CMB power spectrum parameter degeneracies in the era of precision cosmology

Cosmological parameter constraints from the CMB power spectra alone suffer several well-known degeneracies. These degeneracies can be broken by numerical artefacts and also a variety of physical effects that become quantitatively important with high-accuracy data e.g. from the Planck satellite. We study degeneracies in models with flat and non-flat spatial sections, non-trivial dark energy and massive neutrinos, and investigate the importance of various physical degeneracy-breaking effects. We test the CAMB power spectrum code for numerical accuracy, and demonstrate that the numerical calculations are accurate enough for degeneracies to be broken mainly by true physical effects (the integrated Sachs-Wolfe effect, CMB lensing and geometrical and other effects through recombination) rather than numerical artefacts. We quantify the impact of CMB lensing on the power spectra, which inevitably provides degeneracy-breaking information even without using information in the non-Gaussianity. Finally we check the numerical accuracy of sample-based parameter constraints using CAMB and CosmoMC. In an appendix we document recent changes to CAMB's numerical treatment of massive neutrino perturbations, which are tested along with other recent improvements by our degeneracy exploration results.Comment: 27 pages, 28 figures. Latest CAMB version available from http://camb.info/. Reduced number of figures, plot legend corrected and minor edits to match published versio

Generation of Curvature Perturbations with Extra Anisotropic Stress

We study the evolution of curvature perturbations and the cosmic microwave background (CMB) power spectrum in the presence of an hypothesized extra anisotropic stress which might arise, for example, from the dark radiation term in brane-world cosmology. We evolve the scalar modes of such perturbations before and after neutrino decoupling and analyze their effects on the CMB spectrum. A novel result of this work is that the cancellation of the neutrino and extra anisotropic stress could lead to a spectrum of residual curvature perturbations which is similar to the observed CMB power spectrum. This implies a possible additional consideration in the determination of cosmological parameters from the CMB analysis.Comment: 13 pages, 2 figures; improved discussio

Global and regional impacts of climate change at different levels of global temperature increase

The assessment of the impacts of climate change at different levels of global warming helps inform national and international policy discussion around mitigation targets. This paper provides consistent estimates of global and regional impacts and risks at increases in global mean temperature up to 5 °C above pre-industrial levels, for over 30 indicators representing temperature extremes and heatwaves, hydrological change, floods and droughts and proxies for impacts on crop yields. At the global scale, all the impacts that could plausibly be either adverse or beneficial are adverse, and impacts and risks increase with temperature change. For example, the global average chance of a major heatwave increases from 5% in 1981–2010 to 28% at 1.5 °C and 92% at 4 °C, of an agricultural drought increases from 9 to 24% at 1.5 °C and 61% at 4 °C, and of the 50-year return period river flood increases from 2 to 2.4% at 1.5 °C and 5.4% at 4 °C. The chance of a damaging hot spell for maize increases from 5 to 50% at 4 °C, whilst the chance for rice rises from 27 to 46%. There is considerable uncertainty around these central estimates, and impacts and risks vary between regions. Some impacts—for example heatwaves—increase rapidly as temperature increases, whilst others show more linear responses. The paper presents estimates of the risk of impacts exceeding specific targets and demonstrates that these estimates are sensitive to the thresholds used

Current cosmological constraints from a 10 parameter CMB analysis

We compute the constraints on a ``standard'' 10 parameter cold dark matter (CDM) model from the most recent CMB and data and other observations, exploring 30 million discrete models and two continuous parameters. Our parameters are the densities of CDM, baryons, neutrinos, vacuum energy and curvature, the reionization optical depth, and the normalization and tilt for both scalar and tensor fluctuations. Our strongest constraints are on spatial curvature, -0.24 < Omega_k < 0.38, and CDM density, h^2 Omega_cdm <0.3, both at 95%. Including SN 1a constraints gives a positive cosmological constant at high significance. We explore the robustness of our results to various assumptions. We find that three different data subsets give qualitatively consistent constraints. Some of the technical issues that have the largest impact are the inclusion of calibration errors, closed models, gravity waves, reionization, nucleosynthesis constraints and 10-dimensional likelihood interpolation.Comment: Replaced to match published ApJ version. More details added. 13 ApJ pages. CMB movies and color figs at http://www.hep.upenn.edu/~max/10par_frames.html or from [email protected]

Constraints on the neutrino mass and the primordial magnetic field from the matter density fluctuation parameter σ8\sigma_8

We have made an analysis of limits on the neutrino mass based upon the formation of large-scale structure in the presence of a primordial magnetic field. We find that a new upper bound on the neutrino mass is possible based upon fits to the cosmic microwave background and matter power spectrum when the existing independent constraints on the matter density fluctuation parameter $\sigma_8$ and the primordial magnetic field are taken into account.Comment: 6 pages, 2 figures, final version to appear in Phys. Rev. D, to match proof

Lensed CMB power spectra from all-sky correlation functions

Weak lensing of the CMB changes the unlensed temperature anisotropy and polarization power spectra. Accounting for the lensing effect will be crucial to obtain accurate parameter constraints from sensitive CMB observations. Methods for computing the lensed power spectra using a low-order perturbative expansion are not good enough for percent-level accuracy. Non-perturbative flat-sky methods are more accurate, but curvature effects change the spectra at the 0.3-1% level. We describe a new, accurate and fast, full-sky correlation-function method for computing the lensing effect on CMB power spectra to better than 0.1% at l<2500 (within the approximation that the lensing potential is linear and Gaussian). We also discuss the effect of non-linear evolution of the gravitational potential on the lensed power spectra. Our fast numerical code is publicly available.Comment: 16 pages, 4 figures. Changes to match PRD version including new section on non-linear corrections. CAMB code available at http://camb.info

Comparing the effects of calibration and climate errors on a statistical crop model and a process-based crop model

Understanding the relationship between climate and crop productivity is a key component of projections of future food production, and hence assessments of food security. Climate models and crop yield datasets have errors, but the effects of these errors on regional scale crop models is not well categorized and understood. In this study we compare the effect of synthetic errors in temperature and precipitation observations on the hindcast skill of a process-based crop model and a statistical crop model. We find that errors in temperature data have a significantly stronger influence on both models than errors in precipitation. We also identify key differences in the responses of these models to different types of input data error. Statistical and process-based model responses differ depending on whether synthetic errors are overestimates or underestimates. We also investigate the impact of crop yield calibration data on model skill for both models, using datasets of yield at three different spatial scales. Whilst important for both models, the statistical model is more strongly influenced by crop yield scale than the process-based crop model. However, our results question the value of high resolution yield data for improving the skill of crop models; we find a focus on accuracy to be more likely to be valuable. For both crop models, and for all three spatial scales of yield calibration data, we found that model skill is greatest where growing area is above 10-15 %. Thus information on area harvested would appear to be a priority for data collection efforts. These results are important for three reasons. First, understanding how different crop models rely on different characteristics of temperature, precipitation and crop yield data allows us to match the model type to the available data. Second, we can prioritize where improvements in climate and crop yield data should be directed. Third, as better climate and crop yield data becomes available, we can predict how crop model skill should improve

Internal delensing of Planck CMB temperature and polarization

We present a first internal delensing of CMB maps, both in temperature and polarization, using the public foreground-cleaned (SMICA) Planck 2015 maps. After forming quadratic estimates of the lensing potential, we use the corresponding displacement field to undo the lensing on the same data. We build differences of the delensed spectra to the original data spectra specifically to look for delensing signatures. After taking into account reconstruction noise biases in the delensed spectra, we find an expected sharpening of the power spectrum acoustic peaks with a delensing efficiency of 29 % (TT) 25 % (TE) and 22 % (EE). The detection significance of the delensing effects is very high in all spectra: 12 σ in EE polarization; 18 σ in TE; and 20 σ in TT. The null hypothesis of no lensing in the maps is rejected at 26 σ. While direct detection of the power in lensing B-modes themselves is not possible at high significance at Planck noise levels, we do detect (at 4.5 σ {under the null hypothesis}) delensing effects in the B-mode map, with 7 % reduction in lensing power. Our results provide a first demonstration of polarization delensing, and generally of internal CMB delensing, and stand in agreement with the baseline ΛCDM Planck 2015 cosmology expectations.JC and AL acknowledge support from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. [616170], and AL and AC from the Science and Technology Facilities Council [grant numbers ST/L000652/1 and ST/N000927/1, respectively]. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02- 05CH11231

Clusters of galaxies in the microwave band: influence of the motion of the Solar System

In this work we consider the changes of the SZ cluster brightness, flux and number counts induced by the motion of the Solar System with respect to the frame defined by the cosmic microwave background (CMB). These changes are connected with the Doppler effect and aberration and exhibit a strong spectral and spatial dependence. The correction to the SZ cluster brightness and flux has an amplitude and spectral dependence, which is similar to the first order cluster peculiar velocity correction to the thermal SZ effect. Due to the change in the received cluster CMB flux the motion of the Solar System induces a dipolar asymmetry in the observed number of clusters above a given flux level. Similar effects were discussed for $\gamma$-ray bursts and radio galaxies, but here, due to the very peculiar frequency-dependence of the thermal SZ effect, the number of observed clusters in one direction of the sky can be both, decreased or increased depending on the frequency band. A detection of this asymmetry should be possible using future full sky CMB experiments with mJy sensitivities.Comment: 7 pages, 6 figures, submitted to Astronomy and Astrophysics, corrected pdf-proble