Microwave Background Temperature Fluctuations Research Articles

Optimal estimation of the binned mask-free power spectrum, bispectrum, and trispectrum on the full sky: Scalar edition

We derive optimal estimators for the two-, three-, and four-point correlators of statistically isotropic scalar fields defined on the sphere, such as the cosmic microwave background temperature fluctuations, allowing for arbitrary (linear) masking and inpainting schemes. In each case, we give the optimal unwindowed estimator (obtained via a maximum-likelihood prescription, with an associated Fisher deconvolution matrix), and an idealized form, and pay close attention to their efficient computation. For the trispectrum, we include both parity-even and parity-odd contributions, as allowed by symmetry. The estimators can include arbitrary weighting of the data (and remain unbiased), but are shown to be optimal in the limit of inverse-covariance weighting and Gaussian statistics. The normalization of the estimators is computed via Monte Carlo methods, with the rate-limiting steps (involving spherical harmonic transforms) scaling linearly with the number of bins. An accompanying code package, polybin, implements these estimators in python, and we demonstrate the estimators' efficacy via a suite of validation tests.

Null geodesic congruences, gravitational lensing and CMB intensity profile

It is known that the Cosmic Microwave Background (CMB) temperature fluctuations are modified by gravitational lensing since the angular positions of photons are altered by the metric perturbations. We reconsider this effect in the context of geodesic deviation on a perturbed Friedmann-Robertson-Walker (FRW) spacetime with scalar and tensor modes. We first give an alternative derivation of the Sachs-Wolfe effect by using the solutions of the null geodesic equation. Then, we determine the two-dimensional induced metric on the transverse cross section of the null geodesic congruence corresponding to a beam of photons after decoupling. This metric, whose variation along the congruence can be decomposed as expansion and shear, is shown to produce a nontrivial intensity profile which can be characterized by three variables analogous to the Stokes parameters of the polarization tensor.

Exploring suppressed long-distance correlations as the cause of suppressed large-angle correlations

ABSTRACT The absence of large-angle correlations in the map of cosmic microwave background temperature fluctuations is among the well-established anomalies identified in full-sky and cut-sky maps over the past three decades. Suppressed large-angle correlations are rare statistical flukes in standard inflationary cosmological models. One natural explanation could be that the underlying primordial density perturbations lack correlations on large distance scales. To test this idea, we replace Fourier modes by a wavelet basis with compact spatial support. While the angular correlation function of perturbations can readily be suppressed, the observed monopole- and dipole-subtracted correlation function is not generally suppressed. This suggests that suppression of large-angle temperature correlations requires a mechanism that has both real-space and harmonic-space effects.

Cross-correlation of the kinematic Sunyaev-Zel’dovich effect and 21 cm intensity mapping with tidal reconstruction

We discuss the possibility of studying diffuse baryon distributions with kinematic Sunyaev-Zel'dovich (kSZ) effect by correlating cosmic microwave background (CMB) temperature fluctuations with density fluctuations from 21\,cm intensity mapping (IM). The biggest challenge for the cross-correlation is the loss of large-scale information in IM, due to foregrounds and the zero spacing problem of interferometers. We apply the tidal reconstruction algorithm to restore the lost large-scale modes, which increases the correlation by more than a factor of three. With the predicted foreground level, we expect a $\sim20\,\sigma$ detection of kSZ signal for $0.8\lesssim z\lesssim2.5$ with CHIME and Planck, and a $\sim40\, \sigma$ detection with HIRAX and Planck. The significance can be greatly increased with next-generation facilities of higher spatial resolutions.

Thermal Sunyaev-Zel’dovich anisotropy due to primordial black holes

We investigate the Sunyaev-Zel'dovich (SZ) effect caused by primordial black holes (PBHs) on the cosmic microwave background (CMB) temperature fluctuations. The gas accreting on a PBH heats up by the release of the gravitational energy. As a result, the heated gas in the vicinity of the PBH emits the UV and X-ray photons. These photons can ionize and heat the intergalactic medium (IGM) around the PBH. Assuming the simple model of these emitting photons, we compute the profiles of the IGM ionization fraction and temperature around a PBH. Using these profiles, we evaluate the Compton $y$-parameter created by the IGM gas around a PBH. Finally, we estimate the CMB temperature angular power spectrum due to the PBH SZ effect in our model. We show that the SZ temperature anisotropy due to the PBHs has the flat angular power spectrum on small scale, $l\leq2000$ and could dominate the primordial temperature spectrum on smaller scales than the Silk scale. This flat spectrum extends to the scale of the ionized region by the PBH emission. We also discuss the impact of the small-scale CMB measurement on the PBH abundance based on our results.

Reconstructing small-scale lenses from the cosmic microwave background temperature fluctuations

AbstractCosmic microwave background (CMB) lensing is a powerful probe of the matter distribution in the Universe. The standard quadratic estimator, which is typically used to measure the lensing signal, is known to be suboptimal for low-noise polarization data from next-generation experiments. In this paper, we explain why the quadratic estimator will also be suboptimal for measuring lensing on very small scales, even for measurements in temperature where this estimator typically performs well. Though maximum likelihood methods could be implemented to improve performance, we explore a much simpler solution, revisiting a previously proposed method to measure lensing that involves a direct inversion of the background gradient. An important application of this simple formalism is the measurement of cluster masses with CMB lensing. We find that directly applying a gradient inversion matched filter to simulated lensed images of the CMB can tighten constraints on cluster masses compared to the quadratic estimator. While the difference is not relevant for existing surveys, for future surveys it can translate to significant improvements in mass calibration for distant clusters, where galaxy lensing calibration is ineffective due to the lack of enough resolved background galaxies. Improvements can be as large as ${\sim } 50{{\ \rm per\ cent}}$ for a cluster at z = 2 and a next-generation CMB experiment with 1 $\mu$K arcmin noise, and over an order of magnitude for lower noise levels. For future surveys, this simple matched filter or gradient inversion method approaches the performance of maximum likelihood methods, at a fraction of the computational cost.

Characterizing the epoch of reionization with the small-scale CMB: Constraints on the optical depth and duration

Patchy reionization leaves a number of imprints on the small-scale cosmic microwave background (CMB) temperature fluctuations, the largest of which is the kinematic Sunyaev-Zel'dovich (kSZ), the Doppler shift of CMB photons scattering off moving electrons in ionized bubbles. It has long been known that in the CMB power spectrum, this imprint of reionization is largely degenerate with the kSZ signal produced by late-time galaxies and clusters, thus limiting our ability to constrain reionization. Following Smith & Ferraro (2017), it is possible to isolate the reionization contribution in a model independent way, by looking at the large scale modulation of the small scale CMB power spectrum. In this paper we extend the formalism to use the full shape information of the small scale power spectrum (rather than just its broadband average), and argue that this is necessary to break the degeneracy between the optical depth $\tau$ and parameters setting the duration of reionization. In particular, we show that the next generation of CMB experiments could achieve up to a factor of 3 improvement on the optical depth $\tau$ and at the same time, constrain the duration of reionization to $\sim$ 25 %. This can help tighten the constrains on neutrino masses, which will be limited by our knowledge of $\tau$, and shed light on the physical processes responsible for reionization.

Explaining low ell anomalies in the CMB power spectrum with resonant superstring excitations during inflation

We explore the possibility that both the suppression of the ell = 2 multipole moment of the power spectrum of cosmic microwave background temperature fluctuations and the possible dip for ell = 10–30 can be explained as well as a possible new dip for ell approx 60 as the result of the resonant creation of sequential excitations of a fermionic (or bosonic) closed superstring that couples to the inflaton field. We consider a D,=,26 closed bosonic string with one toroidal compact dimension as an illustration of how string excitations might imprint themselves on the CMB. We analyze the existence of successive momentum states, winding states or oscillations on the string as the source of the three possible dips in the power spectrum. Although the evidence of these dips are of marginal statistical significance, this might constitute the first observational evidence of successive superstring excitations in Nature.

Isotropy analyses of the Planck convergence map

The presence of matter in the path of relic photons causes distortions in the angular pattern of the cosmic microwave background (CMB) temperature fluctuations, modifying their properties in a slight but measurable way. Recently, the Planck Collaboration released the estimated convergence map, an integrated measure of the large-scale matter distribution that produced the weak gravitational lensing (WL) phenomenon observed in Planck CMB data. We perform exhaustive analyses of this convergence map calculating the variance in small and large regions of the sky, but excluding the area masked due to galactic contaminations, and compare them with the features expected in the set of simulated convergence maps, also released by the Planck collaboration. Our goal is to search for sky directions or regions where the WL imprints anomalous signatures to the variance estimator revealed through a $\chi^2$ analyses at a statistically significant level. In the local analysis of the Planck convergence map we identified 8 patches of the sky in disagreement, in more than 2$\sigma$, with what is observed in the average of the simulations. In contrast, in the large regions analysis we found no statistically significant discrepancies, but, interestingly, the regions with the highest $\chi^2$ values are surrounding the ecliptic poles. Thus, our results show a good agreement with the features expected by the $\Lambda$CDM concordance model, as given by the simulations. Yet, the outliers regions found here could suggest that the data still contain residual contamination, like noise, due to over- or under-estimation of systematic effects in the simulation data set.

Planck2015 results

This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlationfunctions of the cosmic microwave background (CMB) temperature and polarization fluctuations that account for relevant uncertainties, both instrumental and astrophysical in nature. They are based on the same hybrid approach used for the previous release, i.e., a pixel-based likelihood at low multipoles (ℓ< 30) and a Gaussian approximation to the distribution of cross-power spectra at higher multipoles. The main improvements are the use of more and better processed data and of Planck polarization information, along with more detailed models of foregrounds and instrumental uncertainties. The increased redundancy brought by more than doubling the amount of data analysed enables further consistency checks and enhanced immunity to systematic effects. It also improves the constraining power of Planck, in particular with regard to small-scale foreground properties. Progress in the modelling of foreground emission enables the retention of a larger fraction of the sky to determine the properties of the CMB, which also contributes to the enhanced precision of the spectra. Improvements in data processing and instrumental modelling further reduce uncertainties. Extensive tests establish the robustness and accuracy of the likelihood results, from temperature alone, from polarization alone, and from their combination. For temperature, we also perform a full likelihood analysis of realistic end-to-end simulations of the instrumental response to the sky, which were fed into the actual data processing pipeline; this does not reveal biases from residual low-level instrumental systematics. Even with the increase in precision and robustness, the ΛCDM cosmological model continues to offer a very good fit to the Planck data. The slope of the primordial scalar fluctuations, ns, is confirmed smaller than unity at more than 5σ from Planck alone. We further validate the robustness of the likelihood results against specific extensions to the baseline cosmology, which are particularly sensitive to data at high multipoles. For instance, the effective number of neutrino species remains compatible with the canonical value of 3.046. For this first detailed analysis of Planck polarization spectra, we concentrate at high multipoles on the E modes, leaving the analysis of the weaker B modes to future work. At low multipoles we use temperature maps at all Planck frequencies along with a subset of polarization data. These data take advantage of Planck’s wide frequency coverage to improve the separation of CMB and foreground emission. Within the baseline ΛCDM cosmology this requires τ = 0.078 ± 0.019 for the reionization optical depth, which is significantly lower than estimates without the use of high-frequency data for explicit monitoring of dust emission. At high multipoles we detect residual systematic errors in E polarization, typically at the μK2 level; we therefore choose to retain temperature information alone for high multipoles as the recommended baseline, in particular for testing non-minimal models. Nevertheless, the high-multipole polarization spectra from Planck are already good enough to enable a separate high-precision determination of the parameters of the ΛCDM model, showing consistency with those established independently from temperature information alone.

Planck2015 results

We present cluster counts and corresponding cosmological constraints from the Planck full mission data set. Our catalogue consists of 439 clusters detected via their Sunyaev-Zeldovich (SZ) signal down to a signal-to-noise ratio of 6, and is more than a factor of 2 larger than the 2013 Planck cluster cosmology sample. The counts are consistent with those from 2013 and yield compatible constraints under the same modelling assumptions. Taking advantage of the larger catalogue, we extend our analysis to the two-dimensional distribution in redshift and signal-to-noise. We use mass estimates from two recent studies of gravitational lensing of background galaxies by Planck clusters to provide priors on the hydrostatic bias parameter, $(1-b)$. In addition, we use lensing of cosmic microwave background (CMB) temperature fluctuations by Planck clusters as an independent constraint on this parameter. These various calibrations imply constraints on the present-day amplitude of matter fluctuations in varying degrees of tension with those from the Planck analysis of primary fluctuations in the CMB; for the lowest estimated values of $(1-b)$ the tension is mild, only a little over one standard deviation, while it remains substantial ($3.7\,\sigma$) for the largest estimated value. We also examine constraints on extensions to the base flat $\Lambda$CDM model by combining the cluster and CMB constraints. The combination appears to favour non-minimal neutrino masses, but this possibility does little to relieve the overall tension because it simultaneously lowers the implied value of the Hubble parameter, thereby exacerbating the discrepancy with most current astrophysical estimates. Improving the precision of cluster mass calibrations from the current 10%-level to 1% would significantly strengthen these combined analyses and provide a stringent test of the base $\Lambda$CDM model.

Lack of large-angle TT correlations persists in WMAP and Planck

The lack of large-angle correlations in the observed microwave background temperature fluctuations persists in the final-year maps from Wilkinson Microwave Anisotropy Probe (WMAP) and the first cosmological data release from Planck. We find a statistically robust and significant result: p-values for the missing correlations lying below 0.24 per cent (i.e. evidence at more than 3σ) for foreground cleaned maps, in complete agreement with previous analyses based upon earlier WMAP data. A cut-sky analysis of the PlanckHFI 100 GHz frequency band, the ‘cleanest CMB channel’ of this instrument, returns a p-value as small as 0.03 per cent, based on the conservative mask defined by WMAP. These findings are in stark contrast to expectations from the inflationary Lambda cold dark matter model and still lack a convincing explanation. If this lack of large-angle correlations is a true feature of our Universe, and not just a statistical fluke, then the cosmological dipole must be considerably smaller than that predicted in the best-fitting model.

Planck2013 results. XII. Diffuse component separation

Planck has produced detailed all-sky observations over nine frequency bands between 30 and 857 GHz. These observations allow robust reconstruction of the primordial cosmic microwave background (CMB) temperature fluctuations over nearly the full sky, as well as new constraints on Galactic foregrounds. This paper describes the component separation framework adopted by Planck. We test four foreground-cleaned CMB maps derived using qualitatively different component separation algorithms. The quality of our reconstructions is evaluated through detailed simulations and internal comparisons, and shown through various tests to be internally consistent and robust for CMB power spectrum and cosmological parameter estimation up to l = 2000. The parameter constraints on LambdaCDM cosmologies derived from these maps are consistent with those presented in the cross-spectrum based Planck likelihood analysis. We choose two of the CMB maps for specific scientific goals. We also present maps and frequency spectra of the Galactic low-frequency, CO, and thermal dust emission. The component maps are found to provide a faithful representation of the sky, as evaluated by simulations. For the low-frequency component, the spectral index varies widely over the sky, ranging from about beta = -4 to -2. Considering both morphology and prior knowledge of the low frequency components, the index map allows us to associate a steep spectral index (beta < -3.2) with strong anomalous microwave emission, corresponding to a spinning dust spectrum peaking below 20 GHz, a flat index of beta > -2.3 with strong free-free emission, and intermediate values with synchrotron emission.

A tale of two paradigms: the mutual incommensurability of ΛCDM and MOND

The concordance model of cosmology, ΛCDM, provides a satisfactory description of the evolution of the universe and the growth of large-scale structure. Despite considerable effort, this model does not at present provide a satisfactory description of small-scale structure and the dynamics of bound objects like individual galaxies. In contrast, MOND provides a unique and predictively successful description of galaxy dynamics, but is mute on the subject of cosmology. Here I briefly review these contradictory world views, emphasizing the wealth of distinct interlocking lines of evidence that went into the development of ΛCDM while highlighting the practical impossibility that it can provide a satisfactory explanation of the observed MOND phenomenology in galaxy dynamics. I also briefly review the baryon budget in groups and clusters of galaxies where neither paradigm provides an entirely satisfactory description of the data. Relatively little effort has been devoted to the formation of structure in MOND; I review some of what has been done. While it is impossible to predict the power spectrum of the microwave background temperature fluctuations in the absence of a complete relativistic theory, the amplitude ratio of the first to second peaks was correctly predicted a priori. However, the simple model that makes this predictions does not explain the observed amplitude of the third and subsequent peaks (3e, 4e, …). MOND anticipates that structure forms more quickly than in ΛCDM. This motivated the prediction that reionization would happen earlier in MOND than originally expected in ΛCDM, as subsequently observed. This also provides a natural explanation for massive, early clusters of galaxies and large, empty voids. However, it is far from obvious that the mass spectrum of galaxy clusters or the power spectrum of galaxies can be explained in MOND, two things that ΛCDM does well. Critical outstanding issues are the development of an acceptable relativistic parent theory for MOND, and the reality of the non-baryonic dark matter of ΛCDM. Do suitable dark matter particles exist, or are they a modern æther?

Seeking inflation fossils in the cosmic microwave background

If during inflation the inflaton couples to a ``fossil'' field---some new scalar, vector, or tensor field---it typically induces a scalar-scalar-fossil bispectrum. Even if the fossil field leaves no direct physical trace after inflation, it gives rise to correlations between different Fourier modes of the curvature or, equivalently, a nonzero curvature trispectrum, but without a curvature bispectrum. Here we quantify the effects of a fossil field on the cosmic microwave background temperature fluctuations in terms of bipolar spherical harmonics (BiPoSHs). The effects of vector and tensor fossils can be distinguished geometrically from those of scalars through the parity of the BiPoSHs they induce. However, the two-dimensional nature of the cosmic microwave background sky does not allow vectors to be distinguished geometrically from tensors. We estimate the detectability of a signal in terms of the scalar-scalar-fossil coupling for scalar, vector, and tensor fossils, assuming a local-type coupling. We comment on a divergence that arises in the quadrupolar BiPoSH from the scalar-scalar-tensor correlation in single-field slow-roll inflation.

THE KINETIC SUNYAEV-ZEL'DOVICH EFFECT AS A PROBE OF THE PHYSICS OF COSMIC REIONIZATION: THE EFFECT OF SELF-REGULATED REIONIZATION

We calculate the angular power spectrum of the Cosmic Microwave Background (CMB) temperature fluctuations induced by the kinetic Sunyaev-Zel'dovich (kSZ) effect from the epoch of reionization (EOR). We use detailed N-body+radiative transfer simulations to follow inhomogeneous reionization of the intergalactic medium (IGM). For the first time we take into account the "self-regulation" of reionization: star formation in low-mass dwarf galaxies (10^8 M_\sun \lesssim M \lesssim 10^9 M_\sun) or minihalos (10^5 M_\sun \lesssim M \lesssim 10^8 M_\sun) is suppressed if these halos form in the regions that were already ionized or Lyman-Werner dissociated. Some previous work suggested that the amplitude of the kSZ power spectrum from the EOR can be described by a two-parameter family: the epoch of half ionization and the duration of reionization. However, we argue that this picture applies only to simple forms of the reionization history which are roughly symmetric about the half-ionization epoch. In self-regulated reionization, the universe begins to be ionized early, maintains a low level of ionization for an extended period, and then finishes reionization as soon as high-mass atomically-cooling halos dominate. While inclusion of self-regulation affects the amplitude of the kSZ power spectrum only modestly (\sim 10 %), it can change the duration of reionization by a factor of more than two. We conclude that the simple two-parameter family does not capture the effect of a physical, yet complex, reionization history caused by self-regulation. When added to the post-reionization kSZ contribution, our prediction for the total kSZ power spectrum is below the current upper bound from the South Pole Telescope. Therefore, the current upper bound on the kSZ effect from the EOR is consistent with our understanding of the physics of reionization.

Statistical properties of thermal Sunyaev–Zel'dovich maps

On small angular scales, i.e. at high angular frequencies, beyond the damping tail of the primary power spectrum, the dominant contribution to the power spectrum of cosmic microwave background temperature fluctuations is the thermal Sunyaev–Zel'dovich (tSZ) effect. We investigate various important statistical properties of the Sunyaev–Zel'dovich maps, using well-motivated models for dark matter clustering to construct statistical descriptions of the tSZ effect to all orders enabling us to determine the entire probability distribution function (PDF). Any generic deterministic biasing scheme can be incorporated in our analysis and the effects of projection, biasing and the underlying density distribution can be analysed separately and transparently in this approach. We introduce the cumulant correlators as tools to analyse tSZ catalogues and relate them to corresponding statistical descriptors of the underlying density distribution. The statistics of hot spots in frequency-cleaned tSZ maps are also developed in a self-consistent way to an arbitrary order, to obtain results complementary to those found using the halo model. We also consider different beam sizes to check the extent to which the PDF can be extracted from various observational configurations. The formalism is presented with two specific models for underlying matter clustering, the hierarchical ansatz and the lognormal distribution. We find both models to be in very good agreement with the simulation results, though the extension of the hierarchical model has an edge over the lognormal model. In addition to testing against simulations made using semi-analytical techniques, we have also used the maps made using Millennium Gas Simulations to prove that the PDF and bias can indeed be predicted with very high accuracy using these models. The presence of significant non-gravitational effects such as preheating, however, cannot be modelled using an analytical approach which is based on the modelling of gravitational clustering alone. Our results indicate that the PDFs we construct are insensitive to the underlying cosmology and can thus provide a useful probe of non-gravitational processes, e.g. preheating or feedback.

Non-Gaussian bubbles in the sky

We point out a possible generation mechanism of non-Gaussian bubbles in the sky due to bubble nucleation in the early universe. We consider a curvaton scenario for inflation and assume that the curvaton field ϕ, whose energy density is subdominant during inflation but which is responsible for the curvature perturbation of the universe, is coupled to another field σ which undergoes false vacuum decay through quantum tunneling. For this model, we compute the skewness of the curvaton fluctuations due to its interaction with σ during tunneling, that is, on the background of an instanton solution that describes false vacuum decay. We find that the resulting skewness of the curvaton can become large in the spacetime region inside the bubble. We then compute the corresponding skewness in the statistical distribution of the cosmic microwave background (CMB) temperature fluctuations. We find a non-vanishing skewness in a bubble-shaped region in the sky. It can be large enough to be detected in the near future, and if detected it will bring us invaluable information about the physics in the early universe.

Spatial curvature falsifies eternal inflation

Inflation creates large-scale cosmological density perturbations that are characterized by an isotropic, homogeneous, and Gaussian random distribution about a locally flat background. Even in a flat universe, the spatial curvature measured within one Hubble volume receives contributions from long wavelength perturbations, and will not in general be zero. These same perturbations determine the Cosmic Microwave Background (CMB) temperature fluctuations, which are \U0001d4aa(10−5). Consequently, the low-l multipole moments in the CMB temperature map predict the value of the measured spatial curvature Ωk. On this basis we argue that a measurement of |Ωk| > 10−4 would rule out slow-roll eternal inflation in our past with high confidence, while a measurement of Ωk < −10−4 (which is positive curvature, a locally closed universe) rules out false-vacuum eternal inflation as well, at the same confidence level. In other words, negative curvature (a locally open universe) is consistent with false-vacuum eternal inflation but not with slow-roll eternal inflation, and positive curvature falsifies both. Near-future experiments will dramatically extend the sensitivity of Ωk measurements and constitute a sharp test of these predictions.

REES–SCIAMA EFFECT AND IMPACT OF FOREGROUND STRUCTURES ON GALAXY REDSHIFTS

We estimate the Rees--Sciama (RS) effect of super structures on the cosmic microwave background (CMB) temperature fluctuations and identify a related effect on galaxy redshifts. By numerically solving the geodesic equation, we find that both superclusters and supervoids can decrease the temperature of the CMB by several micro Kelvin in the central region and increase the temperature slightly in the surrounding area due to the RS effect. The two components of the RS effect, redshift and gravitational time delay, largely cancel each other, leaving an equivalent but much smaller effect on the CMB photons that started out at the same time from the distorted last scattering surface. For galaxies, the time delay effect is separable from the redshift effect, and the slight change to the redshift induced by super structures can be at the percent level of large-scale rms bulk velocities, which might only be detected statistically. On much smaller scales, a tiny redshift difference between two images of a strongly lensed source should exist in general, which is related to the Hubble expansion rate at the source redshift. However, as Loeb (1998) pointed out, observational issues and the proper motion of the structure would make such a measurement impossible.