On the joint analysis of CMB temperature and lensing-reconstruction power spectra

Gravitational lensing provides a significant source of cosmological information in modern CMB parameter analyses. It is measured in both the power spectrum and trispectrum of the temperature fluctuations. These observables are often treated as independent, although as they are both determined from the same map this is impossible. In this paper, we perform a rigorous analysis of the covariance between lensing power spectrum and trispectrum analyses. We find two dominant contributions coming from: (i) correlations between the disconnected noise bias in the trispectrum measurement and sample variance in the temperature power spectrum; and (ii) sample variance of the lenses themselves. The former is naturally removed when the dominant N0 Gaussian bias in the reconstructed deflection spectrum is dealt with via a partially data-dependent correction, as advocated elsewhere for other reasons. The remaining lens-cosmic-variance contribution is easily modeled but can safely be ignored for a Planck-like experiment, justifying treating the two observable spectra as independent. We also test simple likelihood approximations for the deflection power spectrum, finding that a Gaussian with a parameter-independent covariance performs well.Comment: 25+11 pages, 14 figure

Universal Non-Gaussian Initial Conditions for N-body Simulations

In this paper we present the implementation of an efficient formalism for the generation of arbitrary non-Gaussian initial conditions for use in N-body simulations. The methodology involves the use of a separable modal approach for decomposing a primordial bispectrum or trispectrum. This approach allows for the far more efficient generation of the non-Gaussian initial conditions already described in the literature, as well as the generation for the first time of non-separable bispectra and the special class of diagonal-free trispectra. The modal approach also allows for the reconstruction of the spectra from given realisations, a fact which is exploited to provide an accurate consistency check of the simulations.Comment: 7 pages, 3 figure

Modeling Galaxies in Redshift Space at the Field Level

We develop an analytical forward model based on perturbation theory to predict the redshift-space galaxy overdensity at the field level given a realization of the initial conditions. We find that the residual noise between the model and simulated galaxy density has a power spectrum that is white on large scales, with size comparable to the shot noise. In the mildly nonlinear regime, we see a $k^2\mu^2$ correction to the noise power spectrum, corresponding to larger noise along the line of sight and on smaller scales. The parametric form of this correction has been predicted on theoretical grounds before, and our simulations provide important confirmation of its presence. We have also modeled the galaxy velocity at the field-level and compared it against simulated galaxy velocities, finding that about $10\%$ of the galaxies are responsible for half of the rms velocity residual for our simulated galaxy sample.Comment: 21 pages, 12 figures. Code available at https://github.com/mschmittfull/per

Fewer Mocks and Less Noise: Reducing the Dimensionality of Cosmological Observables with Subspace Projections

Creating accurate and low-noise covariance matrices represents a formidable challenge in modern-day cosmology. We present a formalism to compress arbitrary observables into a small number of bins by projection into a model-specific subspace that minimizes the prior-averaged log-likelihood error. The lower dimensionality leads to a dramatic reduction in covariance matrix noise, significantly reducing the number of mocks that need to be computed. Given a theory model, a set of priors, and a simple model of the covariance, our method works by using singular value decompositions to construct a basis for the observable that is close to Euclidean; by restricting to the first few basis vectors, we can capture almost all the constraining power in a lower-dimensional subspace. Unlike conventional approaches, the method can be tailored for specific analyses and captures non-linearities that are not present in the Fisher matrix, ensuring that the full likelihood can be reproduced. The procedure is validated with full-shape analyses of power spectra from BOSS DR12 mock catalogs, showing that the 96-bin power spectra can be replaced by 12 subspace coefficients without biasing the output cosmology; this allows for accurate parameter inference using only $\sim 100$ mocks. Such decompositions facilitate accurate testing of power spectrum covariances; for the largest BOSS data chunk, we find that: (a) analytic covariances provide accurate models (with or without trispectrum terms); and (b) using the sample covariance from the MultiDark-Patchy mocks incurs a $\sim 0.5\sigma$ shift in $\Omega_m$, unless the subspace projection is applied. The method is easily extended to higher order statistics; the $\sim 2000$-bin bispectrum can be compressed into only $\sim 10$ coefficients, allowing for accurate analyses using few mocks and without having to increase the bin sizes.Comment: 22 pages, 6 figures. Accepted by Phys. Rev.

CMB-S4 Science Book, First Edition

This book lays out the scientific goals to be addressed by the next-generation ground-based cosmic microwave background experiment, CMB-S4, envisioned to consist of dedicated telescopes at the South Pole, the high Chilean Atacama plateau and possibly a northern hemisphere site, all equipped with new superconducting cameras. CMB-S4 will dramatically advance cosmological studies by crossing critical thresholds in the search for the B-mode polarization signature of primordial gravitational waves, in the determination of the number and masses of the neutrinos, in the search for evidence of new light relics, in constraining the nature of dark energy, and in testing general relativity on large scales

Planck 2015 results. XIII. Cosmological parameters

We present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB. These data are consistent with the six-parameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar spectral index with n_s = 0.968 +/- 0.006. (We quote 68% errors on measured parameters and 95% limits on other parameters.) Combined with Planck temperature and lensing data, Planck LFI polarization measurements lead to a reionization optical depth of tau = 0.066 +/- 0.016. Combining Planck with other astrophysical data we find N_ eff = 3.15 +/- 0.23 for the effective number of relativistic degrees of freedom and the sum of neutrino masses is constrained to < 0.23 eV. Spatial curvature is found to be |Omega_K| < 0.005. For LCDM we find a limit on the tensor-to-scalar ratio of r <0.11 consistent with the B-mode constraints from an analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP data leads to a tighter constraint of r < 0.09. We find no evidence for isocurvature perturbations or cosmic defects. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. Standard big bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent agreement with observations. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. The Planck results for base LCDM are in agreement with BAO data and with the JLA SNe sample. However the amplitude of the fluctuations is found to be higher than inferred from rich cluster counts and weak gravitational lensing. Apart from these tensions, the base LCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets

CMB-S4: Forecasting Constraints on Primordial Gravitational Waves

CMB-S4---the next-generation ground-based cosmic microwave background (CMB) experiment---is set to significantly advance the sensitivity of CMB measurements and enhance our understanding of the origin and evolution of the Universe, from the highest energies at the dawn of time through the growth of structure to the present day. Among the science cases pursued with CMB-S4, the quest for detecting primordial gravitational waves is a central driver of the experimental design. This work details the development of a forecasting framework that includes a power-spectrum-based semi-analytic projection tool, targeted explicitly towards optimizing constraints on the tensor-to-scalar ratio, $r$, in the presence of Galactic foregrounds and gravitational lensing of the CMB. This framework is unique in its direct use of information from the achieved performance of current Stage 2--3 CMB experiments to robustly forecast the science reach of upcoming CMB-polarization endeavors. The methodology allows for rapid iteration over experimental configurations and offers a flexible way to optimize the design of future experiments given a desired scientific goal. To form a closed-loop process, we couple this semi-analytic tool with map-based validation studies, which allow for the injection of additional complexity and verification of our forecasts with several independent analysis methods. We document multiple rounds of forecasts for CMB-S4 using this process and the resulting establishment of the current reference design of the primordial gravitational-wave component of the Stage-4 experiment, optimized to achieve our science goals of detecting primordial gravitational waves for $r > 0.003$ at greater than $5\sigma$, or, in the absence of a detection, of reaching an upper limit of $r < 0.001$ at $95\%$ CL.Comment: 24 pages, 8 figures, 9 tables, submitted to ApJ. arXiv admin note: text overlap with arXiv:1907.0447

PICO: Probe of Inflation and Cosmic Origins

The Probe of Inflation and Cosmic Origins (PICO) is an imaging polarimeter that will scan the sky for 5 years in 21 frequency bands spread between 21 and 799 GHz. It will produce full-sky surveys of intensity and polarization with a final combined-map noise level of 0.87 \u3bcK arcmin for the required specifications, equivalent to 3300 Planck missions, and with our current best-estimate would have a noise level of 0.61 \u3bcK arcmin (6400 Planck missions). PICO will either determine the energy scale of inflation by detecting the tensor to scalar ratio at a level r=5 710 124 (5\u3c3), or will rule out with more than 5\u3c3 all inflation models for which the characteristic scale in the potential is the Planck scale. With LSST's data it could rule out all models of slow-roll inflation. PICO will detect the sum of neutrino masses at >4\u3c3, constrain the effective number of light particle species with \u394Neff<0.06 (2\u3c3), and elucidate processes affecting the evolution of cosmic structures by measuring the optical depth to reionization with errors limited by cosmic variance and by constraining the evolution of the amplitude of linear fluctuations \u3c38(z) with sub-percent accuracy. Cross-correlating PICO's map of the thermal Sunyaev-Zeldovich effect with LSST's gold sample of galaxies will precisely trace the evolution of thermal pressure with z. PICO's maps of the Milky Way will be used to determine the make up of galactic dust and the role of magnetic fields in star formation efficiency. With 21 full sky legacy maps in intensity and polarization, which cannot be obtained in any other way, the mission will enrich many areas of astrophysics. PICO is the only single-platform instrument with the combination of sensitivity, angular resolution, frequency bands, and control of systematic effects that can deliver this compelling, timely, and broad science

Cosmological Synergies Enabled by Joint Analysis of Multi-probe data from WFIRST, Euclid, and LSST

WFIRST, Euclid, and LSST are all missions designed to perform dedicated cosmology surveys that offer unprecedented statistical constraining power and control of systematic uncertainties. There is a growing realization that these missions will be significantly more powerful when the data are processed and analyzed in unison