Cosmic Microwave Background Angular Power Spectrum Research Articles

Impact of half-wave plate systematics on the measurement of cosmic birefringence from CMB polarization

Polarization of the cosmic microwave background (CMB) can probe new parity-violating physics such as cosmic birefringence (CB), which requires exquisite control over instrumental systematics. The non-idealities of the half-wave plate (HWP) represent a source of systematics when used as a polarization modulator. We study their impact on the CMB angular power spectra, which is partially degenerate with CB and miscalibration of the polarization angle. We use full-sky beam convolution simulations including HWP to generate mock noiseless time-ordered data, process them through a bin averaging map-maker, and calculate the power spectra including TB and EB correlations. We also derive analytical formulae which accurately model the observed spectra. For our choice of HWP parameters, the HWP-induced angle amounts to a few degrees, which could be misinterpreted as CB. Accurate knowledge of the HWP is required to mitigate this. Our simulation and analytical formulae will be useful for deriving requirements for the accuracy of HWP calibration.

Estimation of the Full-sky Power Spectrum between Intermediate and Large Angular Scales from Partial-sky CMB Anisotropies Using an Artificial Neural Network

Reliable extraction of cosmological information from observed cosmic microwave background (CMB) maps may require removal of strongly foreground-contaminated regions from the analysis. In this paper, we employ an artificial neural network (ANN) to predict the full-sky CMB angular power spectrum between intermediate and large angular scales from the partial-sky spectrum obtained from a masked CMB temperature anisotropy map. We use a simple ANN architecture with one hidden layer containing 895 neurons. Using 1.2 × 105 training samples of full-sky and corresponding partial-sky CMB angular power spectra at HEALPix pixel resolution parameter N side = 256, we show that the spectrum predicted by our ANN agrees well with the target spectrum at each realization for the multipole range 2 ≤ l ≤ 512. The predicted spectra are statistically unbiased, and they preserve the cosmic variance accurately. Statistically, the differences between the mean predicted and underlying theoretical spectra are within approximately 3σ. Moreover, the probability densities obtained from predicted angular power spectra agree very well with those obtained from “actual” full-sky CMB angular power spectra for each multipole. Interestingly, our work shows that the significant correlations in input cut-sky spectra due to mode–mode coupling introduced on the partial sky are effectively removed, since the ANN learns the hidden pattern between the partial- and full-sky spectra preserving all of the statistical properties. The excellent agreement of statistical properties between the predicted and the ground truth demonstrates the importance of using artificial intelligence systems in cosmological analysis more widely.

The non-thermal secondary CMB anisotropies from a cosmic distribution of radio galaxy lobes

ABSTRACT Current and upcoming high angular resolution and multifrequency experiments are well poised to explore the rich landscape of secondary cosmic microwave background (CMB) anisotropies. In this context, we compute, for the first time, the power spectrum of CMB fluctuations from a cosmological distribution of evolving lobes of giant radio galaxies. We also explicitly take into account the non-thermal electron distribution, which has important implications for the inference of the CMB angular power spectrum. We calculate the mean global non-thermal y-distortion, 〈y〉NT. For observationally reasonable distribution of the jet luminosities in the range of 1045–1047 erg s−1, we find 〈y〉NT to be less than 10−5, and hence not violating the cosmic background explorer limit as previously claimed. Using the unique spectral dependence of the non-thermal Sunyaev–Zeldovich (SZ), we show that a detection of 〈y〉NT can be within reach at the level of ≳5σ from a future Primordial Inflation Explorer (PIXIE)-like experiment provided we understand the foregrounds precisely. The total non-thermal SZ power spectrum, $C^{\mathrm{ NT}}_\ell$, from the radio lobes peaks at ℓ ∼ 3000 with an amplitude $\sim 1{{\ \rm per\ cent}}$ of thermal SZ power spectrum from galaxy clusters. A detection of the $C^{\mathrm{ NT}}_\ell$, with a PIXIE-like sensitivity experiment, can lead to ∼5σ constraint on the mass dependence of the jet luminosity with the constraint becoming at least ten times better for the proposed more ambitious CMB-HD survey. This will further lead to the tightest constraint on the central black hole mass-to-host halo mass scaling relations.

Primordial non-gaussianities of inflationary step-like models

We use Minkowski Functionals (MF) to explore the possible presence of non-Gaussian signatures in the recently released cosmic microwave background (CMB) Planck maps. In particular, we investigate MF outcomes for two sets of simulated CMB maps: one seeded by the ΛCDM concordance model, another seeded by the ‘best-fit’ CMB angular power spectrum. By ‘best-fit’ we mean a simulated CMB spectrum seeded by an inflationary model that well reproduce the observed low-ℓ features of the CMB temperature power spectrum. In this way, we obtain the spurious signal introduced by the power spectra with different shapes, signal to be taken into account in the corresponding MF analyses. Interestingly, we investigate the response of the four MF (i.e., Area, Perimeter, Genus, Nclusters ) for several sets of simulated maps. Our analyses confirm that, as already reported in the literature, the Perimeter exhibits the best performance. Moreover, our results show that the Perimeter obtained from the Planck maps (2015) is better fitted by the simulated CMB maps seeded by the angular power spectrum with low-ℓ features with respect to the curves obtained from the CMB maps seeded by the ΛCDM model.

A Partial-sky Gibbs ILC Approach for the Estimation of CMB Posterior over Large Angular Scales of the Sky

In this article we present a formalism for incorporating the partial-sky maps into the Gibbs ILC algorithm to estimate the joint posterior density of the cosmic microwave background (CMB) signal and the theoretical CMB angular power spectrum given the observed CMB maps. In order to generate the partial-sky maps, we mask all the observed CMB maps provided by the WMAP and Planck satellite full-sky mission using a mask that removes 22% of the entire sky. The mask we use is based on the strength of the thermal dust emissions in the Planck 353 GHz map. While implementing the Gibbs ILC method on the partial-sky maps, we convert the partial-sky-cleaned angular power spectrum into the full-sky angular power spectrum using the mode-mode coupling matrix estimated from the smoothed mask. The main products of our analysis are a partial-sky cleaned best-fit CMB map and an estimate of the underlying full-sky theoretical CMB angular power spectrum in the multipole range 2 ≤ ℓ ≤ 32 along with their error estimates. We validate the method by performing detailed Monte Carlo simulations after using realistic models of foregrounds and detector noise consistent with the WMAP and Planck frequency channels used in our analysis. We can estimate the posterior density and full-sky theoretical CMB angular power spectrum without any need to explicitly model the foreground components from partial-sky maps using our method. Another important feature of this method is that the power spectrum results along with the error estimates can be directly used for cosmological parameter estimations.

Fluctuations in the Ginzburg–Landau Theory of Dark Energy: Internal (In)consistencies in the Planck Data Set

In this work, predictions of the Ginzburg–Landau theory of dark energy (GLT) for cosmic microwave background (CMB) lensing are studied. We find that the time and scale dependence of the dark energy fluctuations in this semiphenomenological model is favored by data in several ways. First, unlike ΛCDM, ℓ ≤ 801 and ℓ > 801 ranges of the CMB angular power spectrum are consistent in this framework. Second, the lensing amplitude A L is completely consistent with unity when GLT is confronted with CMB data, even without including CMB lensing data. Therefore the lensing anomaly is absent in this model. Although the background evolution of dark energy in this model is able to reconcile the H 0 inferred from CMB with that directly measured through observing nearby standard candles, the inclusion of Baryon Acoustic Oscillations (BAO) data brings the inferred H 0 close to what ΛCDM predicts and hence the Hubble tension is not fully eased. However, this does not affect the posterior on A L and the lensing anomaly is still absent.

A Simulation-based Method for Correcting Mode Coupling in CMB Angular Power Spectra

Abstract Modern cosmic microwave background (CMB) analysis pipelines regularly employ complex time-domain filters, beam models, masking, and other techniques during the production of sky maps and their corresponding angular power spectra. However, these processes can generate couplings between multipoles from the same spectrum and from different spectra, in addition to the typical power attenuation. Within the context of pseudo-C ℓ based, MASTER-style analyses, the net effect of the time-domain filtering is commonly approximated by a multiplicative transfer function, F ℓ , that can fail to capture mode mixing and is dependent on the spectrum of the signal. To address these shortcomings, we have developed a simulation-based spectral correction approach that constructs a two-dimensional transfer matrix, J ℓ ℓ ′ , which contains information about mode mixing in addition to mode attenuation. We demonstrate the application of this approach on data from the first flight of the Spider balloon-borne CMB experiment.

An unbiased estimator of the full-sky CMB angular power spectrum at large scales using neural networks

ABSTRACT Accurate estimation of the cosmic microwave background (CMB) angular power spectrum is enticing due to the prospect for precision cosmology it presents. Galactic foreground emissions, however, contaminate the CMB signal and need to be subtracted reliably in order to lessen systematic errors on the CMB temperature estimates. Typically, bright foregrounds in a region lead to further uncertainty in temperature estimates in the area even after some foreground removal technique is performed and hence determining the underlying full-sky angular power spectrum poses a challenge. We explore the feasibility of utilizing artificial neural networks to predict the angular power spectrum of the full-sky CMB temperature maps from the observed angular power spectrum of the partial sky in which CMB temperatures in some bright foreground regions are masked. We present our analysis at large angular scales with two different masks. We produce unbiased predictions of the full-sky angular power spectrum and recover the underlying theoretical power spectrum using neural networks. Our predictions are also uncorrelated to a large extent. We further show that the multipole-space covariances of the predictions of full-sky spectra made by the artificial neural networks are much smaller than those of the estimates obtained using the pseudo-Cℓ method.

CMB anisotropies generated by cosmic string loops

We investigate the contribution of cosmic string loops to the cosmic microwave background (CMB) anisotropies. This is done by extending the unconnected segment model (USM) to include the contribution of the cosmic string loops created throughout the cosmological evolution of a cosmic string network to the stress-energy tensor. We then implement this extended USM in the publicly available CMBACT code and obtain the linear cold dark matter power spectrum and the CMB angular power spectra generated by cosmic string loops. We find that the shape of the angular power spectra generated by loops is, in general, similar to that of long strings. However, there is generally an enhancement of the anisotropies on small angular scales. Vector modes produced by loops dominate over those produced by long strings for large multipole moments $\ensuremath{\ell}$. The contribution of loops to the CMB anisotropies generated by cosmic string networks may reach a level of 10% for large loops but decreases as the size of loops decreases. This contribution may then be significant and, thus, this extension provides a more accurate prediction of the CMB anisotropies generated by cosmic string networks.

Nonthermal hot dark matter from inflaton or moduli decay: Momentum distribution and relaxation of the cosmological mass bound

Decay of the inflaton or moduli which dominated the energy density of the universe at early times leads to a matter to radiation transition epoch. We consider non-thermal sterile dark matter particles produced as decay product during such transitions. The particles have a characteristic energy distribution - that associated with decays taking place in a matter dominated universe evolving to radiation domination. We primarily focus on the case when the particles are hot dark matter, and study their effects on the Cosmic Microwave Background (CMB) and Large Scale Structure (LSS), explicitly taking into account their non-thermal momentum distribution. Our results for CMB angular power and linear matter power spectra reveal interesting features - such as an order of magnitude higher values of hot dark matter mass in comparison to the thermal case being consistent with the present data. We observe that this is related to the fact that $\Delta N_{\rm eff}$ and the hot DM energy density can be independent of each other unlike the case of thermal or non-resonantly produced sterile hot DM. We also find features in the CMB at low $\ell$ angular power potentially related to supersonic transmission of hot dark matter through the photon-baryon plasma.

An accurate reconstruction of CMB E-mode signal over large angular scales using prior information of CMB covariance matrix in ILC algorithm

ABSTRACT Recently, the internal-linear-combination (ILC) method was investigated extensively in the context of reconstruction of Cosmic Microwave Background (CMB) temperature anisotropy signal using observations obtained by WMAP and Planck satellite missions. In this article, we, for the first time, apply the ILC method to reconstruct the large-scale CMB E mode polarization signal, which could probe the ionization history, using simulated observations of 15 frequency CMB polarization maps of future generation Cosmic Origin Explorer (COrE) satellite mission. We find that the clean power spectra, from the usual ILC, are strongly biased due to non-zero CMB-foregrounds chance correlations. In order to address the issues of bias and errors we extend and improve the usual ILC method for CMB E-mode reconstruction by incorporating prior information of theoretical E-mode angular power spectrum while estimating the weights for linear combination of input maps (Sudevan & Saha 2018b). Using the E-mode covariance matrix effectively suppresses the CMB-foreground chance correlation power leading to an accurate reconstruction of cleaned CMB E-mode map and its angular power spectrum. We compare the performance of the usual ILC and the new method over large angular scales and show that the later produces significantly statistically improved results than the former. The new E-mode CMB angular power spectrum contains neither any significant negative bias at the low multipoles nor any positive foreground bias at relatively higher mutltipoles. The error estimates of the cleaned spectrum agree very well with the cosmic variance induced error.

On the Impact of Random Residual Calibration Error on the Gibbs ILC CMB Estimates over Large Angular Scales

Abstract Residual errors in calibration coefficients corresponding to observed cosmic microwave background (CMB) maps are an important issue when estimating a pure CMB signal. These errors in the input-foreground-contaminated CMB maps, if not properly taken into account in a component separation method, may lead to bias in the cleaned CMB map and estimated CMB angular power spectrum. But the inability to exactly determine the calibration coefficients corresponding to each observed CMB map from a multifrequency CMB experiment makes it very difficult to incorporate their exact and actual values during the component separation method. Hence, the effect of any random and residual calibration error in the cleaned CMB map and its angular power spectrum of a component separation problem can only be understood by performing detailed Monte Carlo simulations. In this paper, we investigate the impact of using input-observed CMB maps with random calibration errors on the posterior density of a cleaned CMB map and theoretical CMB angular power spectrum over large angular scales of the sky following the Gibbs Internal-Linear-Combination (ILC) method. By performing detailed Monte Carlo simulations of WMAP and Planck temperature anisotropy observations, including their estimate on calibration errors, we show that the best-fit map corresponding to the posterior maximum is minimally biased in the Gibbs ILC method by a CMB normalization bias and residual foreground bias. The residual calibration-induced error in the best-fit power spectrum causes an overall 6% increase of the net error when added in quadrature with the cosmic-variance-induced error.

A fast and accurate algorithm for spherical harmonic analysis on HEALPix grids with applications to the cosmic microwave background radiation

The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) scheme is used extensively in astrophysics for data collection and analysis on the sphere. The scheme was originally designed for studying the Cosmic Microwave Background (CMB) radiation, which represents the first light to travel during the early stages of the universe's development and gives the strongest evidence for the Big Bang theory to date. Refined analysis of the CMB angular power spectrum can lead to revolutionary developments in understanding the nature of dark matter and dark energy. In this paper, we present a new method for performing spherical harmonic analysis for HEALPix data, which is a central component to computing and analyzing the angular power spectrum of the massive CMB data sets. The method uses a novel combination of a non-uniform fast Fourier transform, the double Fourier sphere method, and Slevinsky's fast spherical harmonic transform [38]. For a HEALPix grid with N pixels (points), the computational complexity of the method is O(Nlog2⁡N), with an initial set-up cost of O(N3/2log⁡N). This compares favorably with O(N3/2) runtime complexity of the current methods available in the HEALPix software when multiple maps need to be analyzed at the same time. Using numerical experiments, we demonstrate that the new method also appears to provide better accuracy over the entire angular power spectrum of synthetic data when compared to the current methods, with a convergence rate at least two times higher.

Principal component analysis of the primordial tensor power spectrum

We study how the shape of the spectrum of primordial gravitational waves can be constrained by future experiments looking at the B-mode of the Cosmic Microwave Background (CMB) polarization. We implement a Principal Component Analysis (PCA) including the effects of diffuse foreground residuals, following component separation, in the uncertainty of CMB angular power spectra, and taking into account the gravitational lensing by Large Scale Structure. We perform our study by considering the capabilities of future B-mode CMB experiments such as LiteBIRD, the Simons Observatory (SO) and Stage-IV (CMB-S4), in particular in detecting deviations of the primordial tensor spectrum from the scale-invariant behavior. We find that diffuse foreground residuals impact substantially both the derivation of the PCA basis and the corresponding constraining power, in all cases. In particular, depending on which experimental specifications and which value r of tensor-to-scalar ratio for cosmological perturbations are considered, adding foregrounds residuals can determine an increase as large as a factor ∼ 4 both on the uncertainty on r and on the recovery of the PCA modes. We study the limitations of the methodology, including the effect of physicality priors on the PCA, which we quantify via a Monte Carlo Markov chain (MCMC) analysis of the combined cosmological and PCA power spectrum parameter space.

The CMB angular power spectrum via component separation: a study on Planck data

Aims. We investigate the extent to which foreground-cleaned cosmic microwave background (CMB) maps can be used to estimate cosmological parameters at small scales. Methods. We use the SMICA method, a blind separation technique that works directly at the spectral level. In this work we focus on the small scales of the CMB angular power spectrum, which are chiefly affected by noise and extragalactic foregrounds, such as point sources. We adapt SMICA to use only cross-spectra between data maps, thus avoiding the noise bias. In this study, performed using both simulations and Planck 2015 data, we fit for extragalactic point sources by modelling them as shot noise of two independent populations. Results. In simulations, we correctly recover the point-source emission law, and obtain a CMB angular power spectrum that has an average foreground residual of one fifth of the CMB power at ℓ ≥ 2200. With Planck data, the recovered point-source emission law corresponds to external estimates, with some offsets at the highest and lowest frequencies, possibly due to frequency decoherence of point sources. The CMB angular power spectrum residuals are consistent with what we find in simulations. The cosmological parameters obtained from the simulations and the data show offsets up to 1σ on average from their expected values. Biases on cosmological parameters in simulations represent the expected level of bias in Planck data. Conclusions. The results on cosmological parameters depend on the detail of the foreground residual contamination in the spectrum, and therefore a tailored modelling of the likelihood foreground model is required.

Finsler space–time can explain both parity asymmetry and power deficit seen in CMB temperature anisotropies

We propose a framework of Finsler space-time to explain the observed parity asymmetry and the power deficit in the low-$\ell$ ($2\leqslant \ell \leqslant 29$) multipole range of cosmic microwave background (CMB) temperature anisotropies. In the $3+1$ dimensional space-time, the three-dimensional space is described by a Randers-Finsler space, which is spatially irreversible, inducing the parity asymmetry in the CMB angular power spectrum. We estimate the constraints on the two parameters introduced by Finsler space-time via analyzing the low-$\ell$ angular power spectrum in PLANCK 2015 CMB temperature data. We see that the low-$\ell$ power suppression in the CMB temperature anisotropies can also be resolved in this scenario. Our study shows that the two low-$\ell$ anomalies, i.e., parity asymmetry and power deficit, may have a common origin.

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 < 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.

Integrated Sachs-Wolfe map reconstruction in the presence of systematic errors

The decay of gravitational potentials in the presence of dark energy leads to an additional, late-time contribution to anisotropies in the cosmic microwave background (CMB) at large angular scales. The imprint of this so-called integrated Sachs-Wolfe (ISW) effect to the CMB angular power spectrum has been detected and studied in detail, but reconstructing its spatial contributions to the CMB $\textit{map}$, which would offer the tantalizing possibility of separating the early- from the late-time contributions to CMB temperature fluctuations, is more challenging. Here we study the technique for reconstructing the ISW map based on information from galaxy surveys and focus in particular on how its accuracy is impacted by the presence of photometric calibration errors in input galaxy maps, which were previously found to be a dominant contaminant for ISW signal estimation. We find that both including tomographic information from a single survey and using data from multiple, complementary galaxy surveys improve the reconstruction by effectively self-calibrating the estimator against spurious power contributions from calibration errors. A high-fidelity reconstruction further requires one to account for the contribution of calibration errors to the observed galaxy power spectrum in the model used to construct the ISW estimator. We find that if the photometric calibration errors in galaxy surveys can be independently controlled at the level required to obtain unbiased dark energy constraints, then it is possible to reconstruct ISW maps with excellent accuracy using a combination of maps from two galaxy surveys with properties similar to Euclid and SPHEREx.

SU(2) Yang-Mills thermodynamics: A priori estimate and radiative corrections

We review and explain essential characteristics of the a priori estimate of the thermal ground state and its excitations in the deconfining phase of SU(2) Quantum Yang-Mills thermodynamics. This includes the spatially central and peripheral structure of Harrington-Shepard (anti)calorons, a sketch on how a spatial coarse-graining over (anti)caloron centers yields an inert scalar field, which is responsible for an adjoint Higgs mechanism, the identification of (anti)caloron action with ħ, a discussion of how, owing to (anti)caloron structure, the thermal ground state can be excited (wave-like and particlelike massless modes, massive thermal quasiparticle fluctuations), the principle role of and accounting for radiative corrections, the exclusion of energy-sign combinations due to constraints on momenta transfers in four-vertices in a completely fixed, physical gauge, dihedral diagrams and their resummation up to infinite loop order in the massive sector, and the resummation of the one-loop polarisation tensor of the massless modes. We also outline applications of deconfining SU(2) Yang-Mills thermodynamics to the Cosmic Microwave Background (CMB) which affect the cosmological model at high redshifts, the redshift for re-ionization of the Universe, the CMB angular power spectra at low l, and the late-time emergence of intergalactic magnetic fields.

CMB anisotropies from patchy reionisation and diffuse Sunyaev-Zel'dovich effects

Anisotropies in the Cosmic Microwave Background (CMB) can be induced during the later stages of cosmic evolution, and in particular during and after the Epoch of Reionisation. Inhomogeneities in the ionised fraction, but also in the baryon density, in the velocity fields and in the gravitational potentials are expected to generate correlated CMB perturbations. We present a complete relativistic treatment of all these effects, up to second order in perturbation theory, that we solve using the numerical Boltzmann code {\\SONG}. The physical origin and relevance of all second order terms are carefully discussed. In addition to collisional and gravitational contributions, we identify the diffuse analogue of the blurring and kinetic Sunyaev-Zel'dovich (SZ) effects. Our approach naturally includes the correlations between the imprint from patchy reionisation and the diffuse SZ effects thereby allowing us to derive reliable estimates of the induced temperature and polarisation CMB angular power spectra. In particular, we show that the B-modes generated at intermediate length-scales (ℓ ≃ 100) have the same amplitude as the B-modes coming from primordial gravitational waves with a tensor-to-scalar ratio r=10−4.