Cosmic Microwave Background Sky Research Articles

Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds

If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the amplitudes of Fourier modes of primordial scalar curvature perturbations. Topological boundary conditions replace the full set of Fourier modes with specific linear combinations of selected Fourier modes as the eigenmodes of the scalar Laplacian. We present formulas for eigenmodes in orientable Euclidean manifolds with the topologies E 1–E 6, E 11, E 12, E 16, and E 18 that encompass the full range of manifold parameters and observer positions, generalizing previous treatments. Under the assumption that the amplitudes of primordial scalar curvature eigenmodes are independent random variables, for each topology we obtain the correlation matrices of Fourier-mode amplitudes (of scalar fields linearly related to the scalar curvature) and the correlation matrices of spherical-harmonic coefficients of such fields sampled on a sphere, such as the temperature of the cosmic microwave background (CMB). We evaluate the detectability of these correlations given the cosmic variance of the observed CMB sky. We find that topologies where the distance to our nearest clone is less than about 1.2 times the diameter of the last scattering surface of the CMB give a correlation signal that is larger than cosmic variance noise in the CMB. This implies that if cosmic topology is the explanation of large-angle anomalies in the CMB, then the distance to our nearest clone is not much larger than the diameter of the last scattering surface. We argue that the topological information is likely to be better preserved in three-dimensional data, such as will eventually be available from large-scale structure surveys.

Spectro-spatial evolution of the CMB. Part III. Transfer functions, power spectra and Fisher forecasts

In this paper, we provide the first computations for the distortion transfer functions of the cosmic microwave background (CMB) in the perturbed Universe, following up on paper I and II in this series. We illustrate the physical effects inherent to the solutions, discussing and demonstrating various limiting cases for the perturbed photon spectrum. We clarify the relationship between distortion transfer functions and the photon spectrum itself, providing the machinery that can then compute constrainable CMB signal power spectra including spectral distortions for single energy injection and decaying particle scenarios. Our results show that the μ × T and y × T power spectra reach levels that can be constrained with current and future CMB experiments without violating existing constraints from COBE/FIRAS. The amplitude of the cross-correlation signal directly depends on the average distortion level, therefore establishing a novel fundamental link between the state of the primordial plasma from redshift 103 ≲ z ≲ 3 × 106 and the frequency-dependent CMB sky. This providesa new method to constrain average early energy release using CMB imagers. As an example we derive constraints on single energy release and decaying particle scenarios. This shows that LiteBIRD may be able to improve the energy release limits of COBE/FIRAS by up to a factor of ≃ 2.5, while PICO could tighten the constraints by more than one order of magnitude. The signals considered here could furthermore provide a significant challenge to reaching cosmic variance-limited constraints on primordial non-Gaussianity from distortion anisotropy studies. Our work further highlights the immense potential for a synergistic spectroscopic approach to future CMB measurements and analyses.

Unraveling the CMB lack-of-correlation anomaly with the cosmological gravitational wave background

Since the very first observations, the Cosmic Microwave Background (CMB) has revealed on large-scales unexpected features known as anomalies, which challenge the standard Λ cold dark matter (ΛCDM) cosmological model. One such anomaly is the “lack-of-correlation”, where the measured two-point angular correlation function of CMB temperature anisotropies is compatible with zero, differently from the predictions of the standard model. This anomaly could indicate a deviation from the standard model, unknown systematics, or simply a rare realization of the model itself. In this study, we explore the possibility that the lack-of-correlation anomaly is a consequence of living in a rare realization of the standard model, by leveraging the potential information provided by the cosmological gravitational wave background (CGWB) detectable by future gravitational wave (GW) interferometers. We analyze both constrained and unconstrained realizations of the CGWB to investigate the extent of information that GWs can offer. To quantify the impact of the CGWB on the lack-of-correlation anomaly, we employ established estimators and introduce a new estimator that addresses the “look-elsewhere” effect. Additionally, we consider three different maximum multipoles, denoted as ℓ max, to account for the anticipated capabilities of future GW detectors (ℓ max = 4, 6, 10). Summarizing our findings for the case of ℓ max = 4, we identify the angular range [63∘ - 180∘] as the region where future observations of the CGWB maximize the probability of rejecting the standard model. Furthermore, we calculate the expected significance of this observation, demonstrating that 98.81% (81.67%) of the constrained GW realizations enhance the current significance of the anomaly when considering the full-sky (masked) Planck SMICA map as our CMB sky.

Cosmic Microwave Background Recovery: A Graph-Based Bayesian Convolutional Network Approach

The cosmic microwave background (CMB) is a significant source of knowledge about the origin and evolution of our universe. However, observations of the CMB are contaminated by foreground emissions, obscuring the CMB signal and reducing its efficacy in constraining cosmological parameters. We employ deep learning as a data-driven approach to CMB cleaning from multi-frequency full-sky maps. In particular, we develop a graph-based Bayesian convolutional neural network based on the U-Net architecture that predicts cleaned CMB with pixel-wise uncertainty estimates. We demonstrate the potential of this technique on realistic simulated data based on the Planck mission. We show that our model ac- accurately recovers the cleaned CMB sky map and resulting angular power spectrum while identifying regions of uncertainty. Finally, we discuss the current challenges and the path forward for deploying our model for CMB recovery on real observations.

Searching for ring-like structures in the cosmic microwave background

ABSTRACTIn this research, we present an alternative methodology to search for ring-like structures in the sky with unusually large temperature gradients, namely, Hawking points (HPs), in the Cosmic Microwave Background (CMB), which are possible observational effects associated with Conformal Cyclic Cosmology (CCC). To assess the performance of our method, we constructed an artificial data set of HP, according to CCC, and we were able to retrieve $95 {{\ \rm per\ cent}}$ of ring-like anomalies from it. Furthermore, we scanned the Planck CMB sky map and compared it to simulations according to ΛCDM, where we applied robust statistical tests to assess the existence of HP. Even though no significant ring-like structures were observed, we report the largest excess of HP candidates found at α =1 per cent significance level for the analysed sky maps (CMB at 70GHz, SEVEM, SMICA, and Commander-Ruler), and we stress the need to continue the theoretical and experimental research in this direction.

Examining statistical isotropy of CMB low multipoles from Planck PR4 data

Low multipoles (l) in cosmic microwave background (CMB) temperature anisotropies have shown some ‘peculiarities’ when examined since the release of the full sky CMB maps, using a variety of tests. In this paper, we concern ourselves with the very first peculiarities seen in CMB data viz., a breakdown of statistical isotropy in the form of axiality and planarity of these low-l modes, and preferred alignments among them. We scrutinize the latest CMB data from ESA's Planck mission, PR4, to evaluate the current status of these deviations. We employ the Power tensor method which allows an invariant characterization of the distribution of power in a given multipole, and apply it to probe the first sixty multipoles i.e., l=2 to 61. We find that there are significant number of modes that are intrinsically anisotropic with a cumulative probability of 0.3%. However since the planarity study reveals that those modes that are unusually planar are subset of these anisotropic modes, we conclude that they may not be intrinsically planar. The quadrupole is still well aligned with the octopole. Besides, l=3, higher multipoles aligned with quadrupole are found to be insignificant. Interestingly, the collective alignment axis of the first sixty multipoles is found to be broadly closer to the axis of dipole, quadrupole, octopole and other modes aligned with l=2.

Consistency of Planck Data With Power-law Primordial Scalar Power Spectrum

Abstract In this work we explore the possibility of variations in the primordial scalar power spectrum around the power-law shape, as predicted by single-field slow-roll inflationary scenarios. We search for a trace of these fluctuations in a semiblind, model-independent way in observations of the cosmic microwave background (CMB) sky. In particular, we use two sets of perturbation patterns, specific patterns with typical features such as oscillations, bumps, and transitions, as well as perturbation modes, constructed from eigenanalysis of the forecasted or measured covariance of perturbation parameters. These modes, in principle, span the parameter space of all possible perturbations to the primordial spectrum and, when rank ordered, the ones with the highest detectability would suffice to explore the constrainable features around the power-law spectrum in a data-driven (and not theoretically biased) manner. With Planck measurements of CMB anisotropies, the amplitudes of all perturbation patterns considered in this work are found to be consistent with zero. This finding confirms, in the absence of theoretical biases, the consistency of the Planck data with the assumption of a power-law inflationary pattern for the primordial spectrum.

Determining our peculiar velocity from the aberration in the cosmic microwave background

ABSTRACT The motion of our Solar system relative to the cosmic microwave background (CMB) rest frame leads to subtle distortions in the observed CMB sky map due to the aberration effect. Usually the corresponding peculiar velocity is determined from the CMB dipole but neglecting intrinsic dipole contributions. Here, it is investigated whether certain invariant scalar measures, which are derived from first and second order covariant derivatives on the sphere, can detect the distortions caused by the aberration effect at high multipoles. This would in principle allow to disentangle the Doppler from intrinsic dipole contributions providing an independent method for the determination of our peculiar velocity. It is found that the eigenvalues of the Hessian matrix of the temperature field are well suited for that task.

Explaining cosmological anisotropy: evidence for causal horizons from CMB data

ABSTRACT The origin of power asymmetry and other measures of statistical anisotropy on the largest scales of the universe, as manifested in cosmic microwave background (CMB) and large-scale structure data, is a long-standing open question in cosmology. In this paper, we analyse the Planck Legacy temperature anisotropy data and find strong evidence for a violation of the Cosmological principle of isotropy, with a probability of being a statistical fluctuation of the order of ∼10−9. The detected anisotropy is related to large-scale directional ΛCDM cosmological parameter variations across the CMB sky, which are sourced by three distinct patches in the maps with circularly averaged sizes between 40° and 70° in radius. We discuss the robustness of our findings to different foreground separation methods and analysis choices, and find consistent results from WMAP data when limiting the analysis to the same scales. We argue that these well-defined regions within the cosmological parameter maps may reflect finite and casually disjoint horizons across the observable universe. In particular, we show that the observed relation between horizon size and mean dark energy density within a given horizon is in good agreement with expectations from a recently proposed model of the universe that explains cosmic acceleration and cosmological parameter tensions between the high- and low-redshift universe from the existence of casual horizons within our universe.

CMB Cold Spot in the Planck Light

Abstract The Cold Spot, with an unusually cold region surrounded by a hot ring, is a statistically significant anomaly in the cosmic microwave background (CMB) sky. In this work we assess whether different sets of multiple subvoids based on the 2dF-VST ATLAS Cold Spot galaxy redshift survey or a collapsing cosmic texture could have produced such an anomaly through a simultaneous search for their gravitational redshift and lensing signatures on the Planck CMB temperature anisotropies. We use patches with radii R = 10° and R = 20° to account for the inner cold region as well as the outer hot ring. As the void model, we explore two sets of ΛLTB templates characterized by different values of the model’s free parameters, and a top-hat void template. We detect higher than expected gravitational redshift amplitudes for the first two sets, and , and lower than expected for the top-hat model, . The amplitudes for the lensing imprint are consistent with zero for all these subvoid models. The estimated amplitude for the texture imprint from the gravitational redshift measurement implies the energy scale of the texture, parameterized by ϵ, to be ϵ = (7.6 ± 2.0) × 10−5, with no detection of the lensing trace. We note that the deviation of the subvoid amplitudes from unity and the inability of the texture and some of the void profiles to reproduce the hot ring indicate theoretical insufficiencies, either in the construction of the model or in the assumed gravitational and cosmological framework leading to the imprints for the structures.

Parity in Planck full-mission CMB temperature maps

In the standard model of cosmology, Cosmic Microwave Background (CMB) sky is expected to preserve spatial symmetries. Following our previous studies, we search for evidence of a parity preference in the latest full-mission CMB temperature maps from ESA’s Planck probe. Specifically, we probe (a)symmetry in power between even and odd multipoles of CMB, that corresponds to a particular parity preference under inversion, in Planck 2015 angular power spectrum measurements. We also assess any specific preference for mirror parity (a)symmetry, by analysing the power contained in l+m=even or odd mode combinations.

Minimizing gravitational lensing contributions to the primordial bispectrum covariance

The next generation of ground-based CMB experiments aim to measure temperature and polarization fluctuations up to $\ell_{\rm max} \approx 5000$ over half of the sky. Combined with Planck data on large scales, this will provide improved constraints on primordial non-Gaussianity. However, the impressive resolution of these experiments will come at a price. Besides signal confusion from galactic foregrounds, extra-galactic foregrounds and late-time gravitational effects, gravitational lensing will introduce large non-Gaussianity that can become the leading contribution to the bispectrum covariance through the connected 4-point function. Here, we compute this effect analytically for the first time on the full sky for both temperature and polarization. We compare our analytical results with those obtained directly from map-based simulations of the CMB sky for several levels of instrumental noise. Of the standard shapes considered in the literature, the local shape is most affected, resulting in a 35\% increase of the estimator standard deviation for an experiment like the Simons Observatory (SO) and a 110\% increase for a cosmic-variance limited experiment, including both temperature and polarization modes up to $\ell_{\rm max} = 3800$. Because of the nature of the lensing 4-point function, the impact on other shapes is reduced while still non negligible for the orthogonal shape. Two possible avenues to reduce the non-Gaussian contribution to the covariance are proposed. First by marginalizing over lensing contributions, such as the ISW-lensing 3pt function in temperature, and second by delensing the CMB. We show the latter method can remove almost all extra covariance, reducing the effect to below $<$5\% for local bispectra. At the same time, delensing would remove signal biases from secondaries induced by lensing, such as ISW-lensing.

Apparent evidence for Hawking points in the CMB Sky★

ABSTRACT This paper presents strong observational evidence of numerous previously unobserved anomalous circular spots, of significantly raised temperature, in the cosmic microwave background sky. The spots have angular radii between 0.03 and 0.04 rad (i.e. angular diameters between about 3° and 4°). There is a clear cut-off at that size, indicating that each anomalous spot would have originated from a highly energetic point-like source, located at the end of inflation – or else point-like at the conformally expanded Big Bang, if it is considered that there was no inflationary phase. The significant presence of these anomalous spots, was initially noticed in the Planck 70 GHz satellite data by comparison with 1000 standard simulations, and then confirmed by extending the comparison to 10 000 simulations. Such anomalous points were then found at precisely the same locations in the WMAP (Wilkinson Microwave Anisotropy Probe) data, their significance was confirmed by comparison with 1000 WMAP simulations. Planck and WMAP have very different noise properties and it seems exceedingly unlikely that the observed presence of anomalous points in the same directions on both maps may come entirely from the noise. Subsequently, further confirmation was found in the Planck data by comparison with 1000 FFP8.1 MC simulations (with l ≤ 1500). The existence of such anomalous regions, resulting from point-like sources at the conformally stretched-out big bang, is a predicted consequence of conformal cyclic cosmology, these sources being the Hawking points of the theory, resulting from the Hawking radiation from supermassive black holes in a cosmic aeon prior to our own.

Likelihood Methods for CMB Experiments

A great deal of experimental effort is currently being devoted to the precise measurements of the cosmic microwave background (CMB) sky in temperature and polarisation. Satellites, balloon-borne, and ground-based experiments scrutinize the CMB sky at multiple scales, and therefore enable to investigate not only the evolution of the early Universe, but also its late-time physics with unprecedented accuracy. The pipeline leading from time ordered data as collected by the instrument to the final product is highly structured. Moreover, it has also to provide accurate estimates of statistical and systematic uncertainties connected to the specific experiment. In this paper, we review likelihood approaches targeted to the analysis of the CMB signal at different scales, and to the estimation of key cosmological parameters. We consider methods that analyze the data in the spatial (i.e., pixel-based) or harmonic domain. We highlight the most relevant aspects of each approach and compare their performance.

Sitoolbox: A package for Bayesian estimation of the isotropy violation in the CMB sky

ABSTRACT The standard model of cosmology predicts a statistically isotropic (SI) cosmic microwave background (CMB) sky. However, the SI violation signals are always present in an observed sky-map. Different cosmological artefacts, measurement effects, and unavoidable effects during data analysis, etc. may lead to isotropy violation in an otherwise SI sky. Therefore, a proper data analysis technique should calculate all these SI violation signals, so that they can be matched with SI violation signals from the known sources, and then conclude if there is any intrinsic SI violation in the CMB sky. In one of our recent works, we presented a general Bayesian formalism for measuring the isotropy violation signals in the CMB sky in the presence of an idealized isotropic noise. In this paper, we have extended the mechanism and develop a software package, sitoolbox, for measuring SI violation in presence of anisotropic noise and masking.

Constraints on non-resonant photon-axion conversion from the Planck satellite data

The non-resonant conversion of Cosmic Microwave Background (CMB) photons into scalar as well as light pseudoscalar particles such as axion-like particles (ALPs) in the presence of turbulent magnetic fields can cause a unique, spatially fluctuating spectral distortion in the CMB. We use the publicly available Planck temperature maps for the frequency channels (70–545 GHz) to obtain the first ALP distortion map using 45% clean part of the sky. The 95th percentile upper limit on the RMS fluctuation of ALP distortions from the cleanest part of the CMB sky at 15 arcmin angular resolution is 18.5 × 10−6. The RMS fluctuation in the distortion map is also consistent with different combinations of frequency channels and sky-fractions.

Real-space computation of E/B-mode maps. Part I. Formalism, compact kernels, and polarized filaments

We derive full-sky, real-space operators that convert between polarization Stokes Q/U parameters and the coordinate-independent scalar E/B modes that are widely used in Cosmic Microwave Background (CMB) and cosmic shear analysis. We also derive real space operators that decompose the measured Stokes parameters into those corresponding to E-modes and B-modes respectively, without ever evaluating the scalar fields themselves. We cast the standard CMB polarization analysis operators in a matrix-vector notation which elucidates these derivations. For all these real space operators we show that the kernels split naturally into angular and radial parts and we show explicitly how the radial extent of these kernels depends on the targeted band-limit. We show that the kernels can be interpreted either as a complex convolving beam or as a Green's function when they are expressed in terms of the forward or inverse rotation Euler angles. We show that an arbitrary radial function can produce E/B-like maps, provided it vanishes at the origin and the antipodal point. These maps are simply filtered versions of the standard E/B maps. We can recover the standard power spectrum of the polarized CMB sky by correcting the power spectra of these maps with a simple window function, which we show how to derive for any radial dependence. For these reasons we can compute E/B maps in real space with a compactly-supported kernel, an approach that can guarantee the avoidance of known foreground regions and could be employed in a massively-parallel scheme at high-resolution. We show that the spin raising and lowering operators ð2/ð2 are special cases of these generalized radial functions, and present their band limited versions. The spatial structure of the real space operators provides great intuition for the E/B structure of polarized, filamentary galactic foregrounds. We predict a non-zero B-mode signature that is expected from polarized filaments in the sky. This paper is the first part in a series of papers that explore real-space computation of polarization modes and their applications.

Cosmological zero modes

We introduce a new family of primordial cosmological perturbations that are not described by traditional power spectra. At the linear level, these perturbations live in the kernel of the spatial Laplacian operator, and thus we call them cosmological zero modes. We compute the cosmic microwave background (CMB) temperature and polarization anisotropy induced by these modes, and forecast their detection sensitivity using a cosmic-variance limited experiment. In particular, we consider two configurations for the zero modes: The first configuration consists of stochastic metric perturbations described by white noise on a "holographic screen" located at our cosmological horizon. The amplitude of the power spectrum of this white noise can be constrained to be $\lesssim 9 \times 10^{-14}$. The second configuration is a primordial monopole beyond our cosmological horizon. We show that such a monopole, with "charge" $Q$, can be detected in the CMB sky up to a distance of $11.6 ~ Q^{1/4}\times$ horizon radius (or $160~ Q^{1/4}$ Gpc). More generally, observational probes of cosmological zero modes can shed light on non-perturbative phenomena in the primordial universe, beyond our observable horizon.

Alignments of parity even/odd-only multipoles in CMB

We compare the statistics of parity even and odd multipoles of the cosmic microwave background (CMB) sky from PLANCK full mission temperature measurements. An excess power in odd multipoles compared to even multipoles has previously been found on large angular scales. Motivated by this apparent parity asymmetry, we evaluate directional statistics associated with even compared to odd multipoles, along with their significances. Primary tools are the \emph{Power Tensor} and \emph{Alignment Tensor} statistics. We limit our analysis to the first sixty multipoles i.e., $l=[2,61]$. We find no evidence for statistically unusual alignments of even parity multipoles. More than one independent statistic finds evidence for alignments of anisotropy axes of odd multipoles, with a significance equivalent to $\sim 2 \sigma$ or more. The robustness of alignment axes is tested by making galactic cuts and varying the multipole range. Very interestingly, the region spanned by the (a)symmetry axes is found to broadly contain other parity (a)symmetry axes previously observed in the literature.

Red, Straight, no bends: primordial power spectrum reconstruction from CMB and large-scale structure

We present a minimally parametric, model independent reconstruction of the shape of the primordial power spectrum. Our smoothing spline technique is well-suited to search for smooth features such as deviations from scale invariance, and deviations from a power law such as running of the spectral index or small-scale power suppression. We use a comprehensive set of the state-of the art cosmological data: Planck observations of the temperature and polarisation anisotropies of the cosmic microwave background, WiggleZ and Sloan Digital Sky Survey Data Release 7 galaxy power spectra and the Canada-France-Hawaii Lensing Survey correlation function. This reconstruction strongly supports the evidence for a power law primordial power spectrum with a red tilt and disfavours deviations from a power law power spectrum including small-scale power suppression such as that induced by significantly massive neutrinos. This offers a powerful confirmation of the inflationary paradigm, justifying the adoption of the inflationary prior in cosmological analyses.