EE Power Spectra Research Articles

Consistency of the Planck CMB data and ΛCDM cosmology

We test the consistency between Planck temperature and polarization power spectra and the concordance model of Λ Cold Dark Matter cosmology (ΛCDM) within the framework of Crossing statistics. We find that Planck TT best fit ΛCDM power spectrum is completely consistent with EE power spectrum data while EE best fit ΛCDM power spectrum is not consistent with TT data. However, this does not point to any systematic or model-data discrepancy since in the Planck EE data, uncertainties are much larger compared to the TT data. We also investigate the possibility of any deviation from ΛCDM model analyzing the Planck 2015 data. Results from TT, TE and EE data analysis indicate that no deviation is required beyond the flexibility of the concordance ΛCDM model. Our analysis thus rules out any strong evidence for beyond the concordance model in the Planck spectra data. We also report a mild amplitude difference comparing temperature and polarization data, where temperature data seems to have slightly lower amplitude than expected (consistently at all multiples), as we assume both temperature and polarization data are realizations of the same underlying cosmology.

The information content of cosmic microwave background anisotropies

The cosmic microwave background (CMB) contains perturbations that are close to Gaussian and isotropic. This means that its information content, in the sense of the ability to constrain cosmological models, is closely related to the number of modes probed in CMB power spectra. Rather than making forecasts for specific experimental setups, here we take a more pedagogical approach and ask how much information we can extract from the CMB if we are only limited by sample variance. We show that, compared with temperature measurements, the addition of E-mode polarization doubles the number of modes available out to a fixed maximum multipole, provided that all of the TT, TE, and EE power spectra are measured. However, the situation in terms of constraints on particular parameters is more complicated, as we explain and illustrate graphically. We also discuss the enhancements in information that can come from adding B-mode polarization and gravitational lensing. We show how well one could ever determine the basic cosmological parameters from CMB data compared with what has been achieved with Planck, which has already probed a substantial fraction of the TT information. Lastly, we look at constraints on neutrino mass as a specific example of how lensing information improves future prospects beyond the current 6-parameter model.

Cosmic microwave background anisotropies generated by domain wall networks

We develop a numerical tool for the fast computation of the temperature and polarization power spectra generated by domain wall networks, by extending the publicly available CMBACT code --- that calculates the CMB signatures generated by active sources --- to also describe domain wall networks. In order to achieve this, we adapt the Unconnected Segment model for cosmic strings to also describe domain wall networks, and use it to model the energy-momentum of domain wall networks throughout their cosmological history. We use this new tool to compute and study the TT, EE, TE and BB power spectra generated by standard domain wall networks, and derive a conservative constraint on the energy scale of the domain wall-forming phase transition of $\upeta <0.92\,\,{\rm MeV}$ (which is a slight improvement over the original Zel'dovich bound of $1\,\,{\rm MeV}$).

NEW CONSTRAINTS ON COSMIC POLARIZATION ROTATION FROM THE ACTPol COSMIC MICROWAVE BACKGROUND B-MODE POLARIZATION OBSERVATION AND THE BICEP2 CONSTRAINT UPDATE

Recently ACTPol has measured the cosmic microwave background (CMB) B-mode and E-mode polarizations and obtained TE, EE, BB, TB and EB power spectra in the multipole range 225-8725. In our previous paper (Ap. J. 792 (2014) 35 [Paper I]), we have analyzed jointly the results of three experiments on the CMB B-mode polarization -- SPTpol, POLARBEAR and BICEP2 to include in the model, in addition to the gravitational lensing and the inflationary gravitational waves components, also the fluctuation effects induced by the cosmic polarization rotation (CPR), if it exists within the upper limits at the time. In this paper, we fit both the mean CPR angle <{\alpha}> and its fluctuation <{\delta}{\alpha}2> from the new ACTPol data, and update our fitting of CPR fluctuations using BICEP2 data taking the new Planck dust measurement results into consideration. We follow the method of Paper I. The mean CPR angle is constrained from the EB correlation power spectra to |<{\alpha}>| < 14 mrad (0.8{\deg}) and the fluctuation (rms) is constrained from the BB correlation power spectra to <{\delta}{\alpha}2>1/2 < 29.3 mrad (1.68{\deg}). Assuming that the polarization angle of Tau A does not change from 89.2 to 146 GHz, the ACTPol data give <{\alpha}> = 1.0 {\pm} 0.63{\deg}. These results suggest that the inclusion of the present ACTPol data is consistent with no CPR detection. With the new Planck dust measurement, we update our fits of the BICEP2 CPR fluctuation constraint to be 32.8 mrad (1.88{\deg}). The joint ACTpol-BICEP2-POLARBEAR CPR fluctuation constraint is 23.7 mrad (1.36{\deg}).

The Atacama Cosmology Telescope: CMB polarization at 200 < ℓ < 9000

We report on measurements of the cosmic microwave background (CMB) and celestial polarization at 146 GHz made with the Atacama Cosmology Telescope Polarimeter (ACTPol) in its first three months of observing. Four regions of sky covering a total of 270 square degrees were mapped with an angular resolution of 1.3′. The map noise levels in the four regions are between 11 and 17 μK-arcmin. We present TT, TE, EE, TB, EB, and BB power spectra from three of these regions. The observed E-mode polarization power spectrum, displaying six acoustic peaks in the range 200 < ℓ < 3000, is an excellent fit to the prediction of the best-fit cosmological models from WMAP9+ACT and Planck data. The polarization power spectrum, which mainly reflects primordial plasma velocity perturbations, provides an independent determination of cosmological parameters consistent with those based on the temperature power spectrum, which results mostly from primordial density perturbations. We find that without masking any point sources in the EE data at ℓ < 9000, the Poisson tail of the EE power spectrum due to polarized point sources has an amplitude less than 2.4 μ 2 at ℓ = 3000 at 95% confidence. Finally, we report that the Crab Nebula, an important polarization calibration source at microwave frequencies, has 8.7% polarization with an angle of 150.7̂ ± 0.6̂ when smoothed with a 5′ Gaussian beam.

A needlet ILC analysis of WMAP 9-year polarization data: CMB polarization power spectra

We estimate Cosmic Microwave Background (CMB) polarisation power spectra, and temperature-polarisation cross-spectra, from the 9-year data of the Wilkinson Microwave Anisotropy Probe (WMAP). Foreground cleaning is implemented using minimum variance linear combinations of the coefficients of needlet decompositions of sky maps for all WMAP channels, to produce maps for CMB temperature anisotropies (T-mode) and polarisation (E-mode and B-mode), for 9 different years of observation. The final power spectra are computed from averages of all possible cross-year power spectra obtained using foreground-cleaned maps for the different years. Our analysis technique yields a measurement of the EE spectrum that is in excellent agreement with theoretical expectations from the current cosmological model. By comparison, the publicly available WMAP EE power spectrum is higher on average (and significantly higher than the predicted EE spectrum from the current best fit) at scales larger than about a degree, an excess that is not confirmed by our analysis.

SECOND SEASON QUIET OBSERVATIONS: MEASUREMENTS OF THE COSMIC MICROWAVE BACKGROUND POLARIZATION POWER SPECTRUM AT 95 GHz

The Q/U Imaging ExperimenT (QUIET) has observed the cosmic microwave background (CMB) at 43 and 95GHz. The 43-GHz results have been published in QUIET Collaboration et al. (2011), and here we report the measurement of CMB polarization power spectra using the 95-GHz data. This data set comprises 5337 hours of observations recorded by an array of 84 polarized coherent receivers with a total array sensitivity of 87 uK sqrt(s). Four low-foreground fields were observed, covering a total of ~1000 square degrees with an effective angular resolution of 12.8', allowing for constraints on primordial gravitational waves and high-signal-to-noise measurements of the E-modes across three acoustic peaks. The data reduction was performed using two independent analysis pipelines, one based on a pseudo-Cl (PCL) cross-correlation approach, and the other on a maximum-likelihood (ML) approach. All data selection criteria and filters were modified until a predefined set of null tests had been satisfied before inspecting any non-null power spectrum. The results derived by the two pipelines are in good agreement. We characterize the EE, EB and BB power spectra between l=25 and 975 and find that the EE spectrum is consistent with LCDM, while the BB power spectrum is consistent with zero. Based on these measurements, we constrain the tensor-to-scalar ratio to r=1.1+0.9-0.8 (r<2.8 at 95% C.L.) as derived by the ML pipeline, and r=1.2+0.9-0.8 (r<2.7 at 95% C.L.) as derived by the PCL pipeline. In one of the fields, we find a correlation with the dust component of the Planck Sky Model, though the corresponding excess power is small compared to statistical errors. Finally, we derive limits on all known systematic errors, and demonstrate that these correspond to a tensor-to-scalar ratio smaller than r=0.01, the lowest level yet reported in the literature.

FIRST SEASON QUIET OBSERVATIONS: MEASUREMENTS OF COSMIC MICROWAVE BACKGROUND POLARIZATION POWER SPECTRA AT 43 GHz IN THE MULTIPOLE RANGE 25 ⩽ $\ell$ ⩽ 475

The Q/U Imaging ExperimenT (QUIET) employs coherent receivers at 43GHz and 95GHz, operating on the Chajnantor plateau in the Atacama Desert in Chile, to measure the anisotropy in the polarization of the CMB. QUIET primarily targets the B modes from primordial gravitational waves. The combination of these frequencies gives sensitivity to foreground contributions from diffuse Galactic synchrotron radiation. Between 2008 October and 2010 December, >10,000hours of data were collected, first with the 19-element 43GHz array (3458hours) and then with the 90-element 95GHz array. Each array observes the same four fields, selected for low foregrounds, together covering ~1000deg^2. This paper reports initial results from the 43GHz receiver which has an array sensitivity to CMB fluctuations of 69uK sqrt(s). The data were extensively studied with a large suite of null tests before the power spectra, determined with two independent pipelines, were examined. Analysis choices, including data selection, were modified until the null tests passed. Cross correlating maps with different telescope pointings is used to eliminate a bias. This paper reports the EE, BB and EB power spectra in the multipole range ell=25-475. With the exception of the lowest multipole bin for one of the fields, where a polarized foreground, consistent with Galactic synchrotron radiation, is detected with 3sigma significance, the E-mode spectrum is consistent with the LCDM model, confirming the only previous detection of the first acoustic peak. The B-mode spectrum is consistent with zero, leading to a measurement of the tensor-to-scalar ratio of r=0.35+1.06-0.87. The combination of a new time-stream double-demodulation technique, Mizuguchi-Dragone optics, natural sky rotation, and frequent boresight rotation leads to the lowest level of systematic contamination in the B-mode power so far reported, below the level of r=0.1

FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: ANGULAR POWER SPECTRA

We present the temperature and polarization angular power spectra of the cosmic microwave background derived from the first five years of Wilkinson Microwave Anisotropy Probe data. The five-year temperature spectrum is cosmic variance limited up to multipole l = 530, and individual l-modes have signal-to-noise ratio S/N >1 for l < 920. The best-fitting six-parameter ΛCDM model has a reduced χ2 for l = 33-1000 of χ2/ν = 1.06, with a probability to exceed of 9.3%. There is now significantly improved data near the third peak which leads to improved cosmological constraints. The temperature-polarization correlation is seen with high significance. After accounting for foreground emission, the low-l reionization feature in the EE power spectrum is preferred by Δχ2 = 19.6 for optical depth τ = 0.089 by the EE data alone, and is now largely cosmic variance limited for l = 2-6. There is no evidence for cosmic signal in the BB, TB, or EB spectra after accounting for foreground emission. We find that, when averaged over l = 2-6, l(l + 1)C BB l/(2π) < 0.15 μK2 (95% CL).

Constraints on brane inflation and cosmic strings

By considering simple, but representative, models of brane inflation from a singlebrane–antibrane pair in the slow roll regime, we provide constraints on the parametersof the theory imposed by measurements of the cosmic microwave background(CMB) anisotropies by WMAP (Wilkinson Microwave Anisotropy Probe) includinga cosmic string component. We find that inclusion of the string component iscritical in constraining parameters. In the most general model studied, whichincludes an inflaton mass term, as well as the brane–antibrane attraction, valuesns<1.02 are compatiblewith the data at 95% confidence level. We are also able to constrain the volume of the warped throat region(modulo factors dependent on the warp factor) and the value of the inflaton field to be<0.66MP at horizon exit. We also investigate models with a mass term.These observational considerations suggest that such models haver<2 × 10−5, whichcan only be circumvented in the fast roll regime, or by increasing the number of antibranes. Such a valueof r would not be detectable in any CMB polarization experiment likely in the near future, but theB-mode signal from the cosmic strings could be detectable. We present forecasts of what a similaranalysis using PLANCK data would yield and find that it should be possible to rule outGμ>6.5 × 10−8 usingjust the TT, TE and EE power spectra.

Is there a need and another way to measure the cosmic microwave background temperature more accurately?

The recombination history of the Universe depends exponentially on the temperature, T0, of the cosmic microwave background. Therefore tiny changes of T0 are expected to lead to significant changes in the free electron fraction. Here we show that even the current 1σ-uncertainty in the value of T0 results in more than half a percent ambiguity in the ionization history, and more than 0.1% uncertainty in the TT and EE power spectra at small angular scales. We discuss how the value of T0 affects the highly redshifted cosmological hydrogen recombination spectrum and demonstrate that T0 could, in principle, be measured by looking at the low frequency distortions of the cosmic microwave background spectrum. For this no absolute measurements are necessary, but sensitivities on the level of ∼30 nK are required to extract the quasi-periodic frequency-dependent signal with typical ∆ν/ν ∼ 0.1 coming from cosmological recombination. We also briefly mention the possibility of obtaining additional information on the specific entropy of the Universe, and other cosmological parameters.

Cosmological hydrogen recombination: Lynline feedback and continuum escape

We compute the corrections to the cosmological hydrogen recombination history due to delayed feedback of Lyman-series photons and the escape in the Lyman-continuum. The former process is expected to slightly delay recombination, while the latter should allow the medium to recombine a bit faster. It is shown that the subsequent feedback of released Lyman-n photons on the lower lying Lyman-(n-1) transitions yields a maximal correction of DN_e/N_e 0.22% at z~ 1050. Including only Lyman-\beta feedback onto the Lyman-\alpha transition, accounts for most of the effect. We find corrections to the cosmic microwave background TT and EE power spectra \change{with typical peak to peak amplitude |DC^{TT}_l/C^{TT}_l|~0.15% and |\Delta C^{EE}_l/C^{EE}_l|~0.36% at l<~3000. The escape in the Lyman-continuum and feedback of Lyman-\alpha photons on the photoionization rate of the second shell lead to modifications of the ionization history which are very small (less than |DN_e/N_e|~few x 10^{-6}).

Bianchi model CMB polarization and its implications for CMB anomalies

We derive the cosmic microwave background (CMB) radiative transfer equation in the form of a multipole hierarchy in the nearly Friedmann–Robertson–Walker limit of homogeneous, but anisotropic, universes classified via their Bianchi type. Compared with previous calculations, this allows a more sophisticated treatment of recombination, produces predictions for the polarization of the radiation and allows for reionization. Our derivation is independent of any assumptions about the dynamical behaviour of the field equations, except that it requires anisotropies to be small back to recombination; this is already demanded by observations. We calculate the polarization signal in the Bianchi VIIh case, with the parameters recently advocated to mimic the several large-angle anomalous features observed in the CMB. We find that the peak polarization signal is ∼1.2 μK for the best-fitting model to the temperature anisotropies, and is mostly confined to multipoles l < 10. Remarkably, the predicted large-angle EE and TE power spectra in the Bianchi model are consistent with Wilkinson Microwave Anisotropy Probe (WMAP) observations that are usually interpreted as evidence of early reionization. However, the power in B-mode polarization is predicted to be similar to the E-mode power and parity-violating correlations are also predicted by the model; the WMAP non-detection of either of these signals casts further strong doubts on the veracity of attempts to explain the large-angle anomalies with global anisotropy. On the other hand, given that there exist further dynamical degrees of freedom in the VIIh universes that are yet to be compared with CMB observations, we cannot at this time definitively reject the anisotropy explanation.

On the influence of resonant scattering on cosmic microwave background polarization anisotropies

We implement the theory of resonant scattering in the context of cosmic microwave background (CMB) polarization anisotropies. We compute the changes in the E-mode polarization (EE) and temperature E-mode (TE) CMB power spectra introduced by the scattering on a resonant transition with a given optical depth τ X and polarization coefficient E 1 . The latter parameter, accounting for how anisotropic the scattering is, depends on the exchange of angular momentum in the transition, enabling observational discrimination between different resonances. We use this formalism in two different scenarios: cosmological recombination and cosmological re-ionization. In the context of cosmological recombination, we compute predictions in frequency and multipole space for the change in the TE and EE power spectra introduced by scattering on the Ha and Pa lines of hydrogen. This constitutes a fundamental test of the standard model of recombination, and the sensitivity it requires is comparable to that needed in measuring the primordial CMB B-mode polarization component. In the context of re-ionization, we study the scattering off metals and ions produced by the first stars, and find that polarization anisotropies, apart from providing a consistency test for intensity measurements, give some insight on how re-ionization evolved. Since polarization anisotropies have memory of how anisotropic the line scattering is, they should be able to discern the O 163.2-μm transition from other possible transitions associated to O III, NII, NIII, etc. The amplitude of these signals are, however, between 10 and 100 times below the (already challenging) level of CMB B-mode polarization anisotropies.

MAXIPOL: Data Analysis and Results

We present results from and the analysis of data from MAXIPOL, a balloon-borne experiment designed to measure the polarization in the Cosmic Microwave Background (CMB). MAXIPOL is the first CMB experiment to obtain results using a rotating half-wave plate as a rapid polarization modulator. We report results from observations of a sky area of 8 deg^2 with 10-arcmin resolution, providing information up to l~700. We use a maximum-likelihood method to estimate maps of the Q and U Stokes parameters from the demodulated time streams, and then both Bayesian and frequentist approaches to compute the EE, EB, and BB power spectra. Detailed formalisms of the analyses are given. A variety of tests show no evidence for systematic errors. The Bayesian analysis gives weak evidence for an EE signal. The EE power is 55^{+51}_{-45} \mu K^2 at the 68% confidence level for l=151-693. Its likelihood function is asymmetric and skewed positive such that with a uniform prior the probability of a positive EE power is 96%. The powers of EB and BB signals at the 68% confidence level are 18^{+27}_{-34} \mu K^2 and -31^{+31}_{-19} \mu K^2 respectively and thus consistent with zero. The upper limit of the BB-mode at the 95% confidence level is 9.5 \mu K. Results from the frequentist approach are in agreement within statistical errors. These results are consistent with the current concordance LCDM model.

Implications of the Cosmic Background Imager Polarization Data

We present new measurements of the power spectra of the E-mode of CMB polarization, the temperature T, the cross-correlation of E and T, and upper limits on the B-mode from 2.5 years of dedicated Cosmic Background Imager (CBI) observations. Both raw maps and optimal signal images in the uv-plane and real space show strong detections of the E-mode (11.7 sigma for the EE power spectrum overall) and no detection of the B-mode. The power spectra are used to constrain parameters of the flat tilted adiabatic Lambda-CDM models: those determined from EE and TE bandpowers agree with those from TT, a powerful consistency check. There is little tolerance for shifting polarization peaks from the TT-forecast locations, as measured by the angular sound crossing scale theta = 100 ell_s = 1.03 +/- 0.02 from EE and TE cf. 1.044 +/- 0.005 with the TT data included. The scope for extra out-of-phase peaks from subdominant isocurvature modes is also curtailed. The EE and TE measurements of CBI, DASI and BOOMERANG are mutually consistent, and, taken together rather than singly, give enhanced leverage for these tests.