Cosmic Microwave Background Lensing Potential Research Articles

Cross-correlation between Planck CMB lensing potential and galaxy catalogues from HELP

ABSTRACT We present the study of cross-correlation between Cosmic Microwave Background (CMB) gravitational lensing potential map released by the Planck collaboration and photometric redshift galaxy catalogues from the Herschel Extragalactic Legacy Project (HELP), divided into four sky patches: NGP, Herschel Stripe-82, and two halves of SGP field, covering in total ∼660 deg2 of the sky. We estimate the galaxy linear bias parameter, b0, from joint analysis of cross-power spectrum and galaxy autopower spectrum using Maximum Likelihood Estimation technique to obtain values ranging from 0.70 ± 0.01 for SGP Part-2 to 1.02 ± 0.02 for SGP Part-1 field. We also estimate the amplitude of cross-correlation and find the values spanning from 0.67 ± 0.18 for SGP Part-2 to 0.80 ± 0.23 for SGP Part-1 field, respectively. For NGP and SGP Part-1 fields, the amplitude is consistent with the expected value for the standard cosmological model within $\sim 1\, \sigma$, while for Herschel Stripe-82 and SGP Part-2, we find the amplitude to be smaller than expected with $\sim 1.5\, \sigma$ and $\sim 2\, \sigma$ deviation, respectively. We perform several tests on various systematic errors to study the reason for the deviation, however, value of the amplitude turns out to be robust with respect to these errors. The only significant change in the amplitude is observed when we replace the minimum-variance CMB lensing map, used in the baseline analysis, by the lensing map derived from the CMB temperature map with deprojected thermal Sunyaev–Zeldovich signal.

Ray tracing the integrated Sachs-Wolfe effect through the light cones of the dark energy universe simulation-full universe runs

The late integrated Sachs-Wolfe (ISW) effect correlates the Cosmic Microwave Background (CMB) temperature anisotropies with foreground cosmic large-scale structures. As the correlation depends crucially on the growth history in the era of dark energy, it is a key observational probe for constraining the cosmological model. Here we present a detailed study based on full-sky and deep light cones generated from very large volume numerical N-body simulations, which allow us to avoid the use of standard replica techniques, while capturing the entirety of the late ISW effect on the large scales. We post-process the light cones using an accurate ray-tracing method and construct full-sky maps of the ISW temperature anisotropy for three different dark energy models. We quantify in detail the extent to which the ISW effect can be used to discriminate between different dark energy scenarios when cross-correlated with the matter distribution or the CMB lensing potential. We also investigate the onset of non-linearities, the so-called Rees-Sciama effect which provides a complementary probe of the dark sector. We find the signal of the lensing-lensing and ISW-lensing correlation of the three dark energy models to be consistent with measurements from the Planck satellite. Future surveys of the large-scale structures may provide cross-correlation measurements that are sufficiently precise to distinguish the signal of these models. Our methodology is very general and can be applied to any dark energy or modified gravity scenario as long as the metric seen by photons can still be characterized by a Weyl potential.

An Assessment of Contamination in the Thermal-SZ Map Using Cross-correlations

Abstract We search for potential galactic and extragalactic dust contamination in thermal Sunyaev–Zeldovich maps derived from the Planck data. To test for contamination, we apply a variety of galactic dust and cosmic infrared background (CIB) models to the data as part of the y map reconstruction process. We evaluate the level of contamination by cross-correlating these y maps with mass tracers based on weak lensing data. The lensing data we use are the convergence map, κ, from the Red Sequence Cluster Lensing survey, and the cosmic microwave background (CMB) lensing potential map, ϕ, from the Planck Collaboration. We make a CIB-subtracted y map and measure the cross-correlation between it and the lensing data. By comparing it with CIB-contaminated cross-correlation, we find that the cross-correlation between κ and y is only slightly contaminated by CIB signal, at the level of 6.8 ± 3.5%, which implies that previous detections of κ × y are robust to CIB contamination. However, we find that ϕ × y is more significantly contaminated, by 16.7 ± 3.5%, because the CMB lensing potential probes higher redshift sources that overlap more with the CIB sources. We find that Galactic dust does not significantly contaminate either cross-correlation signal.

CMB lensing reconstruction biases in cross-correlation with large-scale structure probes

The cross-correlation between cosmic microwave background (CMB) gravitational lensing and large-scale structure tracers will be an important cosmological probe in the coming years. Quadratic estimators provide a simple and powerful (if suboptimal) way to reconstruct the CMB lensing potential and are widely used. For Gaussian fields, the cross-correlation of a quadratic-estimator CMB lensing reconstruction with a tracer is exactly unbiased if the power spectra are known and consistent analytic lensing mode response functions are used. However, the bispectrum induced by non-linear large-scale structure growth and post-Born lensing can introduce an additional bias term (NL(3/2)) in the cross-correlation spectrum, similar to the NL(3/2) bias in the auto-spectrum demonstrated in recent works. We give analytic flat-sky results for the cross-correlation bias using approximate models for the post-Born and large-scale structure cross-bispectra, and compare with N-body simulation results using ray-tracing techniques. We show that the bias can be at the 5–15% level in all large-scale structure cross-correlations using small-scale CMB temperature lensing reconstruction, but is substantially reduced using polarization-based lensing estimators or simple foreground-projected temperature estimators. The relative magnitude of these effects is almost three times higher than in the CMB lensing auto-correlation, but is small enough that it can be modelled to sufficient precision using simple analytic models. We show that NL(3/2) effects in cross-correlation will be detected with high significance when using data of future surveys and could affect systematic effects marginalization in cosmic shear measurements mimicking galaxy intrinsic alignment.

DeepCMB: Lensing reconstruction of the cosmic microwave background with deep neural networks

Next-generation cosmic microwave background (CMB) experiments will have lower noise and therefore increased sensitivity, enabling improved constraints on fundamental physics parameters such as the sum of neutrino masses and the tensor-to-scalar ratio r. Achieving competitive constraints on these parameters requires high signal-to-noise extraction of the projected gravitational potential from the CMB maps. Standard methods for reconstructing the lensing potential employ the quadratic estimator (QE). However, the QE performs suboptimally at the low noise levels expected in upcoming experiments. Other methods, like maximum likelihood estimators (MLE), are under active development. In this work, we demonstrate reconstruction of the CMB lensing potential with deep convolutional neural networks (CNN) - ie, a ResUNet. The network is trained and tested on simulated data, and otherwise has no physical parametrization related to the physical processes of the CMB and gravitational lensing. We show that, over a wide range of angular scales, ResUNets recover the input gravitational potential with a higher signal-to-noise ratio than the QE method, reaching levels comparable to analytic approximations of MLE methods. We demonstrate that the network outputs quantifiably different lensing maps when given input CMB maps generated with different cosmologies. We also show we can use the reconstructed lensing map for cosmological parameter estimation. This application of CNN provides a few innovations at the intersection of cosmology and machine learning. First, while training and regressing on images, we predict a continuous-variable field rather than discrete classes. Second, we are able to establish uncertainty measures for the network output that are analogous to standard methods. We expect this approach to excel in capturing hard-to-model non-Gaussian astrophysical foreground and noise contributions.

O(1) eV sterile neutrino in f(R) gravity

We refer [1] to the role of an additional O(1) eV sterile neutrino in modified gravity models. We find parameter constraints in particular f(R) gravity model using following up-to-dated cosmological data: measurements of the cosmic microwave background (CMB) anisotropy, the CMB lensing potential, the baryon acoustic oscillations (BAO), the cluster mass function and the Hubble constant. It was obtained for the sterile neutrino mass 0.47 eV < mν,sterile < 1 eV (2σ) assuming that the sterile neutrinos are thermalized and the active neutrinos are massless, not significantly larger than in the standard cosmology model within the same data set: 0.45 eV < mν,sterile < 0.92 eV (2σ). But, if the mass of sterile neutrino is fixed and equals ≈ 1.5 eV according to various anomalies in neutrino oscillation experiments, f(R) gravity is much more consistent with observation data than the CDM model.

Planckintermediate results

The secondary cosmic microwave background (CMB) $B$-modes stem from the post-decoupling distortion of the polarization $E$-modes due to the gravitational lensing effect of large-scale structures. These lensing-induced $B$-modes constitute both a valuable probe of the dark matter distribution and an important contaminant for the extraction of the primary CMB $B$-modes from inflation. Planck provides accurate nearly all-sky measurements of both the polarization $E$-modes and the integrated mass distribution via the reconstruction of the CMB lensing potential. By combining these two data products, we have produced an all-sky template map of the lensing-induced $B$-modes using a real-space algorithm that minimizes the impact of sky masks. The cross-correlation of this template with an observed (primordial and secondary) $B$-mode map can be used to measure the lensing $B$-mode power spectrum at multipoles up to $2000$. In particular, when cross-correlating with the $B$-mode contribution directly derived from the Planck polarization maps, we obtain lensing-induced $B$-mode power spectrum measurement at a significance level of $12\,\sigma$, which agrees with the theoretical expectation derived from the Planck best-fit $\Lambda$CDM model. This unique nearly all-sky secondary $B$-mode template, which includes the lensing-induced information from intermediate to small ($10\lesssim \ell\lesssim 1000$) angular scales, is delivered as part of the Planck 2015 public data release. It will be particularly useful for experiments searching for primordial $B$-modes, such as BICEP2/Keck Array or LiteBIRD, since it will enable an estimate to be made of the lensing-induced contribution to the measured total CMB $B$-modes.

Quantifying tensions between CMB and distance data sets in models with free curvature or lensing amplitude

Recent measurements of the Cosmic Microwave Background (CMB) by the Planck Collaboration have produced arguably the most powerful observational evidence in support of the standard model of cosmology, i.e. the spatially flat $\Lambda$CDM paradigm. In this work, we perform model selection tests to examine whether the base CMB temperature and large scale polarization anisotropy data from Planck 2015 (P15) prefer any of eight commonly used one-parameter model extensions with respect to flat $\Lambda$CDM. We find a clear preference for models with free curvature, $\Omega_\mathrm{K}$, or free amplitude of the CMB lensing potential, $A_\mathrm{L}$. We also further develop statistical tools to measure tension between datasets. We use a Gaussianization scheme to compute tensions directly from the posterior samples using an entropy-based method, the surprise, as well as a calibrated evidence ratio presented here for the first time. We then proceed to investigate the consistency between the base P15~CMB data and six other CMB and distance datasets. In flat $\Lambda$CDM we find a $4.8\sigma$ tension between the base P15~CMB data and a distance ladder measurement, whereas the former are consistent with the other datasets. In the curved $\Lambda$CDM model we find significant tensions in most of the cases, arising from the well-known low power of the low-$\ell$ multipoles of the CMB data. In the flat $\Lambda$CDM $+A_\mathrm{L}$ model, however, all datasets are consistent with the base P15~CMB observations except for the CMB lensing measurement, which remains in significant tension. This tension is driven by the increased power of the CMB lensing potential derived from the base P15~CMB constraints in both models, pointing at either potentially unresolved systematic effects or the need for new physics beyond the standard flat $\Lambda$CDM model.

Lensing as a probe of early universe: from CMB to galaxies

The Cosmic Microwave Background (CMB) radiation lensing is a promising tool to study the physics of early universe. In this work we probe the imprints of deviations from isotropy and scale invariance of primordial curvature perturbation power spectrum on CMB lensing potential and convergence. Specifically, we consider a scale-dependent hemispherical asymmetry in primordial power spectrum. We show that the CMB lensing potential and convergence and also the cross-correlation of the CMB lensing and late time galaxy convergence can probe the amplitude and the scale dependence of the dipole modulation. As another example, we consider a primordial power spectrum with local feature. We show that the CMB lensing and the cross-correlation of the CMB lensing and galaxy lensing can probe the amplitude and the shape of the local feature. We show that the cross correlation of CMB lensing convergence and galaxy lensing is capable to probe the effects of local features in power spectrum on smaller scales than the CMB lensing. Finally we showed that the current data can constrain the amplitude and moment dependence of dipole asymmetry.

A MEASUREMENT OF THE COSMIC MICROWAVE BACKGROUND GRAVITATIONAL LENSING POTENTIAL FROM 100 SQUARE DEGREES OF SPTPOL DATA

We present a measurement of the cosmic microwave background (CMB) gravitational lensing potential using data from the first two seasons of observations with SPTpol, the polarization-sensitive receiver currently installed on the South Pole Telescope (SPT). The observations used in this work cover 100 deg$^2$ of sky with arcminute resolution at 150 GHz. Using a quadratic estimator, we make maps of the CMB lensing potential from combinations of CMB temperature and polarization maps. We combine these lensing potential maps to form a minimum-variance (MV) map. The lensing potential is measured with a signal-to-noise ratio of greater than one for angular multipoles between $100< L <250$. This is the highest signal-to-noise mass map made from the CMB to date and will be powerful in cross-correlation with other tracers of large-scale structure. We calculate the power spectrum of the lensing potential for each estimator, and we report the value of the MV power spectrum between $100< L <2000$ as our primary result. We constrain the ratio of the spectrum to a fiducial $\Lambda$CDM model to be $A_{\rm MV}=0.92 \pm 0.14 {\rm\, (Stat.)} \pm 0.08 {\rm\, (Sys.)}$. Restricting ourselves to polarized data only, we find $A_{\rm POL}=0.92 \pm 0.24 {\rm\, (Stat.)} \pm 0.11 {\rm\, (Sys.)}$. This measurement rejects the hypothesis of no lensing at $5.9 \sigma$ using polarization data alone, and at $14 \sigma$ using both temperature and polarization data.

New constraints onf(R)gravity from clusters of galaxies

The abundance of massive galaxy clusters is a powerful probe of departures from general relativity (GR) on cosmic scales. Despite current stringent constraints placed by stellar and galactic tests, on larger scales alternative theories of gravity such as $f(R)$ can still work as effective theories. Here we present constraints on two popular models of $f(R)$, Hu-Sawicki and ``designer,'' derived from a fully self-consistent analysis of current samples of x-ray selected clusters and accounting for all the covariances between cosmological and astrophysical parameters. Using cluster number counts in combination with recent data from the cosmic microwave background (CMB) and the CMB lensing potential generated by large scale structures, as well as with other cosmological constraints on the background expansion history and its mean matter density, we obtain the upper bounds ${\mathrm{log}}_{10}|{f}_{R0}|&lt;4.79$ and ${\mathrm{log}}_{10}{B}_{0}&lt;3.75$ at the 95.4% confidence level, for the Hu-Sawicki (with $n=1$) and designer models, respectively. The robustness of our results derives from high-quality cluster growth data for the most massive clusters known out to redshifts $z\ensuremath{\sim}0.5$, a tight control of systematic uncertainties including an accurate and precise mass calibration from weak gravitational lensing data, and the use of the full shape of the halo mass function over the mass range of our data.

Cosmology based on f(R) gravity with \U0001d4aa(1) eV sterile neutrino

We address the cosmological role of an additional \U0001d4aa(1) eV sterile neutrino in modified gravity models. We confront the present cosmological data with predictions of the FLRW cosmological model based on a variant of f(R) modified gravity proposed by one of the authors previously. This viable cosmological model which deviation from general relativity with a cosmological constant Λ decreases as R−2n for large, but not too large values of the Ricci scalar R (while no Λ is introduced by hand at small R) provides an alternative explanation of present dark energy and the accelerated expansion of the Universe (the case n=2 is considered in the paper). Various up-to-date cosmological data sets exploited include measurements of the cosmic microwave background (CMB) anisotropy, the CMB lensing potential, the baryon acoustic oscillations (BAO), the cluster mass function and the Hubble constant. We find that the CMB+BAO constraints strongly restrict the sum of neutrino masses from above. This excludes values of the model parameter λ∼ 1 for which distinctive cosmological features of the model are mostly pronounced as compared to the ΛCDM model, since then free streaming damping of perturbations due to neutrino rest masses is not sufficient to compensate their extra growth occurring in f(R) modified gravity. Thus, in the gravity sector we obtain λ>8.2 (2σ) with the account of systematic uncertainties in galaxy cluster mass function measurements and λ>9.4 (2σ) without them. At the same time in the latter case we find for the sterile neutrino mass 0.47 eV < mν, sterile < 1 eV (2σ) assuming that the sterile neutrinos are thermalized and the active neutrinos are massless, not significantly larger than in the standard ΛCDM with the same data set: 0.45 eV < mν, sterile < 0.92 eV (2σ). However, a possible discovery of a sterile neutrino with the mass mν, sterile ≈ 1.5 eV motivated by various anomalies in neutrino oscillation experiments would favor cosmology based on f(R) gravity rather than the ΛCDM model.

CMB lensing forecasts for constraining the primordial perturbations: adding to the CMB temperature and polarization information

We forecast how current (PLANCK) and future (PRISM) cosmic microwave background (CMB) experiments constrain the adiabatic mode and its admixtures with primordial isocurvature modes. The forecasts are based on measurements of the reconstructed CMB lensing potential and lensing-induced CMB B-mode polarization anisotropies in combination with the CMB temperature and E-mode polarization anisotropies. We first study the characteristic features of the CMB temperature, polarization and lensing spectra for adiabatic and isocurvature modes. We then consider how information from the CMB lensing potential and B-mode polarization induced by lensing can improve constraints on an admixture of adiabatic and three correlated isocurvature modes. We find that the CMB lensing spectrum improves constraints on isocurvature modes by at most 10% for the PLANCK and PRISM experiments. The limited improvement is a result of the low amplitude of isocurvature lensing spectra and cancellations between these spectra that render them only slightly detectable. There is a larger gain from using the lensing-induced B-mode polarization spectrum measured by PRISM. In this case constraints on isocurvature mode amplitudes improve by as much as 40% relative to the CMB temperature and E-mode polarization constraints. The addition of both lensing and lensing-induced B-mode polarization information constrains isocurvature mode amplitudes at the few percent level or better. In the case of admixtures of the adiabatic mode with one or two correlated isocurvature modes we find that constraints at the percent level or better are possible. We investigate the dependence of our results to various assumptions in our analysis, such as the inclusion of dark energy parameters, the CMB temperature-lensing correlation, and the presence of primordial tensor modes, and find that these assumptions do not significantly change our main results.

Systematic errors in the measurement of neutrino masses due to baryonic feedback processes: Prospects for stage IV lensing surveys

We examine the importance of baryonic feedback effects on the matter power spectrum on small scales, and the implications for the precise measurement of neutrino masses through gravitational weak lensing. Planned large galaxy surveys such as the Large Synoptic Sky Telescope (LSST) and Euclid are expected to measure the sum of neutrino masses to extremely high precision, sufficient to detect non-zero neutrino masses even in the minimal mass normal hierarchy. We show that weak lensing of galaxies while being a very good probe of neutrino masses, is extremely sensitive to baryonic feedback processes. We use publicly available results from the Overwhelmingly Large Simulations (OWLS) project to investigate the effects of active galactic nuclei feedback, the nature of the stellar initial mass function, and gas cooling rates, on the measured weak lensing shear power spectrum. Using the Fisher matrix formalism and priors from CMB+BAO data, we show that when one does not account for feedback, the measured neutrino mass may be substantially larger or smaller than the true mass, depending on the dominant feedback mechanism, with the mass error |\Delta m_nu| often exceeding the mass m_nu itself. We also consider gravitational lensing of the cosmic microwave background (CMB) and show that it is not sensitive to baryonic feedback on scales l < 2000, although CMB experiments that aim for sensitivities sigma(m_nu) < 0.02 eV will need to include baryonic effects in modeling the CMB lensing potential. A combination of CMB lensing and galaxy lensing can help break the degeneracy between neutrino masses and baryonic feedback processes. We conclude that future large galaxy lensing surveys such as LSST and Euclid can only measure neutrino masses accurately if the matter power spectrum can be measured to similar accuracy.

Non-Gaussianity in WMAP data due to the correlation of CMB lensing potential with secondary anisotropies

We measure the skewness power spectrum of the Cosmic Microwave Background (CMB) anisotropies optimized for a detection of the secondary bispectrum generated by the correlation of the CMB lensing potential with integrated Sachs-Wolfe effect and the Sunyaev-Zel'dovich effect. The covariance of our measurements is generated by Monte-Carlo simulations of Gaussian CMB fields with noise properties consistent with Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data. When interpreting multi-frequency measurements we also take into account the confusion resulting from unresolved radio point sources. We analyze Q, V and W-band WMAP 5-year raw and foreground-cleaned maps using the KQ75 mask out to l_max=600. We find no significant evidence for a non-zero non-Gaussian signal from the lensing-secondary correlation in all three bands and we constrain the overall amplitude of the cross power spectrum between CMB lensing potential and the sum of SZ and ISW fluctuations to be 0.42 \pm 0.86 and 1.19 \pm 0.86 in combined V and W-band raw and foreground-cleaned maps provided by the WMAP team, respectively. The point source amplitude at the bispectrum level measured with this skewness power spectrum is higher than previous measurements of point source non-Gaussianity. We also consider an analysis where we also account for the primordial non-Gaussianity in addition to lensing-secondary bispectrum and point sources. The focus of this paper is on secondary anisotropies. Consequently the estimator is not optimised for primordial non-Gaussianity and the limit we find on local non-Gaussianity from the foreground-cleaned V+W maps is f_NL = -13 \pm 62, when marginalized over point sources and lensing-ISW/SZ constributions to the total bispectrum.

Detectability of CMB tensorBmodes via delensing with weak lensing galaxy surveys

We analyze the possibility of delensing cosmic microwave background (CMB) polarization maps using foreground weak lensing (WL) information. We build an estimator of the CMB lensing potential out of optimally combined projected-potential estimators to different source redshift bins. Our estimator is most sensitive to the redshift depth of the WL survey, less so to the shape noise level. Estimators built using galaxy surveys like the Large Synoptic Survey Telescope and the Supernova Acceleration Probe recover up to 80%--90% of the potential fluctuations power at $l\ensuremath{\le}100$ but only $\ensuremath{\approx}10%--20%$ of the small-angular-scale power ($l\ensuremath{\le}1000$). This translates into a 30%--50% reduction in the lensing $B$-mode power. We illustrate the potential advantages of a 21 cm survey by considering a fiducial WL survey for which we take the redshift depth ${z}_{\mathrm{max}}$ and the effective angular concentration of sources $\overline{n}$ as free parameters. For a noise level of $1\text{ }\text{ }\ensuremath{\mu}\mathrm{K}\text{ }\mathrm{arcmin}$ in the polarization map itself, as projected for a CMBPol experiment, and a beam with ${\ensuremath{\theta}}_{\mathrm{FWHM}}=10\text{ }\text{ }\mathrm{arcmin}$, we find that going to ${z}_{\mathrm{max}}=20$ at $\overline{n}=100\text{ }\text{ }\mathrm{galaxies}/{\mathrm{arcmin}}^{2}$ yields a delensing performance similar to that of a quadratic lensing potential estimator applied to small-scale CMB maps: the lensing $B$-mode contamination is reduced by almost an order of magnitude. In this case, there is also a reduction by a factor of $\ensuremath{\approx}4$ in the detectability threshold of the tensor $B$-mode power. At this CMB noise level, the $B$-mode detection threshold is only $3\ifmmode\times\else\texttimes\fi{}$ lower even for perfect delensing, so there is little gain from sources with ${z}_{\mathrm{max}}&gt;20$. The delensing gains are lost if the CMB beam exceeds $\ensuremath{\sim}20\text{ }\text{ }\mathrm{arcmin}$. The delensing gains and useful ${z}_{\mathrm{max}}$ depend acutely on the CMB map noise level, but beam sizes below 10 arcmin do not help. Delensing via foreground sources does not require arc-minute-resolution CMB observations, a substantial practical advantage over the use of CMB observables for delensing.