We present new constraints on cosmic variations of Newton's gravitational constant by making use of the latest CMB data from WMAP, BOOMERANG, CBI and ACBAR experiments and independent constraints coming from Big Bang Nucleosynthesis. We found that current CMB data provide constraints at the 10% level, that can be improved to 3% by including BBN data. We show that future data expected from the Planck satellite could constrain G at the 1.5% level while an ultimate, cosmic variance limited, CMB experiment could reach a precision of about 0.4%, competitive with current laboratory measurements.
The merger rate of primordial black holes depends on their initial clustering. In the absence of primordial non-Gaussianity correlating short and large-scales, primordial black holes are distributed à la Poisson at the time of their formation. However, primordial non-Gaussianity of the local-type may correlate primordial black holes on large-scales. We show that future experiments looking for CMB $μ$-distortion would test the hypothesis of initial primordial black hole clustering induced by local non-Gaussianity, while existing limits already show that significant non-Gaussianity is necessary …
We propose a theoretical framework that can possibly constrain the initial vacuum by Cosmic Microwave Background (CMB) observations. With a generic vacuum without any particular choice a priori, thereby keeping both the Bogolyubov coefficients in the analysis, we compute observable parameters from two- and three-point correlation functions. We are thus left with constraining four model parameters from the two complex Bogolyubov coefficients. We also demonstrate a method of finding out the constraint relations between the Bogolyubov coefficients using the theoretical normalization condition and…
Many extensions of Standard Model (SM) include a dark sector which can interact with the SM sector via a light mediator. We explore the possibilities to probe such a dark sector by studying the distortion of the CMB spectrum from the blackbody shape due to the elastic scatterings between the dark matter and baryons through a hidden light mediator. We in particular focus on the model where the dark sector gauge boson kinetically mixes with the SM and present the future experimental prospect for a PIXIE-like experiment along with its comparison to the existing bounds from complementary terrestri…
We briefly discuss the intriguing case of a phenomenological non-gravitational coupling in the dark sector, where the interaction is parameterized as an energy transfer either from dark matter to dark energy or the opposite. We show that a non-zero coupling with an energy flow from the latter to the former leads to a full reconciliation of the tension between high- and low-redshift observations present in the standard cosmological model.
We forecast combined future constraints from the cosmic microwave background and large-scale structure on the models of primordial non-Gaussianity. We study the generalized local model of non-Gaussianity, where the parameter f_NL is promoted to a function of scale, and present the principal component analysis applicable to an arbitrary form of f_NL(k). We emphasize the complementarity between the CMB and LSS by using Planck, DES and BigBOSS surveys as examples, forecast constraints on the power-law f_NL(k) model, and introduce the figure of merit for measurements of scale-dependent non-Gaussia…
We consider the dark matter (DM) scenarios consisting of the mixture of WIMPs and PBHs and study how much fraction of the total DM can be PBHs. In such scenarios, PBHs can accrete the WIMPs and consequently enhance the heating and ionization in the intergalactic medium due to WIMP annihilations. We demonstrate that the CMB data can give the stringent bounds on the allowed PBH fraction which are comparable or even tighter than those from the gamma ray data depending on the DM masses. For instance, the MCMC likelihood analysis using the Planck CMB data leads to the bound on PBH DM fraction with …
Tensor non-Gaussianities are a key ingredient to test the symmetries and the presence of higher spin fields during the inflationary epoch. Indeed, the shape of the three point correlator of the graviton is totally fixed by the symmetries of the de Sitter stage and, in the case of parity conservation, gets contributions only from the ordinary gravity action plus a higher derivative term called the (Weyl)$^3$ action. We discuss current and future bounds on the three point tensor contribution from the (Weyl)$^3$ term using cosmic microwave background (CMB) bispectra. Our results indicate that for…
A stochastic gravitational wave background (SGWB) will affect the CMB anisotropies via weak lensing. Unlike weak lensing due to large scale structure which only deflects photon trajectories, a SGWB has an additional effect of rotating the polarization vector along the trajectory. We study the relative importance of these two effects, deflection \& rotation, specifically in the context of E-mode to B-mode power transfer caused by weak lensing due to SGWB. Using weak lensing distortion of the CMB as a probe, we derive constraints on the spectral energy density ($Ω_{GW}$) of the SGWB, sourced at …
In the inhomogeneous Universe, the cosmological conversion of dark photons into ordinary photons (and vice versa) may happen at a great number of resonance redshifts. This alters the CMB observed energy spectrum and degree of small-scale anisotropies. We utilize results from the EAGLE simulation to obtain the conversion probability along random line-of-sights to quantify these effects. We then apply our results to the case where dark photons are sourced by dark matter decay and their high-redshift conversion into ordinary photons modify the global 21 cm signal expected from the cosmic dawn era…
We impose constraints on the topology of the Universe determined from a search for matched circles in the cosmic microwave background (CMB) temperature anisotropy patterns of the 7-year WMAP data. We pay special attention to the sensitivity of the method to residual foreground contamination of the sky maps. A search for pairs of matched back-to-back circles in the higher resolution WMAP W-band map allows tighter constraints to be imposed on topology. Our results rule out universes with topologies that predict pairs of such circles with radii larger than approximately 10 degrees. This places a …
We investigate the possibilities of constraining the light gravitino mass m_{3/2} from future cosmic microwave background (CMB) surveys. A model with light gravitino with the mass m_{3/2}<O(10) eV is of great interest since it is free from the cosmological gravitino problem and, in addition, can be compatible with many baryogenesis/leptogenesis scenarios such as the thermal leptogenesis. We show that the lensing of CMB anisotropies can be a good probe for m_{3/2} and obtain an expected constraint on m_{3/2} from precise measurements of lensing potential in the future CMB surveys, such as the P…
The $β$-exponential inflation is driven by a class of primordial potentials, derived in the framework of braneworld scenarios, that generalizes the well-known power law inflation. In this paper we update previous constraints on the minimal coupled $β$-exponential model [1] and extend the results also deriving the equations for the non-minimal coupled scenario. The predictions of both models are tested in light of the latest temperature and polarization maps of the Cosmic Microwave Background and clustering data. We also compare the predictions of these models with the standard $Λ$CDM cosmology…
We present proof of principle for a two way interplay between physics at very early Universe and late time observations. We find a relation between primordial mechanisms responsible for large scale power suppression in the primordial power spectrum and the value of reionization optical depth $τ$. Such mechanisms can affect the estimation of $τ$. We show that using future measurements of $τ$, one can obtain constraints on the pre-inflationary dynamics, providing a new window on the physics of the very early Universe. Furthermore, the new, re-estimated $τ$ can potentially resolve moderate discre…
The statistics of extremal points in the cosmic microwave background (CMB) temperature (hot and cold spots) have been well explored in the literature, and have been used to constrain models of the early Universe. Here, we extend the study of critical points in the CMB to the set that remains after removing extrema, namely the saddle points. We perform stacks of temperature and polarization about temperature saddle points in simulations of the CMB, as well as in data from the Planck satellite. We then compute the theoretical profile of saddle-point stacks, given the underlying power spectra of …
We study the possibility for constraining the topology of the Universe by means of the matched circles statistic applied to polarised cosmic microwave background (CMB) anisotropy maps. The advantages of using the CMB polarisation maps in studies of the topology over simply analysing the temperature data as has been done to-date are clearly demonstrated. We test our algorithm to search for pairs of matched circles on simulated CMB maps for a universe with the topology of 3-torus. It is found that the noise levels of both Planck and next generation CMB experiments data are no longer prohibitive …
The dispersion measure of extragalactic radio transients, such as of recently discovered Fast Radio Burst FRB150418, can be used to measure the column density of free electrons in the intergalactic medium. The same electrons also scatter the Cosmic Microwave Background (CMB) photons, affecting precision measurements of cosmological parameters. We explore the connection between the dispersion measure of radio transients existing during the Epoch of Reionization (EoR) and the total optical depth for the CMB, $τ_{CMB}$, showing that the existence of such transients would provide a new sensitive p…
Next-generation galaxy surveys will be able to measure perturbations on scales beyond the equality scale. On these ultra-large scales, primordial non-Gaussianity leaves signatures that can shed light on the mechanism by which perturbations in the early Universe are generated. We perform a forecast analysis for constraining local type non-Gaussianity and its two-parameter extension with a simple scale-dependence. We combine different clustering measurements from future galaxy surveys -- a 21cm intensity mapping survey and two photometric galaxy surveys -- via the multi-tracer approach. Furtherm…
The CMB temperature-redshift relation, T_CMB(z)=T_0(1+z), is a key prediction of the standard cosmology, but is violated in many non standard models. Constraining possible deviations to this law is an effective way to test the LambdaCDM paradigm and to search for hints of new physics. We have determined T_CMB(z), with a precision up to 3%, for a subsample (104 clusters) of the Planck SZ cluster catalog, at redshift in the range 0.01-- 0.94, using measurements of the spectrum of the Sunyaev Zel'dovich effect obtained from Planck temperature maps at frequencies from 70 to 353 GHz. The method ado…
We study the Hybrid Natural Inflation (HNI) model and some of its realisations in the light of recent CMB observations, mainly Planck temperature and WMAP-9 polarization, and compare with the recent release of BICEP2 dataset. The inflationary sector of HNI is essentially given by the potential $V(ϕ) = V_0(1+a\cos (\fracϕ{f} ) )$, where $a$ is a positive constant smaller or equal to one and $f$ is the scale of (pseudo Nambu-Goldstone) symmetry breaking. We show that to describe the HNI model realisations we only need two observables; the spectral index $n_s$, the tensor-to-scalar ratio, and a f…
Observational searches for large-scale vorticity modes in the late time Universe are underexplored. Within the standard $Λ$CDM model, this is well motivated given the observed properties of the cosmic microwave background (CMB). However, this means that searches for cosmic vorticity modes can serve as a powerful consistency test of our cosmological model. We show that through combining CMB measurements of the kinetic Sunyaev-Zel'dovich and the moving lens effects with galaxy survey data we can constrain vorticity fields independently from the large scale cosmic velocity field. This approach ca…
We present current and future constraints on equations of state for dark sector perturbations. The equations of state considered are those corresponding to a generalized scalar field model and time-diffeomorphism invariant $L(g)$ theories that are equivalent to models of a relativistic elastic medium and also Lorentz violating massive gravity. We develop a theoretical understanding of the observable impact of these models. In order to constrain these models we use CMB temperature data from Planck, BAO measurements, CMB lensing data from Planck and the South Pole Telescope, and weak galaxy lens…
The Planck experiment will soon provide a very accurate measurement of Cosmic Microwave Background anisotropies. This will let cosmologists determine most of the cosmological parameters with unprecedented accuracy. Future experiments will improve and complement the Planck data with better angular resolution and better polarization sensitivity. This unexplored region of the CMB power spectrum contains information on many parameters of interest, including neutrino mass, the number of relativistic particles at recombination, the primordial Helium abundance and the injection of additional ionizing…
Measuring the total neutrino mass is one of the most exciting opportunities available with next-generation cosmological data sets. We study the possibility of detecting the total neutrino mass using large-scale clustering in 21cm intensity mapping and photometric galaxy surveys, together with CMB information. We include the scale-dependent halo bias contribution due to the presence of massive neutrinos, and use a multi-tracer analysis in order to reduce cosmic variance. The multi-tracer combination of an SKAO-MID 21cm intensity map with Stage~4 CMB dramatically shrinks the uncertainty on total…
It is commonly assumed that the stochastic background of gravitational waves on cosmological scales follows an almost scale-independent power spectrum, as generically predicted by the inflationary paradigm. However, it is not inconceivable that the spectrum could have strongly scale-dependent features, generated, e.g., via transient dynamics of spectator axion-gauge fields during inflation. Using the temperature and polarisation maps from the \textit{Planck} and BICEP/Keck datasets, we search for such features, taking the example of a log-normal bump in the primordial tensor spectrum at CMB sc…
We forecast the number of galaxy clusters that can be detected via the thermal Sunyaev-Zeldovich (tSZ) signals by future cosmic microwave background (CMB) experiments, primarily the wide area survey of the CMB-S4 experiment but also CMB-S4's smaller delensing survey and the proposed CMB-HD experiment. We predict that CMB-S4 will detect 75,000 clusters with its wide survey of $f_{\rm sky}$ = 50% and 14,000 clusters with its deep survey of $f_{\rm sky}$ = 3%. Of these, approximately 1350 clusters will be at $z \ge 2$, a regime that is difficult to probe by optical or X-ray surveys. We assume CMB…
We present a new study on the elastic scattering cross section of dark matter (DM) and neutrinos using the latest cosmological data from Planck and large-scale structure experiments. We find that the strongest constraints are set by the Lyman-alpha forest, giving sigma_{DM-neutrino} < 10^{-33} (m_DM/GeV) cm^2 if the cross section is constant and a present-day value of sigma_{DM-neutrino} < 10^{-45} (m_DM/GeV) cm^2 if it scales as the temperature squared. These are the most robust limits on DM-neutrino interactions to date, demonstrating that one can use the distribution of matter in the Univer…
We confront the warm inflation observational predictions directly with the latest CMB data. We focus on a linear temperature (T) dissipative coefficient combined with the simplest model of inflation, a quartic chaotic potential. Although excluded in its standard cold inflation version, dissipation reduces the tensor-to-scalar ratio and brings the quartic chaotic model within the observable allowed range. We will use the CosmoMC package to derive constraints on the model parameters: the combination of coupling constants giving rise to dissipation, the effective number of relativistic degrees of…
We forecast the constraints on the parameters of neutrino physics with the constructions of Cosmic Microwave Background (CMB) temperature, E-mode polarization and lensing spectra for the ground-based Ali Cosmic Microwave Background Polarization Telescope (AliCPT). To implement the forecast calculations, we perform numerical simulations which show that AliCPT would yield the result $σ(N_{\mathrm{eff}})=0.42$ and $σ(M_ν)=0.18$ for the first year observation. Moreover, we investigate how the instrumental parameters, such as noise level, full width at half maxima (FWHM), and sky coverage can affec…
We revisit the method of using the photon-graviton conversion mechanism in the presence of the external magnetic field to probe small-scale primordial magnetic fields that may exist between the last scattering surface and present. Specifically, we investigate impacts on the conversion efficiency due to the presence of matter, including the plasma collective effect and the atomic polarizability. In general, these effects tend to reduce the conversion probability. Under this more realistic picture and based on the precision of COBE's measurement of CMB (cosmic microwave background) blackbody spe…
We forecast how current ({\planck}) and future ({\prism}) cosmic microwave background (CMB) experiments constrain the adiabatic mode and its admixtures with primordial isocurvature modes, using measurements of the reconstructed CMB lensing potential and lensing-induced CMB B-mode polarization anisotropies in combination with the CMB temperature and E-mode polarization anisotropies. We first study the characteristic features of the CMB temperature, polarization and lensing spectra for adiabatic and isocurvature modes. We then consider how lensing-induced B-mode polarization and lensing potentia…
We discuss the thermodynamic and dynamical properties of a variable dark energy model with density scaling as $ρ_x \propto (1+z)^{m}$, z being the redshift. These models lead to the creation/disruption of matter and radiation, which affect the cosmic evolution of both matter and radiation components in the Universe. In particular, we have studied the temperature-redshift relation of radiation, which has been constrained using a recent collection of cosmic microwave background (CMB) temperature measurements up to $z \sim 3$. We find that, within the uncertainties, the model is indistinguishable…
We present constraints on a cosmic string network with a measurement of weak gravitational lensing from CMB temperature map. The cosmic string network between observer and last scattering surface of CMB photons generates vector and/or tensor metric perturbations, and the deflection of CMB photons by these gravitational fields has curl mode which is not produced by the scalar metric perturbations. In this paper, we use the power spectrum of curl mode obtained from Planck to constrain the string tension, Gμ, and the reconnection probability, P. In demonstrating the parameter constraints with Pla…
We study the cross correlation of damped Ly$α$ systems (DLAs) and their background quasars, using the most updated DLA catalog and the Planck 2018 CMB lensing convergence field. Our measurement suggests that the DLA bias $b_{\rm DLA}$ is smaller than $3.1$, corresponding to $\log(M/M_\odot h^{-1})\leq 12.3$ at a confidence of $90\%$. These constraints are broadly consistent with Alonso et al. (2018) and previous measurements by cross-correlation between DLAs and the Ly$α$ forest (e.g. Font-Ribera et al. 2012; Perez-Rafols et al. 2018). Further, our results demonstrate the potential of obtainin…
We study the predictions for structure formation in an induced gravity dark energy model with a quartic potential. By developing a dedicated Einstein-Boltzmann code, we study self-consistently the dynamics of homogeneous cosmology and of linear perturbations without using any parametrization. By evolving linear perturbations with initial conditions in the radiation era, we accurately recover the quasi-static analytic approximation in the matter dominated era. We use Planck 2013 data and a compilation of baryonic acoustic oscillation (BAO) data to constrain the coupling $γ$ to the Ricci curvatu…
A period of early matter domination can give rise to the correct dark matter abundance for a broad range of dark matter annihilation rate $\langle σ_{\rm ann} v \rangle_{\rm f}$. Here, we examine this scenario for situations where $\langle σ_{\rm ann} v \rangle_{\rm f}$ is below the nominal value for thermal dark matter $3 \times 10^{-26}$ cm$^3$ s$^{-1}$ as possibly indicated by some recent experiments. We show that obtaining the correct relic abundance sets a lower bound on the duration of early matter domination era in this case. On the other hand, provided that the post-inflationary univer…
The Sunyaev-Zel'dovich (SZ) effects are produced by the interaction of cosmic microwave background (CMB) photons with the ionized and diffuse gas of electrons inside galaxy clusters integrated along the line of sight. The two main effects are the thermal SZ (tSZ) produced by thermal pressure inside galaxy clusters and the kinetic SZ (kSZ) produce by peculiar motion of galaxy clusters compared to CMB rest-frame. The kSZ effect is particularly challenging to measure as it follows the same spectral behavior as the CMB, and consequently can not be separated from the CMB using spectral consideratio…
Constraining Inflationary Particle Production with CMB Polarization
Columbia University（哥伦比亚大学）；Leinweber Institute for Theoretical Physics at Stanford（斯坦福莱因韦伯理论物理研究所）；Kavli Institute for Particle Astrophysics and Cosmology（卡弗里粒子天体物理学与宇宙学研究所）；Simons Society of Fellows, Simons Foundation（西蒙斯基金会西蒙斯研究员协会）
The measurement of the optical depth to free electrons, tau_r, in the cosmic microwave background (CMB) provides an important constraint on reionization, but is degenerate to more complex reionization models. Small angular-scale CMB measurements of the kinetic Sunyaev-Zeldovich (kSZ) and Ostriker-Vishniac (OV) effects have the potential to break this degeneracy. We calculate the OV signal for various extended reionization histories described by a simple analytic form. These models are parametrized by dz, the duration of the reionization event. For reionization histories with identical values o…
In this paper, we perform a forecast analysis to test the capacity of future baryon acoustic oscillation (BAO) and cosmic microwave background (CMB) experiments to constrain phenomenological interacting dark energy models using the Fisher matrix formalism. We consider a Euclid-like experiment, in which BAO measurements is one of the main goals, to constrain the cosmological parameters of alternative cosmological models. Moreover, additional experimental probes can more efficiently provide information on the parameters forecast, justifying also the inclusion in the analysis of a future ground-b…
We forecast the prospective constraints on the ionized gas model $f_{\rm gas}(z)$ at different evolutionary epochs via the tomographic cross-correlation between kinetic Sunyaev-Zeldovich (kSZ) effect and the reconstructed momentum field at different redshifts. The experiments we consider are the Planck and CMB Stage-4 survey for CMB and the SDSS-III for the galaxy spectroscopic survey. We calculate the tomographic cross-correlation power spectrum, and use the Fisher matrix to forecast the detectability of different $f_{\rm gas}(z)$ models. We find that for constant $f_{\rm gas}$ model, Planck …
We constrain the deviation of adiabatic evolution of the Universe using the data on the Cosmic Microwave Background (CMB) temperature anisotropies measured by the {\it Planck} satellite and a sample of 481 X-ray selected clusters with spectroscopically measured redshifts. To avoid antenna beam effects, we bring all the maps to the same resolution. We use a CMB template to subtract the cosmological signal while preserving the Thermal Sunyaev-Zeldovich (TSZ) anisotropies; next, we remove galactic foreground emissions around each cluster and we mask out all known point sources. If the CMB black-b…
I summarize the recent advances in determining the effects of self-annihilating WIMP dark matter on the modification of the recombination history, at times earlier than the formation of astrophysical objects. Depending on mass and self-annihilation cross section, WIMP DM can reproduce sizable amounts of the total free electron abundance at z > 6; as known, this affects the CMB temperature and polarization correlation spectra, and can be used to place stringent bounds in the particle mass vs cross-section plane. WMAP5 data already strongly disfavor the region capable to explain the recent cosmi…
The hypothesis of the self-induced collapse of the inflaton wave function was proposed as responsible for the emergence of inhomogeneity and anisotropy at all scales. This proposal was studied within an almost de Sitter space-time approximation for the background, which led to a perfect scale-invariant power spectrum, and also for a quasi-de Sitter background, which allows to distinguish departures from the standard approach due to the inclusion of the collapse hypothesis. In this work we perform a Bayesian model comparison for two different choices of the self-induced collapse in a full quasi…
We explore constraints on dark energy and modified gravity with forecast 21cm intensity mapping measurements using the Effective Field Theory approach. We construct a realistic mock data set forecasting a low redshift 21cm signal power spectrum $P_{21}(z,k)$ measurement from the MeerKAT radio-telescope. We compute constraints on cosmological and model parameters through Monte Carlo Markov chain techniques, testing both the constraining power of $P_{21}(k)$ alone and its effect when combined with the latest Planck 2018 CMB data. We complement our analysis by testing the effects of tomography fr…
In this paper I provide a general framework based on $δN$ formalism to study the features of unavoidable higher dimensional non-renormalizable Kähler operators for ${\cal N}=1$ supergravity (SUGRA) during primordial inflation from the combined constraint on non-Gaussianity, sound speed and CMB dipolar asymmetry as obtained from the recent Planck data. In particular I study the nonlinear evolution of cosmological perturbations on large scales which enables us to compute the curvature perturbation, $ζ$, without solving the exact perturbed field equations. Further I compute the non-Gaussian param…
Constraining Primordial Black Holes via p-wave annihilation in light of CMB Spectral Distortion and 21-cm global signal
National Institute of Technology, Meghalaya（梅加拉亚国立技术学院）；Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院）；University of Chinese Academy of Sciences（中国科学院大学）
We investigate the constraints on the reionization history of the Universe from a joint analysis of the cosmic microwave background and neutral hydrogen fraction data. The $\tanh$ parametrization and principal component analysis methods are applied to the reionization history respectively. The commonly used $\tanh$ parametrization is oversimplistic when the neutral hydrogen fraction data are taken into account. Using the principal component analysis method, the reconstructed reionization history is consistent with the neutral hydrogen fraction data. With the principal component analysis method…
The presence of a primordial magnetic field would have induced resonant conversions between photons and axion-like particles (ALPs) during the thermal history of the Universe. These conversions would have distorted the blackbody spectrum of the cosmic microwave background (CMB). In this context, we derive bounds on the photon-ALP resonant conversions using the high precision CMB spectral data collected by the FIRAS instrument on board of the Cosmic Background Explorer. We obtain upper limits on the product of the photon-ALP coupling constant g times the magnetic field strength B down to g B > …
With future galaxy surveys, a huge number of Fourier modes of the distribution of the large scale structures in the Universe will become available. These modes are complementary to those of the CMB and can be used to set constraints on models of the early universe, such as inflation. Using a MCMC analysis, we compare the power of the CMB with that of the combination of CMB and galaxy survey data, to constrain the power spectrum of primordial fluctuations generated during inflation. We base our analysis on the Planck satellite and a spectroscopic redshift survey with configuration parameters cl…
The Sunyaev-Zel'dovich (SZ) effect introduces a specific distortion of the blackbody spectrum of the cosmic microwave background (CMB) radiation when it scatters off hot gas in clusters of galaxies. The frequency dependence of the distortion is only independent of the cluster redshift when the evolution of the CMB radiation is adiabatic. Using 370 clusters within the redshift range $0.07\lesssim z\lesssim1.4$ from the largest SZ-selected cluster sample to date from the Atacama Cosmology Telescope, we provide new constraints on the deviation of CMB temperature evolution from the standard model …
Primordial magnetic fields could provide an explanation for the galactic magnetic fields observed today, in which case they may also leave interesting signals in the CMB and the small-scale matter power spectrum. We discuss how to approximately calculate the important non-linear magnetic effects within the guise of linear perturbation theory, and calculate the matter and CMB power spectra including the SZ contribution. We then use various cosmological datasets to constrain the form of the magnetic field power spectrum. Using solely large-scale CMB data (WMAP7, QUaD and ACBAR) we find a 95% CL …
