B-type Polarization Research Articles

Statistical imprints of CMB B-type polarization leakage in an incomplete sky survey analysis

One of the main goals of modern cosmology is to search for primordial gravitational waves by looking on their imprints in the B-type polarization in the cosmic microwave background radiation. However, this signal is contaminated by various sources, including cosmic weak lensing, foreground radiations, instrumental noises, as well as the E-to-B leakage caused by the partial sky surveys, which should be well understood to avoid the misinterpretation of the observed data. In this paper, we adopt the E/B decomposition method suggested by Smith in 2006, and study the imprints of E-to-B leakage residuals in the constructed B-type polarization maps, ℬ(n̂), by employing various statistical tools. We find that the effects of E-to-B leakage are negligible for the ℬ-mode power spectrum, as well as the skewness and kurtosis analyses of ℬ-maps. However, if employing the morphological statistical tools, including Minkowski functionals and/or Betti numbers, we find the effect of leakage can be detected at very high confidence level, which shows that in the morphological analysis, the leakage can play a significant role as a contaminant for measuring the primordial B-mode signal and must be taken into account for a correct explanation of the data.

High-impedance NbSi TES sensors for studying the cosmic microwave background radiation

Precise measurements of the cosmic microwave background (CMB) are crucial in cosmology, because any proposed model of the universe must account for the features of this radiation. Of all CMB measurements that the scientific community has not yet been able to perform, the CMB B-mode polarization is probably the most challenging from the instrumental point of view. The signature of primordial gravitational waves, which give rise to a B-type polarization, is one of the goals in cosmology today and amongst the first objectives in the field. For this purpose, high-performance low-temperature bolometric cameras, made of thousands of pixels, are currently being developed by many groups, which will improve the sensitivity to B-mode CMB polarization by one or two orders of magnitude compared to the Planck satellite HFI detectors. We present here a new bolometer structure that is able to increase the pixel sensitivities and to simplify the fabrication procedure. This innovative device replaces delicate membrane-based structures and eliminates the mediation of phonons: the incoming energy is directly captured and measured in the electron bath of an appropriate sensor and the thermal decoupling is achieved via the intrinsic electron-phonon decoupling of the sensor at very low temperature. Reported results come from a 204-pixel array of Nb$_{x}$Si$_{1-x}$ transition edge sensors with a meander structure fabricated on a 2-inch silicon wafer using electron-beam co-evaporation and a cleanroom lithography process. To validate the application of this device to CMB measurements, we have performed an optical calibration of our sample in the focal plane of a dilution cryostat test bench. We have demonstrated a light absorption close to 20% and an NEP of about 7$\times10^{-16}$ W/$\sqrt{Hz}$, which is highly encouraging given the scope for improvement in this type of detectors.

Tensor power spectrum with holonomy corrections in loop quantum cosmology

In this paper we consider tensor perturbations produced at a bounce phase in the presence of holonomy corrections. Here, the bounce phase and holonomy corrections originate from loop quantum cosmology. We rederive formulas for the corrections of a model with scalar field content. Background dynamics with a free scalar field and multifluid potential are considered. Because the considerations are semiclassical, effects of quantum fluctuations of the background dynamics are not taken into account. Quantum and classical backreaction effects are also neglected. To find the spectrum of the gravitational waves, both analytical approximations and numerical investigations are performed. We have found analytical solutions on superhorizontal and subhorizontal regimes and derived the corresponding tensor power spectra. Also, the occupation number ${n}_{\mathbf{k}}$ and the parameter ${\ensuremath{\Omega}}_{\mathrm{gw}}$ were derived in the subhorizontal limit, leading to the extremely low present value of ${\ensuremath{\Omega}}_{\mathrm{gw}}$. The final results are the numerical power spectra of the gravitational waves produced in the presence of quantum holonomy corrections. The spectrum obtained has two UV and IR branches where ${\mathcal{P}}_{T}\ensuremath{\propto}{k}^{2}$; however, they have different prefactors. The spectrum connecting these regions is in the form of oscillations. We have found good agreement between the numerical spectrum and the spectrum obtained from the analytical model. The obtained spectrum can be directly applied as an initial condition for the inflationary modes. Based on our results, we discuss implications on the CMB radiation, in particular, on B-type polarization.

Effects of a primordial magnetic field on low and high multipoles of the cosmic microwave background

The existence of a primordial magnetic field (PMF) would affect both the temperature and polarization anisotropies of the cosmic microwave background (CMB). It also provides a plausible explanation for the possible disparity between observations and theoretical fits to the CMB power spectrum. Here we report on calculations of not only the numerical CMB power spectrum from the PMF, but also the correlations between the CMB power spectrum from the PMF and the primary curvature perturbations. We then deduce a precise estimate of the PMF effect on all modes of perturbations. We find that the PMF affects not only the CMB TT (temperature fluctuation), TE (cross correlation as temperature--E-type polarization) modes on small angular scales, but also on large angular scales. The introduction of a PMF leads to a better fit to the CMB power spectrum for the higher multipoles, and the fit at lowest multipoles can be used to constrain the correlation of the PMF with the density fluctuations for large negative values of the spectral index. Our prediction for the BB (B-type polarization) mode for a PMF average field strength |B{sub {lambda}}|=4.0 nG is consistent with the upper limit on the BB mode deduced from the latest CMB observations.more » We find that the BB mode is dominated by the vector mode of the PMF for higher multipoles. We also show that by fitting the complete power spectrum one can break the degeneracy between the PMF amplitude and its power spectral index.« less

Erratum: Bounds on cosmic strings from WMAP and SDSS [Phys. Rev. D72, 23513 (2005)

We find the constraints from WMAP and SDSS data on the fraction of cosmological fluctuations sourced by local cosmic strings using a Markov Chain Monte Carlo (MCMC) analysis. In addition to varying the usual 6 cosmological parameters and the string tension ($\mu$), we also varied the amount of small-scale structure on the strings. Our results indicate that cosmic strings can account for up to 7 (14)% of the total power of the microwave anisotropy at 68 (95)% confidence level. The corresponding bound on the string mass per unit length, within our string model, is $G\mu < 1.8 (2.7) \times 10^{-7}$ at 68 (95)% c.l., where this constraint has been altered from what appears below following the correction of errors in our cosmic string code outlined in a recent erratum, astro-ph/0604141. We also calculate the B-type polarization spectra sourced by cosmic strings and discuss the prospects of their detection.

Bpolarization of the CMB from Faraday rotation

We study the effect of Faraday rotation due to a uniform magnetic field on the polarization of the cosmic microwave background. Scalar fluctuations give rise only to parity-even E-type polarization of the cosmic microwave background. However in the presence of a magnetic field, a nonvanishing parity-odd B-type polarization component is produced through Faraday rotation. We derive the exact solution for the E and B modes generated by scalar perturbations including the Faraday rotation effect of a uniform magnetic field, and evaluate their cross correlations with temperature anisotropies. We compute the angular autocorrelation function of the B-modes in the limit that the Faraday rotation is small. We find that uniform primordial magnetic fields of present strength around B{sub 0}=10{sup -9} G rotate E-modes into B-modes with amplitude comparable to those due to the weak gravitational lensing effect at frequencies around {nu}=30 GHz. The strength of B-modes produced by Faraday rotation scales as B{sub 0}/{nu}{sup 2}. We evaluate also the depolarizing effect of Faraday rotation upon the cross correlation between temperature anisotropy and E-type polarization.

Gravitational lensing as a contaminant of the gravity wave signal in the CMB

Gravity waves (GWs) in the early Universe generate B-type polarization in the cosmic microwave background (CMB), which can be used as a direct way to measure the energy scale of inflation. Gravitational lensing contaminates the GW signal by converting the dominant E polarization into B polarization. By reconstructing the lensing potential from the CMB itself one can decontaminate the B mode induced by lensing. We present results of numerical simulations of B mode delensing using quadratic and iterative maximum-likelihood lensing reconstruction methods as a function of detector noise and beam. In our simulations we find that the quadratic method can reduce the lensing B noise power by up to a factor of 7, close to the no noise limit. In contrast, the iterative method shows significant improvements even at the lowest noise levels we tested. We demonstrate explicitly that with this method at least a factor of 40 noise power reduction in lensing induced B power is possible, suggesting that ${r=P}_{h}{/P}_{R}\ensuremath{\sim}{10}^{\ensuremath{-}6}$ may be achievable in the absence of sky cuts, foregrounds, and instrumental systematics. While we do not find any fundamental lower limit due to lensing, we find that for high-sensitivity detectors residual lensing noise dominates over the detector noise.

Signatures of primordial helicity in the CMBR

This work was done in collaboration with Tanmay Vachaspati and Serge Winitzki. We have studied ways in which helical primordial magnetic fields could be constrained by measurements of the cosmic microwave background radiation (CMBR). If there were helical flows in the primordial plasma at the time of recombination, they would produce parity violating temperature-polarization correlations ( C l TB and C l EB ). However, the magnitude of helical flows induced by helical magnetic fields is unobservably small. We discuss an alternate scheme for extracting the helicity of a stochastically homogeneous and isotropic primordial magnetic field using Faraday rotation measure maps of the CMBR and the power spectrum of B-type polarization ( C l BB ).

CMB polarization at large angular scales: Data analysis of the POLAR experiment

The coming flood of cosmic microwave background (CMB) polarization experiments, spurred by the recent detection of CMB polarization by the DASI and WMAP instruments, will be confronted by many new analysis tasks specific to polarization. For the analysis of CMB polarization data sets, the devil is truly in the details. With this in mind, we present details of the data analysis for the POLAR experiment, which recently led to the tightest upper limits on the polarization of the cosmic microwave background radiation at large angular scales. We discuss the data selection process, map-making algorithms, offset removal, and likelihood analysis which were used to find upper limits on the polarization. Stated using the modern convention for reporting CMB Stokes parameters, these limits are 5.0 \ensuremath{\mu}K on both E- and B-type polarization at 95% confidence. Finally, we discuss simulations used to test our analysis techniques and to probe the fundamental limitations of the experiment.

Small-scale cosmic microwave background polarization anisotropies due to tangled primordial magnetic fields

Tangled, primordial cosmic magnetic fields create small rotational velocity perturbations on the last scattering surface (LSS) of the cosmic microwave background radiation (CMBR). Such perturbations can contribute significantly to the CMBR temperature and polarization anisotropies at large l > 1000 or so, like the excess power detected by the Cosmic Background Imager (CBI) experiment. The magnetic contribution can be distinguished from most conventional signals, as they lead to CMBR polarization dominated by the odd-parity, B-type signal. Experiments like the Degree Angular Scale Interferometer (DASI) and the Wilkinson Microwave Anisotropy Probe (WMAP) have detected evidence for CMBR polarization at low l. Many experiments will also probe the large l regime. Therefore we calculate the polarization signals due to primordial magnetic fields for different spectra and different cosmological parameters. A scale-invariant spectrum of tangled fields which redshifts to a present value of B0= 3 × 10−9 G produces B-type polarization anisotropies of ∼0.3–0.4 μK between l∼ 1000 and 5000. Larger signals result if the spectral index of magnetic tangles is steeper, n > −3. The peak of the signal shifts to larger l for a Λ-dominated universe or if the baryon density is larger. The signal will also have non-Gaussian statistics. We also predict the much smaller E-type polarization and T–E cross-correlations for these models.

Signatures of primordial helicity in the CMBR

We have studied ways in which helical primordial magnetic fields could be constrained by measurements of the cosmic microwave background radiation (CMBR). If there were helical flows in the primordial plasma at the time of recombination, they would produce parity violating temperature-polarization correlations ( C l TB and C l EB ). However, the magnitude of helical flows induced by helical magnetic fields is unobservably small. We discuss an alternate scheme for extracting the helicity of a stochastically homogeneous and isotropic primordial magnetic field using Faraday rotation measure maps of the CMBR and the power spectrum of B-type polarization ( C l BB ).

Signatures of kinetic and magnetic helicity in the cosmic microwave background radiation

$P$ and $\mathrm{CP}$ violation in cosmology can be manifested as large-scale helical velocity flows in the ambient plasma and as primordial helical magnetic fields. We show that kinetic helicity at last scattering leads to temperature-polarization correlations ${(C}_{l}^{\mathrm{TB}}$ and ${C}_{l}^{\mathrm{EB}})$ in the cosmic microwave background radiation (CMBR) and calculate the magnitude of the effect. Helical primordial magnetic fields, expected from cosmic events such as electroweak baryogenesis, can lead to helical velocity flows and hence to nonvanishing correlations of the temperature and B-type polarization. However, we show that the magnitude of the induced helical flow is unobservably small because the helical component of a magnetic field is almost force-free. We discuss an alternate scheme for extracting the helicity of a stochastically homogeneous and isotropic primordial magnetic field using observations of the CMBR. The scheme involves constructing Faraday rotation measure maps of the CMBR and thus determining the sum of the helical and nonhelical components of the primordial magnetic field. The power spectrum of B-type polarization fluctuations, on the other hand, are sensitive only to the nonhelical component of the primordial magnetic field. The primordial magnetic helicity can then be derived by combining these two sets of observations.

CMBBpolarization to map the large-scale structures of the universe

We explore the possibility of using B-type polarization of the cosmic microwave background to map the large-scale structures of the Universe taking advantage of the lens effects on the CMB polarization. The functional relation between the $B$ component with the primordial CMB polarization and the line-of-sight mass distribution is explicated. Noting that a sizable fraction (at least 40%) of the dark halo population which is responsible for this effect can also be detected in a galaxy weak lensing survey, we present statistical quantities that should exhibit a strong sensitivity to this overlapping. We stress that it would be a sound test of the gravitational instability picture, independent of many systematic effects that may hamper lensing detection in CMB or a galaxy survey alone. Moreover, we estimate the intrinsic cosmic variance of the amplitude of this effect to be less than 8% for a $100 {\mathrm{deg}}^{2}$ survey with a ${10}^{\ensuremath{'}}$ CMB beam. Its measurement would then provide us with an original means for constraining the cosmological parameters, more particularly, as it turns out, the cosmological constant $\ensuremath{\Lambda}.$

Cosmic string lens effects on CMB polarization patterns

Extending the Kaiser-Stebbins mechanism we propose here a method for detecting relics of topological defects such as cosmic strings based on lens-induced small-scale B-type polarization in the cosmic microwave background. Models of inflation, in which large-scale structures of the Universe emerge from the inflaton fluctuations, do not exclude the formation of topological defects at the end of the inflationary phase. In such a case, we show that the lens effect of a string on the small-scale E-type polarization of the cosmic microwave background induces a significant amount of B-type polarization along the line of sight. The amplitude of the effect is estimated for different resolutions of cosmic microwave background experiments.