Planck Cosmic Microwave Background Lensing Research Articles

The cosmic microwave background lensing imprint of cosmic voids detected in the WISE-Pan-STARRS luminous red galaxy catalog

The cross-correlation of cosmic voids with the lensing convergence (kappa ) map of cosmic microwave background (CMB) fluctuations offers a powerful tool with which to refine our understanding of the dark sector in the consensus cosmological model. Our principal aim is to compare the lensing signature of our galaxy dataset with simulations based on the concordance model and to characterize the results with an $A_ kappa $ consistency parameter normalized to unity. In particular, our measurements contribute to the understanding of the “lensing-is-low” tension of the Lambda CDM model. In this analysis, we selected luminous red galaxies (LRGs) from the WISE- Pan-STARRS dataset, enabling an extended cross-correlation measurement using a 14,200 deg$^2$ sky area, which offers a more precise measurement than previous studies. We created 2D and 3D void catalogs to cross-correlate their locations with the Planck CMB lensing map and studied their average imprint signal using a stacking methodology. Applying the same procedure, we also generated a mock galaxy catalog from the WebSky simulation to serve as a basis for comparison. The 2D void analysis reveals a good agreement with the standard cosmological model, with $A_ kappa 0.08$ amplitude; that is, $S/N=13.3$, showing a higher signal-to-noise than previous studies using voids detected in the Dark Energy Survey (DES) dataset. The 3D void analysis exhibited a lower signal-to-noise ratio and demonstrated worse agreement with our mock catalog than the 2D voids. These deviations might be attributed to limitations in the mock catalog, such as imperfections in the LRG selection, as well as a potential asymmetry between the northern and southern patches of the Pan-STARRS dataset in terms of data quality. Overall, we present a significant detection of a CMB lensing signal associated with cosmic voids, largely consistent with the concordance model. Future analyses using even larger datasets also hold great promise of further sharpening these results, given their complementary nature to large-scale structure analyses.

High-accuracy emulators for observables in ΛCDM, Neff, Σmν, and w cosmologies

Abstract We use the emulation framework CosmoPower to construct and publicly release neural network emulators of cosmological observables, including the Cosmic Microwave Background (CMB) temperature and polarization power spectra, matter power spectrum, distance-redshift relation, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) observables, and derived parameters. We train our emulators on Einstein-Boltzmann calculations obtained with high-precision numerical convergence settings, for a wide range of cosmological models including ΛCDM, wCDM, ΛCDM+Neff, and ΛCDM+Σmν. Our CMB emulators are accurate to better than 0.5% out to ℓ = 104 which is sufficient for Stage-IV data analysis, and our P(k) emulators reach the same accuracy level out to k = 50 Mpc−1, which is sufficient for Stage-III data analysis. We release the emulators via an online repository (CosmoPower Organisation), which will be continually updated with additional extended cosmological models. Our emulators accelerate cosmological data analysis by orders of magnitude, enabling cosmological parameter extraction analyses, using current survey data, to be performed on a laptop. We validate our emulators by comparing them to class and camb and by reproducing cosmological parameter constraints derived from Planck TT, TE, EE, and CMB lensing data, as well as from the Atacama Cosmology Telescope Data Release 4 CMB data, Dark Energy Survey Year-1 galaxy lensing and clustering data, and Baryon Oscillation Spectroscopic Survey Data Release 12 BAO and RSD data.

The Atacama Cosmology Telescope: DR6 Gravitational Lensing Map and Cosmological Parameters

We present cosmological constraints from a gravitational lensing mass map covering 9400 deg2 reconstructed from measurements of the cosmic microwave background (CMB) made by the Atacama Cosmology Telescope (ACT) from 2017 to 2021. In combination with measurements of baryon acoustic oscillations and big bang nucleosynthesis, we obtain the clustering amplitude σ 8 = 0.819 ± 0.015 at 1.8% precision, S8≡σ8(Ωm/0.3)0.5=0.840±0.028 , and the Hubble constant H 0 = (68.3 ± 1.1) km s−1 Mpc−1 at 1.6% precision. A joint constraint with Planck CMB lensing yields σ 8 = 0.812 ± 0.013, S8≡σ8(Ωm/0.3)0.5=0.831±0.023 , and H 0 = (68.1 ± 1.0) km s−1 Mpc−1. These measurements agree with ΛCDM extrapolations from the CMB anisotropies measured by Planck. We revisit constraints from the KiDS, DES, and HSC galaxy surveys with a uniform set of assumptions and find that S 8 from all three are lower than that from ACT+Planck lensing by levels ranging from 1.7σ to 2.1σ. This motivates further measurements and comparison, not just between the CMB anisotropies and galaxy lensing but also between CMB lensing probing z ∼ 0.5–5 on mostly linear scales and galaxy lensing at z ∼ 0.5 on smaller scales. We combine with CMB anisotropies to constrain extensions of ΛCDM, limiting neutrino masses to ∑m ν < 0.13 eV (95% c.l.), for example. We describe the mass map and related data products that will enable a wide array of cross-correlation science. Our results provide independent confirmation that the universe is spatially flat, conforms with general relativity, and is described remarkably well by the ΛCDM model, while paving a promising path for neutrino physics with lensing from upcoming ground-based CMB surveys.

Cosmological Tensions and the Transitional Planck Mass Model

In this follow-up analysis, we update previous constraints on the transitional Planck mass (TPM) modified gravity model using the latest version of EFTCAMB and provide new constraints using South Pole Telescope (SPT) and Planck anisotropy data along with Planck cosmic microwave background lensing, baryon acoustic oscillations, and Type Ia supernovae data and a Hubble constant, H 0, prior from local measurements. We find that large shifts in the Planck mass lead to large suppression of power on small scales that is disfavored by both the SPT and Planck data. Using only the SPT temperature-polarization–polarization-polarization (TE-EE) data, this suppression of power can be compensated for by an upward shift of the scalar index to n s = 1.003 ± 0.016, resulting in km m−1 Mpc−1 and a ∼7% shift in the Planck mass. Including the Planck temperature-temperature (TT) ℓ ≤ 650 and Planck TE-EE data restricts the shift to be <5% at 2σ with H 0 = 70.65 ± 0.66 km m−1 Mpc−1. Excluding the H 0 prior, the SPT and Planck data constrain the shift in the Planck mass to be <3% at 2σ with a best-fit value of 0.04%, consistent with the Λ cold dark matter limit. In this case km s−1 Mpc−1, which is partially elevated by the dynamics of the scalar field in the late Universe. This differs from early dark energy models that prefer higher values of H 0 when the high-ℓ Planck TT data are excluded. We additionally constrain TPM using redshift space distortion data from BOSS DR12 and cosmic shear, galaxy–galaxy lensing, and galaxy clustering data from DES Y1, finding both disfavor transitions close to recombination, but earlier Planck mass transitions are allowed.

KiDS-1000: Cross-correlation with Planck cosmic microwave background lensing and intrinsic alignment removal with self-calibration

Context. Galaxy shear and cosmic microwave background (CMB) lensing convergence cross-correlations contain additional information on cosmology with respect to auto-correlations. While remaining immune to certain systemic effects, these cross-correlations are nonetheless affected by the galaxy’s intrinsic alignments (IA). These effects may, in fact, be responsible for the reported low lensing amplitude of the galaxy shear × CMB convergence cross-correlations, compared to the standard PlanckΛCDM (cosmological constant and cold dark matter) cosmology predictions. Aims. In this work, we investigate how IA affects the Kilo-Degree Survey (KiDS) galaxy lensing shear and Planck CMB lensing convergence cross-correlation and we compare it to previous treatments, both with and without IA taken into consideration. Methods. We compared the marginalization over IA parameters and the IA self-calibration (SC) method (with additional observables defined only from the source galaxies) to demonstrate that SC can efficiently break the degeneracy between the CMB lensing amplitude, Alens, and the IA amplitude, AIA. We further investigated how different systematics affect the resulting AIA and Alens and we validated our results with the MICE2 simulation. Results. We find that by including the SC method to constrain IA, the information loss due to the degeneracy between CMB lensing and IA is strongly reduced. The best-fit values are Alens = 0.84−0.22+0.22 and AIA = 0.60−1.03+1.03, while different angular scale cuts can affect Alens by ∼10%. We show that an appropriate treatment of the boost factor, cosmic magnification, and photometric redshift modeling is important for obtaining the correct IA and cosmological results.

New Constraint on the Tensor-to-scalar Ratio from the Planck and BICEP/Keck Array Data Using the Profile Likelihood

Motivated by the discrepancy between Bayesian and frequentist upper limits on the tensor-to-scalar ratio parameter r found by the SPIDER collaboration, we investigate whether a similar trend is also present in the latest Planck and BICEP/Keck Array data. We derive a new upper bound on r using the frequentist profile likelihood method. We vary all the relevant cosmological parameters of the ΛCDM model, as well as the nuisance parameters. Unlike the Bayesian analysis using Markov Chain Monte Carlo (MCMC), our analysis is independent of the choice of priors. Using Planck Public Release 4, BICEP/Keck Array 2018, Planck cosmic microwave background lensing, and baryon acoustic oscillation data, we find an upper limit of r < 0.037 at 95% Confidence Level (C.L.), similar to the Bayesian MCMC result of r < 0.038 for a flat prior on r and a conditioned Planck lowlEB covariance matrix.

Atacama Cosmology Telescope: Constraints on prerecombination early dark energy

The early dark energy (EDE) scenario aims to increase the value of the Hubble constant ($H_0$) inferred from cosmic microwave background (CMB) data over that found in $\Lambda$CDM, via the introduction of a new form of energy density in the early universe. The EDE component briefly accelerates cosmic expansion just prior to recombination, which reduces the physical size of the sound horizon imprinted in the CMB. Previous work has found that non-zero EDE is not preferred by Planck CMB power spectrum data alone, which yield a 95% confidence level (CL) upper limit $f_{\rm EDE} < 0.087$ on the maximal fractional contribution of the EDE field to the cosmic energy budget. In this paper, we fit the EDE model to CMB data from the Atacama Cosmology Telescope (ACT) Data Release 4. We find that a combination of ACT, large-scale Planck TT (similar to WMAP), Planck CMB lensing, and BAO data prefers the existence of EDE at $>99.7$% CL: $f_{\rm EDE} = 0.091^{+0.020}_{-0.036}$, with $H_0 = 70.9^{+1.0}_{-2.0}$ km/s/Mpc (both 68% CL). From a model-selection standpoint, we find that EDE is favored over $\Lambda$CDM by these data at roughly $3\sigma$ significance. In contrast, a joint analysis of the full Planck and ACT data yields no evidence for EDE, as previously found for Planck alone. We show that the preference for EDE in ACT alone is driven by its TE and EE power spectrum data. The tight constraint on EDE from Planck alone is driven by its high-$\ell$ TT power spectrum data. Understanding whether these differing constraints are physical in nature, due to systematics, or simply a rare statistical fluctuation is of high priority. The best-fit EDE models to ACT and Planck exhibit coherent differences across a wide range of multipoles in TE and EE, indicating that a powerful test of this scenario is anticipated with near-future data from ACT and other ground-based experiments.

Cross-correlation of Planck cosmic microwave background lensing with DESI galaxy groups

ABSTRACT We measure the cross-correlation between galaxy groups constructed from DESI Legacy Imaging Survey DR8 and Planck cosmic microwave background (CMB) lensing, over overlapping sky area of 16 876 $\rm deg^2$. The detections are significant and consistent with the expected signal of the large-scale structure of Universe, over group samples of various redshift, mass, and richness Ng, and over various scale cuts. The overall signal-to-noise ratio is 40 for a conservative sample with Ng ≥ 5, and increases to 50 for the sample with Ng ≥ 2. Adopting the Planck 2018 cosmology, we constrain the density bias of groups with Ng ≥ 5 as bg = 1.31 ± 0.10, 2.22 ± 0.10, and 3.52 ± 0.20 at 0.1 &amp;lt; z ≤ 0.33, 0.33 &amp;lt; z ≤ 0.67, and 0.67 &amp;lt; z ≤ 1, respectively. The group catalogue provides the estimation of group halo mass and therefore allows us to detect the dependence of bias on group mass with high significance. It also allows us to compare the measured bias with the theoretically predicted one using the estimated group mass. We find excellent agreement for the two high-redshift bins. However, it is lower than the theory by ∼3σ for the lowest redshift bin. Another interesting finding is the significant impact of the thermal Sunyaev Zel’dovich. It contaminates the galaxy group-CMB lensing cross-correlation at $\sim \! 30{{\ \rm per\ cent}}$ level, and must be deprojected first in CMB lensing reconstruction.

Singling out modified gravity parameters and data sets reveals a dichotomy between Planck and lensing

ABSTRACT An important route to testing general relativity (GR) at cosmological scales is usually done by constraining modified gravity (MG) parameters added to the Einstein perturbed equations. Most studies have analysed so far constraints on pairs of MG parameters, but here, we explore constraints on one parameter at a time while fixing the other at its GR value. This allows us to analyse various models while benefiting from a stronger constraining power from the data. We also explore which specific data sets are in tension with GR. We find that models with (μ = 1, η) and (μ, η = 1) exhibit a 3.9σ and 3.8σ departure from GR when using Planck18 + Supernovae type Ia (SNe) + Baryon acoustic oscillation (BAO), while (μ, η) shows a tension of 3.4σ. We find no tension with GR for models with the MG parameter Σ fixed to its GR value. Using a Bayesian model selection analysis, we find that some one-parameter MG models are moderately favoured over ΛCDM when using all data set combinations except Planck cosmic microwave background lensing and dark energy survey data. Namely, Planck18 shows a moderate tension with GR that only increases when adding any combination of redshift space distortion, SNe, or BAO. However, adding lensing diminishes or removes these tensions, which can be attributed to the ability of lensing in constraining the MG parameter Σ. The two overall groups of data sets are found to have a dichotomy when performing consistency tests with GR, which may be due to systematic effects, lack of constraining power, or modelling. These findings warrant further investigation using more precise data from ongoing and future surveys.

Cross-correlation of Planck CMB lensing with DESI-like LRGs

ABSTRACT Cross-correlations between the lensing of the cosmic microwave background (CMB) and other tracers of large-scale structure provide a unique way to reconstruct the growth of dark matter, break degeneracies between cosmology and galaxy physics, and test theories of modified gravity. We detect a cross-correlation between Dark Energy Spectroscopic Instrument (DESI)-like luminous red galaxies (LRGs) selected from DECam Legacy Survey imaging and CMB lensing maps reconstructed with the Planck satellite at a significance of S/N = 27.2 over scales ℓmin = 30, ℓmax = 1000. To correct for magnification bias, we determine the slope of the LRG cumulative magnitude function at the faint limit as s = 0.999 ± 0.015, and find corresponding corrections of the order of a few per cent for $C^{\kappa g}_{\ell }, C^{gg}_{\ell }$ across the scales of interest. We fit the large-scale galaxy bias at the effective redshift of the cross-correlation zeff ≈ 0.68 using two different bias evolution agnostic models: a HaloFit times linear bias model where the bias evolution is folded into the clustering-based estimation of the redshift kernel, and a Lagrangian perturbation theory model of the clustering evaluated at zeff. We also determine the error on the bias from uncertainty in the redshift distribution; within this error, the two methods show excellent agreement with each other and with DESI survey expectations.

Cross-correlation between Subaru Hyper Suprime-Cam Galaxy Weak Lensing and Planck Cosmic Microwave Background Lensing

Abstract Cross-correlations between galaxy weak lensing (WL) and cosmic microwave background (CMB) lensing are powerful tools to probe matter fluctuations at intermediate redshifts and to detect residual systematics in either probe. In this paper, we study the cross-correlation of galaxy WL from the Hyper Suprime-Cam Subaru Strategic Program (HSC) first data release and CMB lensing from the final Planck data release, for HSC source galaxies at 0.3 ≤ z ≤ 1.5. HSC is the deepest Stage-III galaxy WL survey, and provides a great opportunity to study the high-redshift universe. It also presents new challenges related to its exceptionally high source density, such as source blending. The cross-correlation signal is measured at a significance level of 3.1σ. The amplitude of our best-fit model with respect to the best-fit 2018 Planck cosmology is A = 0.81 ± 0.25, consistent with A = 1. Our result is also consistent with previous CMB lensing and galaxy WL cross-correlation studies using different surveys. We perform tests with respect to the WL B-modes, the point-spread-function, photometric redshift errors, and thermal Sunyaev–Zel’dovich leakage, and find no significant evidence of residual systematics.

Dark Energy Survey Year 1 results: the lensing imprint of cosmic voids on the cosmic microwave background

ABSTRACT Cosmic voids gravitationally lens the cosmic microwave background (CMB) radiation, resulting in a distinct imprint on degree scales. We use the simulated CMB lensing convergence map from the Marenostrum Institut de Ciencias de l’Espai (MICE) N-body simulation to calibrate our detection strategy for a given void definition and galaxy tracer density. We then identify cosmic voids in Dark Energy Survey (DES) Year 1 data and stack the Planck 2015 lensing convergence map on their locations, probing the consistency of simulated and observed void lensing signals. When fixing the shape of the stacked convergence profile to that calibrated from simulations, we find imprints at the 3σ significance level for various analysis choices. The best measurement strategies based on the MICE calibration process yield S/N ≈ 4 for DES Y1, and the best-fitting amplitude recovered from the data is consistent with expectations from MICE (A ≈ 1). Given these results as well as the agreement between them and N-body simulations, we conclude that the previously reported excess integrated Sachs–Wolfe (ISW) signal associated with cosmic voids in DES Y1 has no counterpart in the Planck CMB lensing map.

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.

Halo Pressure Profile through the Skew Cross-power Spectrum of the Sunyaev–Zel’dovich Effect and CMB Lensing in Planck

Abstract We measure the cosmic microwave background (CMB) skewness power spectrum in Planck, using frequency maps of the HFI instrument and the Sunyaev–Zel’dovich (SZ) component map. The two-to-one skewness power spectrum measures the cross-correlation between CMB lensing and the thermal SZ effect. We also directly measure the same cross-correlation using the Planck CMB lensing map and the SZ map and compare it to the cross-correlation derived from the skewness power spectrum. We model fit the SZ power spectrum and CMB lensing–SZ cross-power spectrum via the skewness power spectrum to constrain the gas pressure profile of dark matter halos. The gas pressure profile is compared to existing measurements in the literature including a direct estimate based on the stacking of SZ clusters in Planck.

Planck Lensing and Cosmic Infrared Background Cross-correlation with Fermi-LAT: Tracing Dark Matter Signals in the Gamma-Ray Background

Abstract The extragalactic γ-ray background and its spatial anisotropy could potentially contain a signature of dark matter (DM) annihilation or particle decay. Astrophysical foregrounds, such as blazars and star-forming galaxies (SFGs), however, dominate the γ-ray background, precluding an easy detection of the signal associated with the DM annihilation or decay in the background intensity spectrum. The DM imprint on the γ-ray background is expected to be correlated with large-scale structure tracers. In some cases, such a cross-correlation is even expected to have a higher signal-to-noise ratio than the auto-correlation. One reliable tracer of the DM distribution in the large-scale structure is lensing of the cosmic microwave background (CMB), and the cosmic infrared background (CIB) is a reliable tracer of SFGs. We analyze Fermi-LAT data taken over 92 months and study the cross-correlation with Planck CMB lensing, Planck CIB, and Fermi-γ maps. We put upper limits on the DM annihilation cross-section from the cross-power spectra with the γ-ray background anisotropies. The unbiased power spectrum estimation is validated with simulations that include cross-correlated signals. We also provide a set of systematic tests and show that no significant contaminations are found for the measurements presented here. Using γ-ray background map from data gathered over 92 months, we find the best constraint on the DM annihilation with a 1 σ confidence level upper limit of 10−25–10−24 cm3 s−1, when the mass of DM particles is between 20 and 100 GeV.

Constraining gravity at the largest scales through CMB lensing and galaxy velocities

We demonstrate a new method to constrain gravity on the largest cosmological scales by combining measurements of cosmic microwave background (CMB) lensing and the galaxy velocity field. $E_G$ is a statistic, constructed from a gravitational lensing tracer and a measure of velocities such as redshift-space distortions (RSD), that can discriminate between gravity models while being independent of clustering bias and $\sigma_8$. While traditionally, the lensing field for $E_G$ has been probed through galaxy lensing, CMB lensing has been proposed as a more robust tracer of the lensing field for $E_G$ at higher redshifts while avoiding intrinsic alignments. We perform the largest-scale measurement of $E_G$ ever, up to 150 Mpc/$h$, by cross-correlating the Planck CMB lensing map with the Sloan Digital Sky Survey III (SDSS-III) CMASS galaxy sample and combining this with our measurement of the CMASS auto-power spectrum and the RSD parameter $\beta$. We report $E_G(z=0.57)=0.243\pm0.060$ (stat) $\pm0.013$ (sys), a measurement in tension with the general relativity prediction at a level of 2.6$\sigma$. Note that our $E_G$ measurement deviates from GR only at scales greater than 80 Mpc/$h$, scales which have not been probed by previous $E_G$ tests. Upcoming surveys, which will provide an order-of-magnitude reduction in statistical errors, can significantly constrain alternative gravity models when combined with better control of systematics.

Constraining multiplicative bias in CFHTLenS weak lensing shear data

Several recent cosmological analyses have found tension between constraints derived from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) data and those derived from other data sets, such as the Planck cosmic microwave background (CMB) temperature anisotropies. Similarly, a direct cross-correlation of the CFHTLenS data with Planck CMB lensing data yielded an anomalously low amplitude compared to expectations based on Planck or WMAP-derived cosmological parameters (Liu & Hill 2015). One potential explanation for these results is a multiplicative bias afflicting the CFHTLenS galaxy shape measurements, from which shears are inferred. Simulations are used in the CFHTLenS pipeline to calibrate such biases, but no data-driven constraints have been presented to date. In this paper, we cross-correlate CFHTLenS galaxy density maps with CFHTLenS shear maps and Planck CMB lensing maps to calibrate an additional multiplicative shear bias (m) in CFHTLenS (beyond the multiplicative correction that has already been applied to the CFHTLenS galaxy shears), following methods suggested by Vallinotto (2012) and Das et al. (2013). We analyze three magnitude-limited galaxy samples, finding 2-4sigma evidence for m<1 using the deepest sample (i<24), while the others are consistent with m=1 (no bias). This matches the expectation that the shapes of faint galaxies are the most prone to measurement biases. Our results for m are essentially independent of the assumed cosmology, and only weakly sensitive to assumptions about the galaxy bias. We consider three galaxy bias models, finding in all cases that the best-fit multiplicative shear bias is less than unity. A value of m~0.9 would suffice to reconcile the amplitude of density fluctuations inferred from the CFHTLenS shear two-point statistics with that inferred from Planck CMB temperature data. This scenario is consistent with our results.

Cosmological implications of baryon acoustic oscillation measurements

We derive constraints on cosmological parameters and tests of dark energy models from the combination of baryon acoustic oscillation (BAO) measurements with cosmic microwave background (CMB) and Type Ia supernova (SN) data. We take advantage of high-precision BAO measurements from galaxy clustering and the Ly-alpha forest (LyaF) in the BOSS survey of SDSS-III. BAO data alone yield a high confidence detection of dark energy, and in combination with the CMB angular acoustic scale they further imply a nearly flat universe. Combining BAO and SN data into an "inverse distance ladder" yields a 1.7% measurement of $H_0=67.3 \pm1.1$ km/s/Mpc. This measurement assumes standard pre-recombination physics but is insensitive to assumptions about dark energy or space curvature, so agreement with CMB-based estimates that assume a flat LCDM cosmology is an important corroboration of this minimal cosmological model. For open LCDM, our BAO+SN+CMB combination yields $\Omega_m=0.301 \pm 0.008$ and curvature $\Omega_k=-0.003 \pm 0.003$. When we allow more general forms of evolving dark energy, the BAO+SN+CMB parameter constraints remain consistent with flat LCDM. While the overall $\chi^2$ of model fits is satisfactory, the LyaF BAO measurements are in moderate (2-2.5 sigma) tension with model predictions. Models with early dark energy that tracks the dominant energy component at high redshifts remain consistent with our constraints. Expansion history alone yields an upper limit of 0.56 eV on the summed mass of neutrino species, improving to 0.26 eV if we include Planck CMB lensing. Standard dark energy models constrained by our data predict a level of matter clustering that is high compared to most, but not all, observational estimates. (Abridged)

Probing gravity at large scales through CMB lensing

We describe a methodology to probe gravity with the cosmic microwave background (CMB) lensing convergence $\kappa$, specifically by measuring $E_G$, the ratio of the Laplacian of the gravitational scalar potential difference with the velocity divergence. Using CMB lensing instead of galaxy-galaxy lensing avoids intrinsic alignments while also lacking a hard limit on the lens redshift and significant uncertainties in the source plane. We model $E_G$ for general relativity and modified gravity, finding that $E_G$ for $f(R)$ gravity should be scale-dependent due to the scale-dependence of the growth rate $f$. Next, we construct an estimator for $E_G$ in terms of the galaxy-CMB lensing and galaxy clustering angular power spectra, along with the RSD parameter $\beta$. We also forecast statistical errors for $E_G$ from the current Planck CMB lensing map and the spectroscopic galaxy and quasar samples from the Sloan Digital Sky Survey Data Release 11, being 9% with galaxies and 8% when quasars are included. We also find that upcoming spectroscopic and photometric surveys, combined with the final Planck lensing map, can measure precisely the redshift- and scale-dependence of $E_G$ out to redshifts $z=2$ and higher, with photometric surveys having an advantage due to their high number densities. Advanced ACTPol's lensing map will increase the $E_G$ sensitivity even further. Finally, we find that Advanced ACTPol cross-correlated with spectroscopic (photometric) surveys can differentiate between general relativity and $f(R)$ gravity at the level of $3\sigma$ ($13\sigma$). Performing a $<1$% measurement of $E_G$ requires a 10% precision in $\beta$ from Euclid or LSST, currently achievable with a spectroscopic survey but difficult with only a photometric survey.

Neutrinos and dark energy after Planck and BICEP2: data consistency tests and cosmological parameter constraints

The detection of the B-mode polarization of the cosmic microwave background (CMB) by the BICEP2 experiment implies that the tensor-to-scalar ratio r should be involved in the base standard cosmology. In this paper, we extend the ΛCDM r+neutrino/dark radiation models by replacing the cosmological constant with the dynamical dark energy with constant w. Four neutrino plus dark energy models are considered, i.e., the wCDM r ∑ mν, wCDM r Neff, wCDM r ∑ mν Neff, and wCDM r Neff mν,sterileeff models. The current observational data considered in this paper include the Planck temperature data, the WMAP 9-year polarization data, the baryon acoustic oscillation data, the Hubble constant direct measurement data, the Planck Sunyaev-Zeldovich cluster counts data, the Planck CMB lensing data, the cosmic shear data, and the BICEP2 polarization data. We test the data consistency in the four cosmological models, and then combine the consistent data sets to perform joint constraints on the models. We focus on the constraints on the parameters w, ∑ mν, Neff, and mν,sterileeff.