non-Gaussian Cosmic Microwave Background Research Articles

Denoising diffusion delensing: reconstructing the non-Gaussian CMB lensing potential with diffusion models

ABSTRACT Optimal extraction of cosmological information from observations of the cosmic microwave background (CMB) critically relies on our ability to accurately undo the distortions caused by weak gravitational lensing. In this work, we demonstrate the use of denoising diffusion models in performing Bayesian lensing reconstruction. We show that score-based generative models can produce accurate, uncorrelated samples from the CMB lensing convergence map posterior, given noisy CMB observations. To validate our approach, we compare the samples of our model to those obtained using established Hamiltonian Monte Carlo methods, which assume a Gaussian lensing potential. We then go beyond this assumption of Gaussianity, and train and validate our model on non-Gaussian lensing data, obtained by ray-tracing N-body simulations. We demonstrate that in this case, samples from our model have accurate non-Gaussian statistics beyond the power spectrum. The method provides an avenue towards more efficient and accurate lensing reconstruction, which does not rely on an approximate analytical description of the posterior probability. The reconstructed lensing maps can be used as an unbiased tracer of the matter distribution, and to improve delensing of the CMB, resulting in more precise cosmological parameter inference.

FORSE+: Simulating non-Gaussian CMB foregrounds at 3 arcmin in a stochastic way based on a generative adversarial network

We present FORSE+, a Python package that produces non-Gaussian diffuse Galactic thermal dust emission maps at arcminute angular scales and that has the capacity to generate random realizations of small scales. This represents an extension of the FORSE (Foreground Scale Extender) package, which was recently proposed to simulate non-Gaussian small scales of thermal dust emission using generative adversarial networks (GANs). With the input of the large-scale polarization maps from observations, FORSE+ has been trained to produce realistic polarized small scales at 3′ following the statistical properties, mainly the non-Gaussianity, of observed intensity small scales, which are evaluated through Minkowski functionals. Furthermore, by adding different realizations of random components to the large-scale foregrounds, we show that FORSE+ is able to generate small scales in a stochastic way. In both cases, the output small scales have a similar level of non-Gaussianity compared with real observations and correct amplitude scaling as a power law. These realistic new maps will be useful, in the future, to understand the impact of non-Gaussian foregrounds on the measurements of the cosmic microwave background (CMB) signal, particularly on the lensing reconstruction, de-lensing, and the detection of cosmological gravitational waves in CMB polarization B-modes.

Investigating non-Gaussianity in Cosmic Microwave Background temperature maps using spherical harmonic phases

In the era of precision cosmology, accurate estimation of cosmological parameters is based upon the implicit assumption of the Gaussian nature of Cosmic Microwave Background (CMB) radiation. Therefore, an important scientific question to ask is whether the observed CMB map is consistent with Gaussian prediction. In this work, we extend previous studies based on CMB spherical harmonic phases (SHP) to examine the validity of the hypothesis that the temperature field of the CMB is consistent with a Gaussian random field (GRF). The null hypothesis is that the corresponding CMB SHP are independent and identically distributed in terms of a uniform distribution in the interval [0, 2π] [1,2]. We devise a new model-independent method where we use ordered and non-parametric Rao's statistic, based on sample arc-lengths to comprehensively test uniformity and independence of SHP for a given ℓ mode and independence of nearby ℓ mode SHP. We performed our analysis on the scales limited by spherical harmonic modes ≤ 128, to restrict ourselves to signal-dominated regions. To find the non-uniform or dependent sets of SHP, we calculate the statistic for the data and 10000 Monte Carlo simulated uniformly random sets of SHP and use 0.05 and 0.001 α levels to distinguish between statistically significant and highly significant detections. We first establish the performance of our method using simulated Gaussian, non-Gaussian CMB temperature maps, along with observed non-Gaussian 100 and 143 GHz Planck channel maps. We find that our method, performs efficiently and accurately in detecting phase correlations generated in all of the non-Gaussian simulations and observed foreground contaminated 100 and 143 GHz Planck channel temperature maps. We apply our method on Planck satellite mission's final released CMB temperature anisotropy maps- COMMANDER, SMICA, NILC, and SEVEM along with WMAP 9 year released ILC map. We report that SHP corresponding to some of the m-modes are non-uniform, some of the ℓ mode SHP and neighboring mode pair SHP are correlated in cleaned CMB maps. The detection of non-uniformity or correlation in the SHP indicates the presence of non-Gaussian signals in the foreground minimized CMB maps.

Loop corrections to primordial non-Gaussianity

We discuss quantum gravitational loop effects to observable quantities such as curvature power spectrum and primordial non-Gaussianity of cosmic microwave background (CMB) radiation. We first review the previously shown case where one gets a time dependence for zeta-zeta correlator due to loop corrections. Then we investigate the effect of loop corrections to primordial non-Gaussianity of CMB. We conclude that, even with a single scalar inflaton, one might get a huge value for non-Gaussianity which would exceed the observed value by at least 30 orders of magnitude. Finally we discuss the consequences of this result for scalar driven inflationary models.

Principal components of CMB non-Gaussianity

The skew-spectrum statistic introduced by Munshi & Heavens has recently been used in studies of non-Gaussianity from diverse cosmological data sets including the detection of primary and secondary non-Gaussianity of cosmic microwave background (CMB) radiation. Extending previous work, focused on independent estimation, here we deal with the question of joint estimation of multiple skew-spectra from the same or correlated data sets. We consider the optimum skew-spectra for various models of primordial non-Gaussianity as well as secondary bispectra that originate from the cross-correlation of secondaries and lensing of CMB: coupling of lensing with the Integrated Sachs–Wolfe effect, coupling of lensing with thermal Sunyaev–Zeldovich, as well as from unresolved point sources. For joint estimation of various types of non-Gaussianity, we use the principal component analysis (PCA) to construct the linear combinations of amplitudes of various models of non-Gaussianity, e.g. |$f^{\rm loc}_{\rm NL},f^{\rm eq}_{\rm NL},f^{\rm ortho}_{\rm NL}$| that can be estimated from CMB maps. We describe how the bias induced in the estimation of primordial non-Gaussianity due to secondary non-Gaussianity may be evaluated for arbitrary primordial models using a PCA analysis. The PCA approach allows one to infer approximate (but generally accurate) constraints using CMB data sets on any reasonably smooth model by use of a look-up table and performing a simple computation. This principle is validated by computing constraints on the Dirac–Born–Infeld bispectrum using a PCA analysis of the standard templates.

From data to science: Planck data and the CMB non-Gaussianity

AbstractStudying the non-Gaussianity (NG) of the Cosmic Microwave Background (CMB) is an extremely powerful tool to investigate the properties of the very early Universe. The Planck nominal mission CMB maps yielded unprecedented constraints on primordial non-Gaussianity providing with the highest precision test of the standard model of inflation. Planck's high sensitivity also allowed to find evidence for the first time of the late-time non-Gaussianity arising from the Lensing-Integrated Sachs Wolfe (ISW) cross correlation. In this talk I will give details on the Planck data analysis and I will discuss the theoretical implications of the results.

Primordial magnetic field limits from the CMB trispectrum: Scalar modes and Planck constraints

Cosmic magnetic fields are observed to be coherent on large scales and could have a primordial origin. Non-Gaussian signals in the cosmic microwave background (CMB) are generated by primordial magnetic fields as the magnetic stresses and temperature anisotropy they induce depend quadratically on the magnetic field. We compute the CMB scalar trispectrum on large angular scales, for nearly scale-invariant magnetic fields, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approximately ${10}^{\ensuremath{-}29}$ and ${10}^{\ensuremath{-}19}$, respectively. The scalar anisotropic stress trispectrum is also calculated in the flat-sky approximation and yields a similar result. Observational limits on CMB non-Gaussianity from the Planck mission data allow us to set upper limits of ${B}_{0}\ensuremath{\lesssim}0.6\text{ }\text{ }\mathrm{nG}$ on the present value of the primordial cosmic magnetic field. Considering the inflationary magnetic curvature mode in the trispectrum can further tighten the magnetic field upper limit to ${B}_{0}\ensuremath{\lesssim}0.05\text{ }\text{ }\mathrm{nG}$. These sub-nanoGauss constraints from the magnetic trispectrum are the most stringent limits so far on the strength of primordial magnetic fields, on megaparsec scales, significantly better than the limits obtained from the CMB bispectrum and the CMB power spectrum.

Improved estimator for non-Gaussianity in cosmic microwave background observations

An improved estimator for the amplitude ${f}_{\mathrm{NL}}$ of local-type non-Gaussianity from the cosmic microwave background (CMB) bispectrum is discussed. The standard estimator is constructed to be optimal in the zero-signal (i.e., Gaussian) limit. When applied to CMB maps which have a detectable level of non-Gaussianity the standard estimator is no longer optimal, possibly limiting the sensitivity of future observations to a non-Gaussian signal. Previous studies have proposed an improved estimator by using a realization-dependent normalization. Under the approximations of a flat sky and a vanishingly thin last-scattering surface, these studies showed that the variance of this improved estimator can be significantly smaller than the variance of the standard estimator when applied to non-Gaussian CMB maps. Here this technique is generalized to the full sky and to include the full radiation transfer function, yielding expressions for the improved estimator that can be directly applied to CMB maps. The ability of this estimator to reduce the variance as compared to the standard estimator in the face of a significant non-Gaussian signal is re-assessed using the full CMB transfer function. As a result of the late time integrated Sachs-Wolfe (ISW) effect, the performance of the improved estimator is degraded. If CMB maps are first cleaned of the late-time ISW effect using a tracer of foreground structure, such as a galaxy survey or a measurement of CMB weak lensing, the new estimator does remove a majority of the excess variance, allowing a higher significance detection of ${f}_{\mathrm{NL}}$.

Searching for non-Gaussianity in observational cosmic microwave background data

Methods for searching for non-Gaussianity in the WMAP data are reviewed and the associated problems related to the cosmic microwave background (CMB) data analysis are discussed. Evidence for non-Gaussianity has been obtained by various methods and from a number of multipole ranges. Different approaches to searching for non-Gaussian CMB data are sensitive to different manifestations of non-Gaussianity, which sometimes are due to the primordial non-Gaussianity and sometimes to galactic foregrounds and/or systematic residuals remaining after the data analysis that are difficult to take into account.

Cosmic Microwave Background Trispectrum and Primordial Magnetic Field Limits

Primordial magnetic fields will generate non-gaussian signals in the cosmic microwave background (CMB) as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. We compute a new measure of magnetic non-gaussianity, the CMB trispectrum, on large angular scales, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approximately a few times 10(-29) and 10(-19), respectively. Observational limits on CMB non-gaussianity from WMAP data allow us to conservatively set upper limits of a nG, and plausibly sub-nG, on the present value of the primordial cosmic magnetic field. This represents the tightest limit so far on the strength of primordial magnetic fields, on Mpc scales, and is better than limits from the CMB bispectrum and all modes in the CMB power spectrum. Thus, the CMB trispectrum is a new and more sensitive probe of primordial magnetic fields on large scales.

Hunting for isocurvature modes in the cosmic microwave background non-Gaussianities

We investigate new shapes (in multipole space) of local primordial non-Gaussianities in the cosmic microwave background. Allowing for a primordial isocurvature mode along with the main adiabatic one, the angular bispectrum is in general a superposition of six distinct shapes: the usual adiabatic term, a purely isocurvature component and four additional components that arise from correlations between the adiabatic and the isocurvature modes. We present a class of early Universe models in which various hierarchies between these six components can be obtained, while satisfying the present upper bound on the isocurvature fraction in the power spectrum. Remarkably, even with this constraint, detectable non-Gaussianity could be produced by isocurvature modes. We finally discuss the prospects of detecting these new shapes with the Planck data, including polarization.

Testing gravity with non-Gaussianity

We show that modified gravity presents distinctive nonlinear features on the Cosmic Microwave Background (CMB) anisotropies comparing with General Relativity (GR). We calculate the contribution to the CMB non-Gaussianity from nonlinear Sachs–Wolfe effect in f(R) gravity and show that, contrary to GRʼs contribution which is typically ≲O(1), the contribution in f(R) gravity is sensitive to the nonlinear structure of f(R) and can be large in principle. Optimistically, this gives an alternative origin for the possibly observed large CMB non-Gaussianities besides the primordial ones. On the other hand, such nonlinear features can be employed to provide a new cosmological test of f(R) or other modified theories of gravitation, which is unique and independent of previously known tests.

Constraints on fNL from Wilkinson Microwave Anisotropy Probe 7-year data using a neural network classifier

We present a multi-class neural network (NN) classifier as a method to measure nonGaussianity, characterised by the local non-linear coupling parameter fNL, in maps of the cosmic microwave background (CMB) radiation. The classifier is trained on simulated non-Gaussian CMB maps with a range of known fNL values by providing it with wavelet coefficients of the maps; we consider both the HealPix (HW) wavelet and the spherical Mexican hat wavelet (SMHW). When applied to simulated test maps, the NN classfier produces results in very good agreement with those obtained using standard chi2 minimization. The standard deviations of the fNL estimates for WMAPlike simulations were {\sigma} = 22 and {\sigma} = 33 for the SMHW and the HW, respectively, which are extremely close to those obtained using classical statistical methods in Curto et al. and Casaponsa et al. Moreover, the NN classifier does not require the inversion of a large covariance matrix, thus avoiding any need to regularise the matrix when it is not directly invertible, and is considerably faster.

INTRINSIC BISPECTRA OF COSMIC MAGNETIC FIELDS

Forthcoming data sets from the Planck experiment and others are in a position to probe the cosmic microwave background (CMB) non-Gaussianity with higher accuracy than has yet been possible, and potentially open a new window into the physics of the very early universe. However, a signal need not necessarily be inflationary in origin, and possible contaminants should be examined in detail. One such is provided by early universe magnetic fields, which can be produced by a variety of models including during an inflationary phase, at phase transitions, or seeded by cosmic defects. Should such fields have been extant in the early universe, they would provide a natural source of CMB non-Gaussianity. Knowledge of the CMB angular bispectrum requires the complete Fourier-space (or "intrinsic") bispectrum. In this paper, I consider in detail the intrinsic bispectra of an early-universe magnetic field for a range of power-law magnetic spectra.

Primordial magnetic field limits from cosmic microwave background bispectrum of magnetic passive scalar modes

Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher order effect. Apart from a compensated scalar mode, stochastic primordial magnetic fields also produce scalar anisotropic stress that remains uncompensated till neutrino decoupling. This gives rise to an adiabaticlike scalar perturbation mode that evolves passively thereafter (called the passive mode). We compute the CMB reduced bispectrum (${B}_{{L}_{1}{L}_{2}{L}_{3}}$) induced by this passive mode, sourced via the Sachs-Wolfe effect, on large angular scales. For any configuration of bispectrum, taking a partial sum over mode-coupling terms, we find a typical value of ${l}_{1}({l}_{1}+1){l}_{3}({l}_{3}+1){b}_{{l}_{1}{l}_{2}{l}_{3}}\ensuremath{\sim}6\ensuremath{-}9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$, for a magnetic field of ${B}_{0}\ensuremath{\sim}3\text{ }\text{ }\mathrm{nG}$, assuming a nearly scale-invariant magnetic spectrum. We also evaluate, in full, the bispectrum for the squeezed collinear configuration over all angular mode-coupling terms and find ${l}_{1}({l}_{1}+1){l}_{3}({l}_{3}+1){b}_{{l}_{1}{l}_{2}{l}_{3}}\ensuremath{\approx}\ensuremath{-}1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$. These values are more than $\ensuremath{\sim}{10}^{6}$ times larger than the previously calculated magnetic compensated scalar mode CMB bispectrum. Observational limits on the bispectrum from WMAP7 data allow us to set upper limits of ${B}_{0}\ensuremath{\sim}2\text{ }\text{ }\mathrm{nG}$ on the present value of the cosmic magnetic field of primordial origin. This is over 10 times more stringent than earlier limits on ${B}_{0}$ based on the compensated mode bispectrum.

CMB temperature bispectrum induced by cosmic strings

The cosmic microwave background (CMB) bispectrum of the temperature anisotropies induced by a network of cosmic strings is derived for small angular scales, under the assumption that the principal cause of temperature fluctuations is the Gott-Kaiser-Stebbins effect. We provide analytical expressions for all isosceles triangle configurations in Fourier space. Their overall amplitude is amplified as the inverse cube of the angle and diverges for flat triangles. The isosceles configurations generically lead to a negative bispectrum with a power-law decay ${\ensuremath{\ell}}^{\ensuremath{-}6}$ for large multipole $\ensuremath{\ell}$. However, collapsed triangles are found to be associated with a positive bispectrum whereas the squeezed triangles still exhibit negative values. We then compare our analytical estimates to a direct computation of the bispectrum from a set of 300 statistically independent temperature maps obtained from Nambu-Goto cosmic string simulations in a Friedmann-Lema\^{\i}tre-Robertson-Walker universe. We find good agreement for the overall amplitude, the power-law behavior, and the angle dependency of the various triangle configurations. At $\ensuremath{\ell}\ensuremath{\sim}500$ the cosmic string Gott-Kaiser-Stebbins effect contributes approximately the same equilateral CMB bispectrum amplitude as an inflationary model with $|{f}_{\mathrm{NL}}^{\mathrm{loc}}|\ensuremath{\simeq}{10}^{3}$, if the strings contribute about 10% of the temperature power spectrum at $\ensuremath{\ell}=10$. Current bounds on ${f}_{\mathrm{NL}}$ are not derived using cosmic string bispectrum templates, and so our ${f}_{\mathrm{NL}}$ estimate cannot be used to derive bounds on strings. However it does suggest that string bispectrum templates should be included in the search of CMB non-Gaussianities.

Cosmic Microwave Background Bispectrum from Primordial Magnetic Fields on Large Angular Scales

Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher-order effect. We propose a novel probe of stochastic primordial magnetic fields that exploits the characteristic CMB non-Gaussianity that they induce. We compute the CMB bispectrum (b(l1l2l3)) induced by such fields on large angular scales. We find a typical value of l1(l1 + 1)l3(l3 + 1)b(l1l2l3) approximately 10(-22), for magnetic fields of strength B0 approximately 3 nG and with a nearly scale invariant magnetic spectrum. Observational limits on the bispectrum allow us to set upper limits on B0 approximately 35 nG.

Analysis of non-Gaussian cosmic microwave background maps based on the N-pdf. Application toWilkinson Microwave Anisotropy Probedata

We present a new method based on the N-point probability distribution (pdf) to study non-Gaussianity in cosmic microwave background (CMB) maps. Likelihood and Bayesian estimation are applied to a local non-linear perturbed model up to third order, characterized by a linear term which is described by a Gaussian N-pdf, and a second and third order terms which are proportional to the square and the cube of the linear one. We also explore a set of model selection techniques (the Akaike and the Bayesian Information Criteria, the minimum description length, the Bayesian Evidence and the Generalized Likelihood Ratio Test) and their application to decide whether a given data set is better described by the proposed local non-Gaussian model, rather than by the standard Gaussian temperature distribution. As an application, we consider the analysis of the WMAP 5-year data at a resolution of around 2 degrees. At this angular scale (the Sachs-Wolfe regime), the non-Gaussian description proposed in this work defaults (under certain conditions) to an approximative local form of the weak non-linear coupling inflationary model (e.g. Komatsu & Spergel 2001) previously addressed in the literature. For this particular case, we obtain an estimation for the non-linear coupling parameter of -94 < F_nl < 154 at 95% CL. Equally, model selection criteria also indicate that the Gaussian hypothesis is favored against the particular local non-Gaussian model proposed in this work. This result is in agreement with previous findings obtained for equivalent non-Gaussian models and with different non-Gaussian estimators. However, our estimator based on the N-pdf is more efficient than previous estimators and, therefore, provides tighter constraints on the coupling parameter at degree angular resolution.

Point source contamination in CMB non-Gaussianity analyses

In this paper we analyze the biasing effect of point sources, either thermal Sunyaev-Zeldovich clusters or standard radio sources, on the estimated strength of the non-Gaussianity in the cosmic microwave background (CMB). We show that the biggest contribution comes from the cross correlation of the CMB with the matter density rather than from the Poisson term which is conventionally assumed in these calculations. For the three year WMAP data, we estimate that point sources could produce a non-Gaussian signature equivalent to a bias in fNL of 0.35, 0.24, -0.097, -0.13 in the Ka, Q, V, and W bands, respectively. The level of bias we find is largely insufficient to explain the very high fNL values recently detected by Yadav and Wandelt. For Planck, we estimate the point source bispectra to contaminate the fNL estimator with a bias of 1.3, 0.34, -0.25, -0.48 at 30, 44, 70, 100 GHz, respectively. These results depend on the assumed redshift distribution of the point sources. However, given the projected Planck sensitivity of DeltafNL~=5 (95% C.L.), a good estimate of point sources' properties including their number density and redshift distribution is essential before deriving strong conclusions on primordial non-Gaussianity.

Constraints on the non-linear coupling parameterfnlwith Archeops data

We present a Gaussianity analysis of the Archeops Cosmic Microwave Background (CMB) temperature anisotropy data maps at high resolution to constrain the non-linear coupling parameter fnl characterising well motivated non-Gaussian CMB models. We used the data collected by the most sensitive Archeops bolometer at 143 GHz. The instrumental noise was carefully characterised for this bolometer, and for another Archeops bolometer at 143 GHz used for comparison. Angular scales from 27 arcmin to 1.8 degrees and a large fraction of the sky, 21 %, covering both hemispheres (avoiding pixels with Galactic latitude |b| < 15 degrees) were considered. The three Minkowski functionals on the sphere evaluated at different thresholds were used to construct a chi-squared statistics for both the Gaussian and the non-Gaussian CMB models. The Archeops maps were produced with the Mirage optimal map-making procedure from processed time ordered data. The analysis is based on simulations of signal (Gaussian and non-Gaussian fnl CMB models) and noise which were processed in the time domain using the Archeops pipeline and projected on the sky using the Mirage optimal map-making procedure. The Archeops data were found to be compatible with Gaussianity after removal of highly noisy pixels at high resolution. The non-linear coupling parameter was constrained to -400 < fnl < 590 at 68% CL and -920 < fnl < 1075 at 95% CL, for realistic non-Gaussian CMB simulations.