We explore the low-l likelihood of the angular spectrum C(l) of masked CMB temperature maps using an adaptive importance sampler. We find that, in spite of a partial sky coverage, the likelihood distribution of each C(l) closely follows an inverse gamma distribution. Our exploration is accurate enough to measure the inverse gamma parameters along with the correlation between multipoles. Those quantities are used to build an approximation of the joint posterior distribution of the low-l likelihood. The accuracy of the proposed approximation is established using both statistical criteria and a mock cosmological parameter fit. When applied to the WMAP5 data set, this approximation yields cosmological parameter estimates at the same level of accuracy as the best current techniques but with very significant speed gains.
We have investigated non-Gaussianity of our early Universe by comparing the parity asymmetry of the WMAP power spectrum with simulations. We find that odd-parity preference of the WMAP data (2<= l <=18) is anomalous at 4-in-1000 level. We find it likely that low quadrupole power is part of this parity asymmetry rather than an isolated anomaly. Futher investigation is required to find out whether the origin of this anomaly is cosmological or systematic effect. The data from Planck surveyor, which has systematics distinct from the WMAP, will help us to resolve the origin of the anomalous odd-par…
We apply our symmetry based Power tensor technique to test conformity of PLANCK Polarization maps with statistical isotropy. On a wide range of angular scales (l=40-150), our preliminary analysis detects many statistically anisotropic multipoles in foreground cleaned full sky PLANCK polarization maps viz., COMMANDER and NILC. We also study the effect of residual foregrounds that may still be present in the galactic plane using both common UPB77 polarization mask, as well as the individual component separation method specific polarization masks. However some of the statistically anisotropic mod…
Spherical manifolds yield cosmic spaces with positive curvature. They result by closing pieces from the sphere used by Einstein for his initial cosmology. Harmonic analysis on the manifolds aims at explaining the observed low amplitudes at small multipole orders of the cosmic microwave background. We analyze assumptions of point symmetry and randomness for spherical spaces. There emerge four spaces named orbifolds, with low volume fraction from the sphere and sharp multipole selection rules in their eigenmodes.
On large angular scales (greater than about 60 degrees), the two-point angular correlation function of the temperature of the cosmic microwave background (CMB), as measured (outside of the plane of the Galaxy) by the Wilkinson Microwave Anisotropy Probe, shows significantly lower large-angle correlations than expected from the standard inflationary cosmological model. Furthermore, when derived from the full CMB sky, the two lowest cosmologically interesting multipoles, the quadrupole (l=2) and the octopole (l=3), are unexpectedly aligned with each other. Using randomly generated full-sky and c…
Several anomalies appear to be present in the large-angle cosmic microwave background (CMB) anisotropy maps of WMAP, including the alignment of large-scale multipoles. Models in which isotropy is spontaneously broken (e.g., by a scalar field) have been proposed as explanations for these anomalies, as have models in which a preferred direction is imposed during inflation. We examine models inspired by these, in which isotropy is broken by a multiplicative factor with dipole and/or quadrupole terms. We evaluate the evidence provided by the multipole alignment using a Bayesian framework, finding …
The statistical cosmological principle states that observables on the celestial sphere are sampled from a rotationally invariant distribution. Previously certain large scale anomalies which violate this principle have been found, for example an alignment of the lowest multipoles with the cosmic dipole direction. In this work we continue the search for possible anomalies using multipole vectors which represent a convenient tool for this purpose. In order to study the statistical behavior of multipole vectors, we revisit several construction methods. We investigate all four full-sky foreground-c…
Low multipole amplitudes in the Cosmic Microwave Background CMB radiation can be explained by selection rules from the underlying multiply-connected homotopy. We apply a multipole analysis to the harmonic bases and introduce point symmetry.We give explicit results for two cubic 3-spherical manifolds and lowest polynomial degrees, and derive three new spherical 3-manifolds.
We study several anisotropic inflationary models and their implications for the observed violation of statistical isotropy in the CMBR data. In two of these models the anisotropy decays very quickly during the inflationary phase of expansion. We explicitly show that these models lead to violation of isotropy only for low l CMBR modes. Our primary aim is to fit the observed alignment of l=2,3 multipoles to the theoretical models. We use two measures, based on the power tensor, which contains information about the alignment of each multipole, to quantify the anisotropy in data. One of the measur…
We investigate the abundance of large-scale hot and cold spots in the WMAP-5 temperature maps and find considerable discrepancies compared to Gaussian simulations based on the LCDM best-fit model. Too few spots are present in the reliably observed cosmic microwave background (CMB) region, i.e., outside the foreground-contaminated parts excluded by the KQ75 mask. Even simulated maps created from the original WMAP-5 estimated multipoles contain more spots than visible in the measured CMB maps. A strong suppression of the lowest multipoles would lead to better agreement. The lack of spots is refl…
The Milky Way can act as a large-scale weak gravitational lens of the cosmic microwave background (CMB). We study this effect using a photon ray-tracing code and a Galactic mass distribution with disk, bulge and halo components. For an observer at the Sun's coordinates in the Galaxy, the bending of CMB photon paths is limited to less than one arcsecond, and only for rays that pass within a few degrees of the Galactic Center. However, the entire sky is affected, resulting in global distortions of the CMB on large angular scales. These distortions can cause the low-order multipoles of a spherica…
Since the temperature fluctuations in cosmic microwave background (CMB) on large-angular scales probe length scales that were super-horizon sized at photon decoupling and hence insensitive to microphysical processes, the low-multipole CMB data are supposed to be a good probe to the physics of the primordial Universe. In this letter we will constrain the cosmological parameters in the base $Λ$CDM model with tensor perturbations by only using low-multipole CMB data, including Background Imaging of Cosmic Extragalactic Polarization (B2), Planck released in 2013 (P13) and Wilkinson Microwaves Anis…
Every experiment is affected by systematic effects that hamper the data analysis and have the potential to ultimately degrade its performance. In the case of probes of the cosmic microwave background (CMB) radiation, a minimal set of issues to consider includes asymmetric beam functions, correlated noise, and incomplete sky coverage. Presuming a simplified scanning strategy that allows for an exact analytical treatment of the problem, we study the impact of systematic effects on the likelihood function of the CMB power spectrum. We use the Fisher matrix, a measure of the information content of…
We propose a dipole modulation model for the Cosmic Microwave Background Radiation (CMBR) polarization field. We show that the model leads to correlations between l and l+1 multipoles, exactly as in the case of temperature. We obtain results for the case of TE, EE and BB correlations. An anisotropic or inhomogeneous model of primordial power spectrum which leads to such correlations in temperature field also predicts similar correlations in CMBR polarization. We analyze the CMBR temperature and polarization data in order to extract the signal of these correlation between l and l+1 multipoles. …
We consider the Stokes parameters' frequency spectral distortions arising due to Compton scattering of the anisotropic cosmic microwave background (CMB) radiation, the Sunyaev-Zel' dovich effect (SZ), towards clusters of galaxies. We single out a very special type of such distortions and find simple analytical formulas for them. We show that this kind of distortion has a very distinctive spectral shape and can be separated from other kinds of contaminants. We demonstrate that this effect gives us an opportunity for an independent estimation of the low-multipole angular CMB anisotropies, such a…
The low multipole anomalies of the Cosmic Microwave Background has received much attention during the last few years. It is still not ascertained whether these anomalies are indeed primordial or the result of systematics or foregrounds. An example of a foreground, which could generate some non-Gaussian and statistically anisotropic features at low multipole range, is the very symmetric Kuiper Belt in the outer solar system. In this paper, expanding upon the methods presented by Maris et al. (2011), we investigate the contributions from the Kuiper Belt objects (KBO) to the WMAP ILC 7 map, where…
In this paper we present a simple argument that shows a non-singular bouncing cosmology naturally yields an era of super-inflation which can precede the phase of normal potential driven inflation. One of the consequences of a super-inflation phase is that it might be able to account for suppressing the low multipole in the amplitude of the cosmic microwave background radiation. We are able to constrain the number of e-folds of super-inflation from the current Planck data to be roughly 3 e-folds in a model independent way.
This paper explores methods for constructing low multipole temperature and polarisation likelihoods from maps of the cosmic microwave background anisotropies that have complex noise properties and partial sky coverage. We use Planck 2018 High Frequency Instrument (HFI) and updated SRoll2 temperature and polarisation maps to test our methods. We present three likelihood approximations based on quadratic cross spectrum estimators: (i) a variant of the simulation-based likelihood (SimBaL) techniques used in the Planck legacy papers to produce a low multipole EE likelihood; (ii) a semi-analytical …
We present constraints on primordial B modes from large angular scale cosmic microwave background polarisation anisotropies measured with the Planck satellite. To remove Galactic polarised foregrounds, we use a Bayesian parametric component separation method, modelling synchrotron radiation as a power law and thermal dust emission as a modified blackbody. This method propagates uncertainties from the foreground cleaning into the noise covariance matrices of the maps. We construct two likelihoods: (i) a semi-analytical cross-spectrum-based likelihood-approximation scheme (momento) and (ii) an e…
We test the asymmetry of the Cosmic Microwave Background anisotropy jointly in temperature and polarization. We study the hemispherical asymmetry, previously found only in the temperature field, with respect to the axis identified by Hansen et al. (2009). To this extent, we make use of the low resolution WMAP 5 year temperature and polarization Nside=16 maps and the optimal angular power spectrum estimator BolPol (Gruppuso et al. 2009). We consider two simple estimators for the power asymmetry and we compare our findings with Monte Carlo simulations which take into account the full noise covar…
Damping of magnetic fields via ambipolar diffusion and decay of magnetohydrodynamical (MHD) turbulence in the post decoupling era heats the intergalactic medium (IGM). Delayed recombination of hydrogen atoms in the IGM yields an optical depth to scattering of the cosmic microwave background (CMB). The optical depth generated at $z\gg 10$ does not affect the "reionization bump" of the CMB polarization power spectrum at low multipoles, but affects the temperature and polarization power spectra at high multipoles. Writing the present-day energy density of fields smoothed over the damping scale at…
Statistically anomalous signals in the microwave background have been extensively studied in general in multipole space, and in real space mainly for circular and other simple patterns. In this paper we search for a range of non-trivial patterns in the temperature data from WMAP 7-year observations. We find a very significant detection of a number of such features and discuss their consequences for the essential character of the cosmos.
The motion of our solar system relative to the 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 provi…
In this work we present an extension of the ROMA map-making code for data analysis of Cosmic Microwave Background polarization, with particular attention given to the inflationary polarization B-modes. The new algorithm takes into account a possible cross-correlated noise component among the different detectors of a CMB experiment. We tested the code on the observational data of the BOOMERanG (2003) experiment and we show that we are provided with a better estimate of the power spectra, in particular the error bars of the BB spectrum are smaller up to 20% for low multipoles. We point out the g…
Several claims have been made of anomalies in the large-angle properties of the cosmic microwave background anisotropy as measured by WMAP. In most cases, the statistical significance of these anomalies is hard or even impossible to assess, due to the fact that the statistics used to quantify the anomalies were chosen a posteriori. On the other hand, the possibility of detecting new physics on the largest observable scales is so exciting that, in my opinion, it is worthwhile to examine the claims carefully. I will focus on three particular claims: the lack of large-angle power, the north-south…
We discuss the possibility that the observed low-order multipole features of the cosmic microwave background radiation (CMB) all originate in the termination shock (TS) region of the heliosheath that surrounds the solar system. If the intrinsic CMB spectrum is assumed to be a pure monopole (2.73K) then thermodynamic processes occurring within the plasma region of the TS could imprint the observed power spectrum of the low-order multipoles and their alignment (the so-called "axis of evil") onto this background isotropic CMB. Conditions are outlined for the geometric shape of the TS region. A ke…
We investigate the hemispherical power asymmetry in the cosmic microwave background on small angular scales. We find an anomalously high asymmetry in the multipole range l=601-2048, with a naive statistical significance of 6.5 sigma. However, we show that this extreme anomaly is simply a coincidence of three other effects, relativistic power modulation, edge effects from the mask applied, and inter-scale correlations. After correcting for all of these effects, the significance level drops to ~1 sigma, i.e., there is no anomalous intrinsic asymmetry in the small angular scales. Using this null …
Full-sky maps of the cosmic microwave background temperature reveal a 7% asymmetry of fluctuation power between two halves of the sky. A common phenomenological model for this asymmetry is an overall dipole modulation of statistically isotropic fluctuations, which produces particular off-diagonal correlations between multipole coefficients. We compute these correlations and construct corresponding estimators for the amplitude and direction of the dipole modulation. Applying these estimators to various cut-sky temperature maps from Planck and WMAP data shows consistency with a dipole modulation…
The cosmic microwave background radiation defines a preferred cosmic rest frame, and inflationary cosmological theories predict that the microwave background temperature fluctuations should be statistically isotropic in this rest frame. For observers moving with respect to the rest frame, the temperature fluctuations will no longer be isotropic, due to the preferred direction of motion. The most prominent effect is a dipole temperature variation, which has long been observed with an amplitude of a part in a thousand of the mean temperature. An observer's velocity with respect to the rest frame…
We derive a constraint on patchy screening of the cosmic microwave background from inhomogeneous reionization, using off-diagonal TB and TT correlations in WMAP-7 temperature/polarization data. We interpret this as a constraint on the rms optical-depth fluctuation Δτ as a function of a coherence multipole Lc. We relate these parameters to a comoving coherence scale, of bubble size Rc, in a phenomenological model where reionization is instantaneous but occurs on a crinkly surface, and also to the bubble size in a model of "Swiss cheese" reionization where bubbles of fixed size are spread over s…
The prospect of detecting relic gravitational waves (RGWs), through their imprint in the cosmic microwave background radiation, provides an excellent opportunity to study the very early Universe. In simplest viable theoretical models the RGW background is characterized by two parameters, the tensor-to-scalar ratio $r$ and the tensor spectral index $n_t$. In this paper, we analyze the potential joint constraints on these two parameters, $r$ and $n_t$, using the data from the upcoming cosmic microwave background radiation experiments. Introducing the notion of the best pivot multipole $\ell_t^*$…
We present a novel mathematical formalism that allows to easily compute the expected kinetic Sunyaev Zeldovich (kSZ) signal in intensity and polarization due to an anisotropic primordial Cosmic Microwave Background (CMB). We derive the expected intensity and polarization distortions in the direction of non-moving galaxy clusters and then we generalize our calculations for non-zero peculiar velocity. We show that, in the direction of moving clusters, low CMB multipoles impose intensity and polarization spectral distortions with different frequency dependences. The polarization signal primarily …
Recently, full sky maps from Planck have been made publicly available. In this paper, we do consistency tests for the three Planck CMB sky maps. We assume that the difference between two maps represents the contributions from systematics, noise, foregrounds and other sources, and that a precise representation of the Cosmic Microwave Background should be uncorrelated with it. We investigate the cross correlation in pixel space between the difference maps and the various Planck maps and find no significant correlations, in comparison to 10000 random Gaussian simulated maps. Additionally we inves…
It has been argued recently by Copi etal (2009) that the lack of large angular correlations of the CMB temperature field provides strong evidence against the standard, statistically isotropic, inflationary LambdaCDM cosmology. We compare various estimators of the temperature correlation function showing how they depend on assumptions of statistical isotropy and how they perform on the WMAP 5 year ILC maps with and without a sky cut. We show that the low multipole harmonics that determine the large-scale features of the temperature correlation function can be reconstructed accurately, independe…
We present 30 GHz measurements of the angular power spectrum of the cosmic microwave background (CMB) obtained with the Sunyaev-Zel'dovich Array. The measurements are sensitive to arcminute angular scales, where secondary anisotropy from the Sunyaev-Zel'dovich effect (SZE) is expected to dominate. For a broad bin centered at multipole 4066 we find 67+77-50 uK^2, of which 26+/-5 uK^2 is the expected contribution from primary CMB anisotropy and 80+/-54 uK^2 is the expected contribution from undetected radio sources. These results imply an upper limit of 155 uK^2 (95% CL) on the secondary contrib…
We examine the internal consistency of the Planck 2015 cosmic microwave background (CMB) temperature anisotropy power spectrum. We show that tension exists between cosmological constant cold dark matter (LCDM) model parameters inferred from multipoles l<1000 (roughly those accessible to Wilkinson Microwave Anisotropy Probe), and from l>=1000, particularly the CDM density, Omega_ch^2, which is discrepant at 2.5 sigma for a Planck-motivated prior on the optical depth, tau=0.07+/-0.02. We find some parameter tensions to be larger than previously reported because of inaccuracy in the code used by …
The Sunyaev-Zel'dovich (SZ) effect has a distinct spectral signature that allows its separation from fluctuations in the cosmic microwave background (CMB) and foregrounds. Using CMB anisotropies measured in Wilkinson Microwave Anisotropy Probe's five-year maps, we constrain the SZ fluctuations at large, degree angular scales corresponding to multipoles in the range from 10 to 400. We provide upper bounds on SZ fluctuations at multipoles greater than 50, and find evidence for a hemispherically asymmetric signal at ten degrees angular scales. The amplitude of the detected signal cannot be easily…
The delensing procedure is an effective tool for removing lensing-induced $B$-mode polarization in the Cosmic Microwave Background to allow for deep searches of primordial $B$-modes. However, the delensing algorithm existing in the literature breaks down if the target $B$-mode signals overlap significantly with the lensing $B$-mode ($\sim 300<l<2000$) in multipole-$l$ space. In this paper, we identify the cause of the breakdown to be correlations between the input $B$-map and the deflection field estimator ($EB$). The amplitude of this bias is quantified by numerical simulations and compared t…
Recent cosmic microwave background data in temperature and polarization have reached high precision in estimating all the parameters that describe the current so-called standard cosmological model. Recent results about the integrated Sachs-Wolfe effect from cosmic microwave background anisotropies, galaxy surveys, and their cross-correlations are presented. Looking at fine signatures in the cosmic microwave background, such as the lack of power at low multipoles, the primordial power spectrum and the bounds on non-Gaussianities, complemented by galaxy surveys, we discuss inflationary physics a…
We analyze the spectrum of cosmic microwave background (CMB) anisotropies in the timescape cosmology: a potentially viable alternative to homogeneous isotropic cosmologies without dark energy. We exploit the fact that the timescape cosmology is extremely close to the standard cosmology at early epochs to adapt existing numerical codes to produce CMB anisotropy spectra, and to match these as closely as possible to the timescape expansion history. A variety of matching methods are studied and compared. We perform Markov Chain Monte Carlo analyses on the parameter space, and fit CMB multipoles $5…
The non-linear evolution of the energy density of the radiation is shown to induce spectral distortions of the cosmic microwave background both at recombination and during the reionization era. This distortion has the same spectral signature as the one produced by the re-scattering of photons by non-relativistic hot electrons, the thermal Sunyaev-Zeldovich effect, whose amplitude is quantified by a Compton y parameter. A diffuse y-sky is then expected to emerge from mode couplings in the non-linear evolution of the cosmological perturbations and to superimpose to the point source contributions…
The large-angle, low multipole cosmic microwave background (CMB) provides a unique view of the largest angular scales in the Universe. Study of these scales is hampered by the facts that we have only one Universe to observe, only a few independent samples of the underlying statistical distribution of these modes, and an incomplete sky to observe due to the interposing Galaxy. Techniques for reconstructing a full sky from partial sky data are well known and have been applied to the large angular scales. In this work we critically study the reconstruction process and show that, in practise, the …
We discuss the manner in which the primordial magnetic field (PMF) suppresses the cosmic microwave background (CMB) $B$ mode due to the weak-lensing (WL) effect. The WL effect depends on the lensing potential (LP) caused by matter perturbations, the distribution of which at cosmological scales is given by the matter power spectrum (MPS). Therefore, the WL effect on the CMB $B$ mode is affected by the MPS. Considering the effect of the ensemble average energy density of the PMF, which we call "the background PMF," on the MPS, the amplitude of MPS is suppressed in the wave number range of $k>0.0…
Recent measurements of the temperature field of Cosmic Microwave Background (CMB) provide tantalising evidence for violation of Statistical Isotropy (SI) that constitutes a fundamental tenet of contemporary cosmology. CMB space based missions, WMAP and Planck have observed a $7\%$ departure in the SI temperature field at large angular scales. However, due to higher cosmic variance at low multipoles, the significance of this measurement is not expected to improve from any future CMB temperature measurements. We demonstrate that weak lensing of the CMB due to scalar perturbations produce a corre…
We consider dark matter which have non-zero electromagnetic form factors like electric/magnetic dipole moments and anapole moment for fermionic dark matter and Rayleigh form factor for scalar dark matter. We consider dark matter mass $m_χ> \cal{ O}({\rm MeV})$ and put constraints on their mass and electromagnetic couplings from CMB and LSS observations. Fermionic dark matter with non-zero electromagnetic form factors can annihilate to $e^+ e^-$ and scalar dark matter can annihilate to $2γ$ at the time of recombination and distort the CMB. We analyze dark matter with multipole moments with Plan…
We revisit the physics of transitions from a general equation of state parameter to the final stage of slow-roll inflation. We show that it is unlikely for the modes comprising the cosmic microwave background to contain imprints from a pre-inflationary equation of state transition and still be consistent with observations. We accomplish this by considering observational consistency bounds on the amplitude of excitations resulting from such a transition. As a result, the physics which initially led to inflation likely cannot be probed with observations of the cosmic microwave background. Furthe…
The relic gravitational waves (gw) are the cleanest probe of the violent times in the very early history of the Universe. They are expected to leave signatures in the observed cosmic microwave background anisotropies. We significantly improved our previous analysis [1] of the 5-year WMAP $TT$ and $TE$ data at lower multipoles $\ell$. This more general analysis returned essentially the same maximum likelihood (ML) result (unfortunately, surrounded by large remaining uncertainties): the relic gw are present and they are responsible for approximately 20% of the temperature quadrupole. We identify…
Collisions between cosmic bubbles of different vacua are a generic feature of false vacuum eternal inflation scenarios. While previous studies have focused on the consequences of a single collision event in an observer's past, we begin here an investigation of the more general scenario allowing for many "mild" collisions intersecting our past light cone (and one another). We discuss the general features of multiple collision scenarios and consider their impact on the cosmic microwave background (CMB) temperature power spectrum, treating the collisions perturbatively. In a large class of models…
In models with a light scalar field (the `acceleron') coupled to neutrinos, neutrino masses depend on neutrino density. The resulting coupled system of mass varying neutrinos (MaVaNs) and the acceleron can act as a negative pressure fluid and is a candidate for dark energy \cite{Fardon:2003eh} . MaVaNs also allow for higher $Σ$m$_ν$ than terrestrial bounds, giving late forming warm dark matter. In this paper we study the effect of increasing neutrino mass on the CMB spectrum, implementing MaVaNs cosmology using CMBEASY. We find that the CMB spectrum is only affected at very low multipoles. Cos…
