainty in the mass-observable relationship. Including this uncertainty we find that the inferred level of interaction remains consistent with the data, but so does zero interaction; i.e., there is no longer a detection. We also point out that inference of the shape and amplitude of the matter power spectrum from Ly$\alpha$ forest measurements is highly inconsistent with the predictions of the $\Lambda$CDM model conditioned on Planck CMB temperature, polarization, and lensing power spectra, and that the dark matter-dark radiation model can restore that consistency. We also phenomenologically generalize the model of Buen-Abad et al. (2015) to allow for interaction rates with different scalings with temperature, and find that the original scaling is preferred by the data.

Exploring cosmic origins with CORE: Gravitational lensing of the CMB

Lensing of the cosmic microwave background (CMB) is now a well-developed probe of the clustering of the large-scale mass distribution over a broad range of redshifts. By exploiting the non-Gaussian imprints of lensing in the polarization of the CMB, the CORE mission will allow production of a clean map of the lensing deflections over nearly the full-sky. The number of high-S/N modes in this map will exceed current CMB lensing maps by a factor of 40, and the measurement will be sample-variance limited on all scales where linear theory is valid. Here, we summarise this mission product and discuss the science that will follow from its power spectrum and the cross-correlation with other clustering data. For example, the summed mass of neutrinos will be determined to an accuracy of 17 meV combining CORE lensing and CMB two-point information with contemporaneous measurements of the baryon acoustic oscillation feature in the clustering of galaxies, three times smaller than the minimum total mass allowed by neutrino oscillation measurements. Lensing has applications across many other science goals of CORE, including the search for B-mode polarization from primordial gravitational waves. Here, lens-induced B-modes will dominate over instrument noise, limiting constraints on the power spectrum amplitude of primordial gravitational waves. With lensing reconstructed by CORE, one can “delens” the observed polarization internally, reducing the lensing B-mode power by 60 %. This can be improved to 70 % by combining lensing and measurements of the cosmic infrared background from CORE, leading to an improvement of a factor of 2.5 in the error on the amplitude of primordial gravitational waves compared to no delensing (in the null hypothesis of no primordial B-modes). Lensing measurements from CORE will allow calibration of the halo masses of the tens of thousands of galaxy clusters that it will find, with constraints dominated by the clean polarization-based estimators. The 19 frequency channels proposed for CORE will allow accurate removal of Galactic emission from CMB maps. We present initial findings that show that residual Galactic foreground contamination will not be a significant source of bias for lensing power spectrum measurements with CORE.

Noise estimates for measurements of weak lensing from the Ly α forest

We have proposed a method for measuring weak lensing using the Lyman-alpha forest. Here we estimate the noise expected in weak lensing maps and power spectra for different sets of observational parameters. We find that surveys of the size and quality of the ones being done today and ones planned for the future will be able to measure the lensing power spectrum at a source redshift of z~2.5 with high precision and even be able to image the distribution of foreground matter with high fidelity on degree scales. For example, we predict that Lyman-alpha forest lensing measurement from the Dark Energy Spectroscopic Instrument survey should yield the mass fluctuation amplitude with statistical errors of 1.5%. By dividing the redshift range into multiple bins some tomographic lensing information should be accessible as well. This would allow for cosmological lensing measurements at higher redshift than are accessible with galaxy shear surveys and correspondingly better constraints on the evolution of dark energy at relatively early times.

Fundamental physics from future weak-lensing calibrated Sunyaev-Zel’dovich galaxy cluster counts

Future high-resolution measurements of the cosmic microwave background (CMB) will produce catalogs of tens of thousands of galaxy clusters through the thermal Sunyaev-Zel'dovich (tSZ) effect. We forecast how well different configurations of a CMB Stage-4 experiment can constrain cosmological parameters, in particular the amplitude of structure as a function of redshift $\sigma_8(z)$, the sum of neutrino masses $\Sigma m_{\nu}$, and the dark energy equation of state $w(z)$. A key element of this effort is calibrating the tSZ scaling relation by measuring the lensing signal around clusters. We examine how the mass calibration from future optical surveys like the Large Synoptic Survey (LSST) compares with a purely internal calibration using lensing of the CMB itself. We find that, due to its high-redshift leverage, internal calibration gives constraints on cosmological parameters comparable to the optical calibration, and can be used as a cross-check of systematics in the optical measurement. We also show that in contrast to the constraints using the CMB lensing power spectrum, lensing-calibrated tSZ cluster counts can detect a minimal $\Sigma m_{\nu}$ at the 3-5$\sigma$ level even when the dark energy equation of state is freed up.

Efficient evaluation of angular power spectra and bispectra

Angular statistics of cosmological observables are hard to compute. The main difficulty is due to the presence of highly-oscillatory Bessel functions which need to be integrated over. In this paper, we provide a simple and fast method to compute the angular power spectrum and bispectrum of any observable. The method is based on using an FFTlog algorithm to decompose the momentum-space statistics onto a basis of power-law functions. For each power law, the integrals over Bessel functions have a simple analytical solution. This allows us to efficiently evaluate these integrals, independently of the value of the multipole ℓ. In particular, this method significantly speeds up the evaluation of the angular bispectrum compared to existing methods. To illustrate our algorithm, we compute the galaxy, lensing and CMB temperature angular power spectrum and bispectrum.

KiDS-450 + 2dFLenS: Cosmological parameter constraints from weak gravitational lensing tomography and overlapping redshift-space galaxy clustering

We perform a combined analysis of cosmic shear tomography, galaxy-galaxy lensing tomography, and redshift-space multipole power spectra (monopole and quadrupole) using 450 deg$^2$ of imaging data by the Kilo Degree Survey (KiDS) overlapping with two spectroscopic surveys: the 2-degree Field Lensing Survey (2dFLenS) and the Baryon Oscillation Spectroscopic Survey (BOSS). We restrict the galaxy-galaxy lensing and multipole power spectrum measurements to the overlapping regions with KiDS, and self-consistently compute the full covariance between the different observables using a large suite of $N$-body simulations. We methodically analyze different combinations of the observables, finding that galaxy-galaxy lensing measurements are particularly useful in improving the constraint on the intrinsic alignment amplitude (by 30%, positive at $3.5\sigma$ in the fiducial data analysis), while the multipole power spectra are useful in tightening the constraints along the lensing degeneracy direction (e.g. factor of two stronger matter density constraint in the fiducial analysis). The fully combined constraint on $S_8 \equiv \sigma_8 \sqrt{\Omega_{\rm m}/0.3} = 0.742 \pm 0.035$, which is an improvement by 20% compared to KiDS alone, corresponds to a $2.6\sigma$ discordance with Planck, and is not significantly affected by fitting to a more conservative set of scales. Given the tightening of the parameter space, we are unable to resolve the discordance with an extended cosmology that is simultaneously favored in a model selection sense, including the sum of neutrino masses, curvature, evolving dark energy, and modified gravity. The complementarity of our observables allows for constraints on modified gravity degrees of freedom that are not simultaneously bounded with either probe alone, and up to a factor of three improvement in the $S_8$ constraint in the extended cosmology compared to KiDS alone.

Simulations for 21 cm radiation lensing at EoR redshifts

We introduce simulations aimed at assessing how well weak gravitational lensing of 21cm radiation from the Epoch of Reionization ($z \sim 8$) can be measured by an SKA-like radio telescope. A simulation pipeline has been implemented to study the performance of lensing reconstruction techniques. We show how well the lensing signal can be reconstructed using the three-dimensional quadratic lensing estimator in Fourier space assuming different survey strategies. The numerical code introduced in this work is capable of dealing with issues that can not be treated analytically such as the discreteness of visibility measurements and the inclusion of a realistic model for the antennae distribution. This paves the way for future numerical studies implementing more realistic reionization models, foreground subtraction schemes, and testing the performance of lensing estimators that take into account the non-Gaussian distribution of HI after reionization. If multiple frequency channels covering $z \sim 7-11.6$ are combined, Phase 1 of SKA-Low should be able to obtain good quality images of the lensing potential with a total resolution of $\sim 1.6$ arcmin. The SKA-Low Phase 2 should be capable of providing images with high-fidelity even using data from $z\sim 7.7 - 8.3$. We perform tests aimed at evaluating the numerical implementation of the mapping reconstruction. We also discuss the possibility of measuring an accurate lensing power spectrum. Combining data from $z \sim 7-11.6$ using the SKA2-Low telescope model, we find constraints comparable to sample variance in the range $L<1000$, even for survey areas as small as $25\mbox{ deg}^2$.

Weak-lensing Power Spectrum Reconstruction by Counting Galaxies. I. The ABS Method

Abstract We propose an analytical method of blind separation (ABS) of cosmic magnification from the intrinsic fluctuations of galaxy number density in the observed galaxy number density distribution. The ABS method utilizes the different dependences of the signal (cosmic magnification) and contamination (galaxy intrinsic clustering) on galaxy flux to separate the two. It works directly on the measured cross-galaxy angular power spectra between different flux bins. It determines/reconstructs the lensing power spectrum analytically, without assumptions of galaxy intrinsic clustering and cosmology. It is unbiased in the limit of an infinite number of galaxies. In reality, the lensing reconstruction accuracy depends on survey configurations, galaxy biases, and other complexities due to a finite number of galaxies and the resulting shot noise fluctuations in the cross-galaxy power spectra. We estimate its performance (systematic and statistical errors) in various cases. We find that stage IV dark energy surveys such as Square Kilometre Array and Large Synoptic Survey Telescope are capable of reconstructing the lensing power spectrum at and accurately. This lensing reconstruction only requires counting galaxies and is therefore highly complementary to cosmic shear measurement by the same surveys.

Two-season Atacama Cosmology Telescope polarimeter lensing power spectrum

We report a measurement of the power spectrum of cosmic microwave background (CMB) lensing from two seasons of Atacama Cosmology Telescope Polarimeter (ACTPol) CMB data. The CMB lensing power spectrum is extracted from both temperature and polarization data using quadratic estimators. We obtain results that are consistent with the expectation from the best-fit Planck LCDM model over a range of multipoles L=80-2100, with an amplitude of lensing A_lens = 1.06 +/- 0.15 (stat.) +/- 0.06 (sys.) relative to Planck. Our measurement of the CMB lensing power spectrum gives sigma_8 Omega_m^0.25 = 0.643 +/- 0.054; including baryon acoustic oscillation scale data, we constrain the amplitude of density fluctuations to be sigma_8 = 0.831 +/- 0.053. We also update constraints on the neutrino mass sum. We verify our lensing measurement with a number of null tests and systematic checks, finding no evidence of significant systematic errors. This measurement relies on a small fraction of the ACTPol data already taken; more precise lensing results can therefore be expected from the full ACTPol dataset.

Calibrating cluster number counts with CMB lensing

CMB Stage-4 experiments will reduce the uncertainties on the gravitational lensing potential by an order of magnitude compared to current measurements, and will also produce a Sunyaev-Zel'dovich (SZ) cluster catalog containing $\sim10^{5}$ objects, two orders of magnitudes higher than what is currently available. In this paper we propose to combine these two observables and show that it is possible to calibrate the masses of the full Stage-4 cluster catalog internally owing to the high signal to noise measurement of the CMB lensing convergence field. We find that a CMB Stage-4 experiment will constrain the hydrostatic bias parameter to sub-percent accuracy. We also show constraints on a non parametric $Y-M$ relationship which could be used to study its evolution with mass and redshift. Finally we present a joint likelihood for thermal SZ (tSZ) flux and mass measurements, and show that it could lead to a $\sim5\sigma$ detection of the lower limit on the sum of the neutrino masses in the normal hierarchy ($\sum m_{\nu}=60 \textrm{meV}$) once combined with measurements of the primordial CMB and CMB lensing power spectra.