Observations of the temperature anisotropies induced as light from the CMB passes through large scale structures in the late universe are a sensitive probe of the interactions of photons in such environments. In extensions of the Standard Model which give rise to mini-charged particles, photons propagating through transverse magnetic fields can be lost to pair production of such particles. Such a decrement in the photon flux would occur as photons from the CMB traverse the magnetic fields of galaxy clusters. Therefore late time CMB anisotropies can be used to constrain the properties of mini-charged particles. We outline how this test is constructed, and present new constraints on mini-charged particles from observations of the Sunyaev-Zel'dovich effect in the Coma cluster.
Mirror dark matter is a dissipative and self-interacting multiparticle dark matter candidate which can explain the DAMA, CoGeNT and CRESST-II direct detection experiments. This explanation requires photon-mirror photon kinetic mixing of strength $ε\sim 10^{-9}$. Mirror dark matter with such kinetic mixing can potentially leave distinctive signatures on the CMB anisotropy spectrum. We show that the most important effect of kinetic mixing on the CMB anisotropies is the suppression of the height of the third and higher odd peaks. If $ε\stackrel{>}{\sim} 10^{-9}$ then this feature can be observed …
CMB photons passing through a collapsing texture knot receive an energy shift, creating characteristic cold and hot spots on the sky. We calculate the anisotropy pattern produced by collapsing texture knots of arbitrary shape. The texture dynamics are solved numerically on a Minkowski background.
Angular power spectra of temperature anisotropies and polarization of the cosmic microwave background (CMB) as well as the linear matter power spectra are calculated for models with three light neutrinos with non-thermal phase-space distributions in the presence of a primordial stochastic magnetic field. The non-thermal phase-space distribution function is assumed to be the sum of a Fermi-Dirac and a gaussian distribution. It is found that the known effective description of the non-thermal model in terms of a twin thermal model with extra relativistic degrees of freedom can also be extended to…
Scattering of cosmic microwave background (CMB) radiation in galaxy clusters induces polarization signals determined by the quadrupole anisotropy in the photon distribution at the location of clusters. This "remote quadrupole" derived from the measurements of the induced polarization in galaxy clusters provides an opportunity of reconstruction of local CMB temperature anisotropies. In this {\em Letter} we develop an algorithm of the reconstruction through the estimation of the underlying primordial gravitational potential, which is the origin of the CMB temperature and polarization fluctuation…
Primordial magnetic fields present since before the epoch of matter-radiation equality have an effect on the anisotropies of the cosmic microwave background. The CMB anisotropies due to scalar perturbations are calculated in the gauge invariant formalism for magnetized adiabatic initial conditions. Furthermore the linear matter power spectrum is calculated. Numerical solutions are complemented by a qualitative analysis.
This PhD thesis (defended in 2014) is focused on the estimation of the CMB polarised anisotropies power spectra on a masked sky and on forecasts of constraints set on the primordial universe physics thanks to these anisotropies. After an introduction on the light polarisation, the standard model of cosmology and the CMB properties, I show the results obtained on the use and efficiency of pseudospectrum methods to correct for the so-called E-to-B leakage. Afterwards, I present the forecasts obtained on the detection of the tensor-to-scalar ratio r and on the detection of chiral gravity, using t…
Spectral distortions and anisotropies of the CMB provide independent and complementary probes to study energy injection processes in the early universe. Here we discuss the synergy between these observables, and show the promising future of spectral distortion missions to constrain both exotic and non-exotic energy injections. We show that conventional probes such as Big Bang Nucleosynthesis and CMB anisotropies can benefit from and even be surpassed by future spectral distortion experiments. For this, we have implemented a unified framework within the Boltzmann code CLASS to consistently trea…
We investigate the contribution of cosmic string loops to the Cosmic Microwave Background (CMB) anisotropies. This is done by extending the Unconnected Segment Model (USM) to include the contribution of the cosmic string loops created throughout the cosmological evolution of a cosmic string network to the stress-energy tensor. We then implement this extended USM in the publicly available CMBACT code and obtain the linear CDM power spectrum and the CMB angular power spectra generated by cosmic string loops. We find that the shape of the angular power spectra generated by loops is, in general, s…
We consider the impact of a stochastic background of primordial magnetic fields with non-vanishing helicity on CMB anisotropies in temperature and polarization. We compute the exact expressions for the scalar, vector and tensor part of the energy-momentum tensor including the helical contribution, by assuming a power-law dependence for the spectra and a comoving cutoff which mimics the damping due to viscosity. We also compute the parity-odd correlator between the helical and non-helical contribution which generate the TB and EB cross-correlation in the CMB pattern. We finally show the impact …
We study how the presence of world-sheet currents affects the evolution of cosmic string networks, and their impact on predictions for the cosmic microwave background (CMB) anisotropies generated by these networks. We provide a general description of string networks with currents and explicitly investigate in detail two physically motivated examples: wiggly and superconducting cosmic string networks. By using a modified version of the CMBact code, we show quantitatively how the relevant network parameters in both of these cases influence the predicted CMB signal. Our analysis suggests that pre…
We point out that if quantum field renormalization is taken into account the predictions of slow-roll inflation for both the scalar and tensorial power spectra change significantly for wavelengths that today are at observable scales
We propose a framework of Finsler space-time to explain the observed parity asymmetry and the power deficit in the low-$\ell$ ($2\leqslant \ell \leqslant 29$) multipole range of cosmic microwave background (CMB) temperature anisotropies. In the $3+1$ dimensional space-time, the three-dimensional space is described by a Randers-Finsler space, which is spatially irreversible, inducing the parity asymmetry in the CMB angular power spectrum. We estimate the constraints on the two parameters introduced by Finsler space-time via analyzing the low-$\ell$ angular power spectrum in PLANCK 2015 CMB temp…
Multi-field inflation models and non-Bunch-Davies vacuum initial conditions both predict sizeable non-Gaussian primordial perturbations and anisotropic $μ$-type spectral distortions of the cosmic microwave background (CMB) blackbody. While CMB anisotropies allow us to probe non-Gaussianity at wavenumbers $k\simeq 0.05\,{\rm Mpc^{-1}}$, $μ$-distortion anisotropies are related to non-Gaussianity of primordial perturbation modes with much larger wavenumbers, $k\simeq 740\,{\rm Mpc^{-1}}$. Through cross-correlations between CMB and $μ$-distortion anisotropies, one can therefore shed light on the a…
We determine the full C_l spectra and correlation functions of the temperature and polarization anisotropies in the CMB, generated by a source modeled by the large N limit of spontaneously broken global O(N)-theories. We point out a problem in the standard approach of treating the radiation-matter transition by interpolating the eigenvectors of the unequal-time correlators of the source energy-momentum tensor. This affects the CMB predictions from all type of cosmic defects. We propose a method to overcome this difficulty, and find that in the large-N global model that we study, differences in…
The primordial magnetic fields (PMFs) produced in the early universe are expected to be the origin of the large-scale cosmic magnetic fields. The PMFs are considered to leave a footprint on the cosmic microwave background (CMB) anisotropies due to both the electromagnetic force and gravitational interaction. In this paper, we investigate how the PMFs affect the CMB anisotropies on smaller scales than the mean-free-path of the CMB photons. We solve the baryon Euler equation with Lorentz force due to the PMFs, and we show that the vector-type perturbations from the PMFs induce the CMB anisotropi…
Anisotropies in distortions to the frequency spectrum of the cosmic microwave background (CMB) can be created through spatially varying heating processes in the early Universe. For instance, the dissipation of small-scale acoustic modes does create distortion anisotropies, in particular for non-Gaussian primordial perturbations. In this work, we derive approximations that allow describing the associated distortion field. We provide a systematic formulation of the problem using Fourier-space window functions, clarifying and generalizing previous approximations. Our expressions highlight the fac…
Recently, BICEP2 has reported the large tensor-to-scalar ratio $r=0.2^{+0.07}_{-0.05}$ from the observation of the cosmic microwave background (CMB) B-mode at degree-scales. Since tensor modes induce not only CMB B-mode but also the temperature fluctuations on large scales, to realize the consistent temperature fluctuations with the Planck result we should consider suppression of scalar perturbations on corresponding large scales. To realize such a suppression, we consider anti-correlated iso-curvature perturbations which could be realized in the simple curvaton model.
We study the effects of pre-recombination physics on the Stochastic Gravitational Wave Background (SGWB) anisotropies induced by the propagation of gravitons through the large-scale density perturbations and their cross-correlation with Cosmic Microwave Background (CMB) temperature and E-mode polarization ones. As examples of Early Universe extensions to the $Λ$CDM model, we consider popular models featuring extra relativistic degrees of freedom, a massless non-minimally coupled scalar field, and an Early Dark Energy component. Assuming the detection of a SGWB, we perform a Fisher analysis to …
We review in a pedagogical way the present status of the impact of non-Gaussianity (NG) on the Cosmic Microwave Background (CMB) anisotropies. We first show how to set the initial conditions at second-order for the (gauge invariant) CMB anisotropies when some primordial NG is present. However, there are many sources of NG in CMB anisotropies, beyond the primordial one, which can contaminate the primordial signal. We mainly focus on the NG generated from the post-inflationary evolution of the CMB anisotropies at second-order in perturbation theory at large and small angular scales, such as the …
We develop a linear perturbation theory for the spectral $y$-distortions of the cosmic microwave background (CMB). The $y$-distortions generated during the recombination epoch are usually negligible because the energy transfer due to the Compton scattering is strongly suppressed at that time, but they can be significant if there is a considerable amount of compensated isocurvature perturbation (CIP), which is not tightly constrained from the present CMB observations. The linear $y$-distortions explicitly depend on the baryon density fluctuations, therefore $y$ anisotropies can completely resol…
We propose a new mechanism of generating the $μ$ distortion in cosmic microwave background (CMB) originated from primordial gravitational waves. Such $μ$ distortion is generated by the damping of the temperature anisotropies through the Thomson scattering, even on scales larger than that of Silk damping. This mechanism is in sharp contrast with that from the primordial curvature (scalar) perturbations, in which the temperature anisotropies mainly decay by Silk damping effects. We estimate the size of the $μ$ distortion from the new mechanism, which can be used to constrain the amplitude of pri…
While the arcminute-scale Cosmic Microwave Background (CMB) anisotropies are due to secondary effects, point sources dominate the total anisotropy power spectrum. At high frequencies the point sources are primarily in the form of dusty, star-forming galaxies. Both Herschel and Planck have recently measured the anisotropy power spectrum of cosmic infrared background (CIB) generated by dusty, star-forming galaxies from degree to sub-arcminute angular scales, including the non-linear clustering of these galaxies at multipoles of 3000 to 6000 relevant to CMB secondary anisotropy studies. We scale …
We investigate the power spectrum of the distortion of Cosmic Microwave Background (CMB) due to the decay of the primordial magnetic fields. It is known that there are two-types of the CMB distortions, so-called μ- and y-types and we find that the signal of the y-type distortion becomes larger than that of the μ-type one. We also discuss cross power spectra between the CMB distortions and the CMB temperature anisotropy, which are naturally generated due to the existence of the primordial magnetic fields. We find that such cross power spectra have small amplitudes compared with the auto-power s…
Searching for the signal of primordial gravitational waves in the B-modes (BB) power spectrum is one of the key scientific aims of the cosmic microwave background (CMB) polarization experiments. However, this could be easily contaminated by several foreground issues, such as the thermal dust emission. In this paper we study another mechanism, the cosmic birefringence, which can be introduced by a CPT-violating interaction between CMB photons and an external scalar field. Such kind of interaction could give rise to the rotation of the linear polarization state of CMB photons, and consequently i…
We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instance, facilitate the search for primordial non-Gaussianity in future works. It also disentangles the non-…
The anisotropies of the cosmic microwave background (CMB) are computed for the half-turn space E_2 which represents a compact flat model of the Universe, i.e. one with finite volume. This model is inhomogeneous in the sense that the statistical properties of the CMB depend on the position of the observer within the fundamental cell. It is shown that the half-turn space describes the observed CMB anisotropies on large scales better than the concordance model with infinite volume. For most observer positions it matches the temperature correlation function even slightly better than the well studi…
Bulk motions of electrons along the line of sight induce secondary temperature fluctuations in the post-decoupling, reionized universe. In the presence of a magnetic field not only the scalar mode but also the vector mode act as a source for the bulk motion. The resulting angular power spectrum of temperature anisotropies of the cosmic microwave background is calculated assuming a simple model of reionization.Contributions from the standard adiabatic, curvature mode and a non helical magnetic field are included. The contribution due to magnetic fields with field strengths of order nG and negat…
The cosmic microwave background (CMB) anisotropies in spherical 3-spaces with a non-trivial topology are studied. This paper discusses the special class of the so-called double-action manifolds, which are for the first time analysed with respect to their CMB anisotropies. The CMB anisotropies are computed for all prism double-action manifolds generated by a binary dihedral and a cyclic group with a group order of up to 180 leading to 33 different topologies. Several spaces are found which show a suppression of the CMB anisotropies on large angular distances as it is found on the real CMB sky. …
As well as primary fluctuations, CMB temperature maps contain a wealth of additional information in the form of secondary anisotropies. Secondary effects that can be identified with individual objects, such as the thermal and kinetic Sunyaev-Zel'dovich (SZ) effects due to galaxy clusters, are difficult to unambiguously disentangle from foreground contamination and the primary CMB however. We develop a Bayesian formalism for rigorously characterising anisotropies that are localised on the sky, taking the TSZ and KSZ effects as an example. Using a Gibbs sampling scheme, we are able to efficientl…
The cosmic microwave background (CMB) temperature anisotropies from primordial magnetic fields are studied. In addition to the known passive and the compensated mode we discuss an inflationary magnetic mode in the curvature perturbation, present when magnetic fields are generated during inflation. This mode is absent if the generation mechanism is causal, e.g. a phase transition. We compute and discuss the effect of this mode on the observed CMB anisotropy spectrum, in comparison with the passive and compensated ones. We find that it dominates the CMB anisotropy, and consequently leads to stro…
We study Gravitational Waves (GWs) in the context of Massive Gravity, an extension to General Relativity (GR) where the fluctuations of the metric have a nonzero mass, and specifically investigate the effect of the tensor modes on the Cosmic Microwave Background (CMB) anisotropies. We first study the time evolution of the tensor modes in Massive Gravity and show that there is a graviton mass limit $m_l=10^{-66}g\sim 10^{-29}cm^{-1}$, so that for masses $m\leq m_l$ the tensor perturbations in Massive Gravity are indistinguishable from the corresponding ones in GR. Also, we show that short wavel…
We present constraints on the patchy reionization by measuring the trispectrum of the Planck 2015 cosmic microwave background (CMB) temperature anisotropies. The patchy reionization leads to anisotropies in the CMB optical depth, and the statistics of the observed CMB anisotropies is altered. We estimate the trispectrum of the CMB temperature anisotropies to constrain spatial variation of the optical depth. We show that the measured trispectrum is consistent with that from the standard lensed CMB simulation at $2σ$. While no evidence of the patchy reionization is found in the Planck 2015 tempe…
Anisotropies in the Cosmic Microwave Background (CMB) can be induced during the later stages of cosmic evolution, and in particular during and after the Epoch of Reionisation. Inhomogeneities in the ionised fraction, but also in the baryon density, in the velocity fields and in the gravitational potentials are expected to generate correlated CMB perturbations. We present a complete relativistic treatment of all these effects, up to second order in perturbation theory, that we solve using the numerical Boltzmann code SONG. The physical origin and relevance of all second order terms are carefull…
The weak lensing effect on the cosmic microwave background (CMB) induces distortions in spatial pattern of CMB anisotropies, and statistical properties of CMB anisotropies become a weakly non-Gaussian field. We first summarize the weak lensing effect on the CMB (CMB lensing) in the presence of scalar, vector and tensor perturbations. Then we focus on the lensing effect on CMB statistics and methods to estimate deflection angles and their power spectrum. We end by summarizing recent observational progress and future prospect.
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 analyze the alignment of the low multipoles (quadrupole and octupole) of various maps of the WMAP 5yr release: the CMB maps obtained with ILC and MCMC methods, the CMB map in the V band after foreground reduction, and, for comparison, the (not cleaned) V band map. We study how much this alignment is polluted by residuals on the Galactic region. Among the considered maps, the WMAP-ILC turns out to be the most clean map from the point of view of the proposed test. This result has been found studying the redistribution (due to the masking process) of each bin of the probability distribution fu…
Measurements of the cosmic microwave background (CMB) spectral distortions (SDs) will open a new window on the very early universe, providing new information complementary to that gathered from CMB temperature and polarization anisotropies. In this paper, we study their synergy as a function of the characteristics of the considered experiments. In particular, we examine a wide range of sensitivities for possible SD measurements, spanning from FIRAS up to noise levels 1000 times better than PIXIE, and study their constraining power when combined with current or future CMB anisotropy experiments…
We demonstrate that recent measurements of Cosmic Microwave Background temperature and polarization anisotropy made by the ACBAR, QUAD and BICEP experiments substantially improve the cosmological constraints on possible variations of the fine structure constant in the early universe. This data, combined with the five year observations from the WMAP mission yield the constraint alpha/alpha_0 = 0.987 \pm 0.012 at 68% c.l.. The inclusion of the new HST constraints on the Hubble constant further increases the accuracy to alpha/alpha_0 = 1.001 \pm 0.007 at 68% c.l., bringing possible deviations fro…
We propose a multi-scale edge-detection algorithm to search for the Gott-Kaiser-Stebbins imprints of a cosmic string (CS) network on the Cosmic Microwave Background (CMB) anisotropies. Curvelet decomposition and extended Canny algorithm are used to enhance the string detectability. Various statistical tools are then applied to quantify the deviation of CMB maps having a cosmic string contribution with respect to pure Gaussian anisotropies of inflationary origin. These statistical measures include the one-point probability density function, the weighted two-point correlation function (TPCF) of …
The method of weighted addition of multi-frequency maps, more commonly referred to as {\it Internal Linear Combination} (ILC), has been extensively employed in the measurement of cosmic microwave background (CMB) anisotropies and its secondaries along with similar application in 21cm data analysis. Here we argue and demonstrate that ILC methods can also be applied to data from absolutely-calibrated CMB experiments to extract average-sky signals in addition to the conventional CMB anisotropies. The performance of the simple ILC method is, however, limited, but can be significantly improved by a…
We propose a machine learning approach to the blind detection of extragalactic point sources on maps of the temperature anisotropies of the cosmic microwave background. Using realistic simulations of the microwave sky as seen by Planck, we train a convolutional neural network (CNN) that solves source detection as an image segmentation problem. We divide the sky into regions of progressively increasing Galactic foreground intensity and independently train specialized CNNs for each region. This strategy leads to promising levels of completeness and reliability, with our CNN substantially outperf…
Strong foreground contamination in high resolution CMB data requires masking which introduces statistical anisotropies and renders a full maximum likelihood analysis numerically intractable. Standard analysis methods like the pseudo-C_l framework lead to information loss due to estimator suboptimalities. We set out and validate a methodology for numerically efficient estimators for a masked sky that recover nearly as much information as a full maximum likelihood procedure. In addition to the standard pseudo-C_l statistic, the approach introduces an augmented basis designed to account for the m…
Gravitational lensing of the cosmic microwave background (CMB) is expected to be amongst the most powerful cosmological tools for ongoing and upcoming CMB experiments. In this work, we investigate a bias to CMB lensing reconstruction from temperature anisotropies due to the kinematic Sunyaev-Zel'dovich (kSZ) effect, that is, the Doppler shift of CMB photons induced by Compton-scattering off moving electrons. The kSZ signal yields biases due to both its own intrinsic non-Gaussianity and its non-zero cross-correlation with the CMB lensing field (and other fields that trace the large-scale struct…
The cosmic infrared background (CIB) anisotropies and cosmic microwave background (CMB) lensing are powerful measurements for exploring the cosmological and astrophysical problems. In this work, we measure the auto-correlation power spectrum of the CIB anisotropies in the Herschel-SPIRE HerMES Large Mode Survey (HeLMS) field, and the cross power spectrum with the CMB lensing measurements from the Planck satellite. The HeLMS field covers more than 270 deg^2, which is much larger than the previous analysis. We use the Herschel Level 1 time stream data to merge the CIB maps at 250, 350, and 500 u…
Spatially fluctuating primordial magnetic fields (PMFs) inhomogeneously reheat the Universe when they dissipate deep inside the horizon before recombination. Such an energy injection turns into an additional photon temperature perturbation. We investigate secondary cosmic microwave background (CMB) temperature anisotropies originated from this mechanism, which we call {\it inhomogeneous magnetic reheating}. We find that it can bring us information about non-linear coupling between PMFs and primordial curvature perturbations parametrized by $b_{\rm NL}$, which should be important for probing th…
Correlations between cosmic microwave background (CMB) temperature, polarization and spectral distortion anisotropies can be used as a probe of primordial non-Gaussianity. Here, we perform a reconstruction of $μ$-distortion anisotropies in the presence of Galactic and extragalactic foregrounds, applying the so-called Constrained ILC component separation method to simulations of proposed CMB space missions (PIXIE, LiteBIRD, CORE, PICO). Our sky simulations include Galactic dust, Galactic synchrotron, Galactic free-free, thermal Sunyaev-Zeldovich effect, as well as primary CMB temperature and $μ…
y-type spectral distortions of the cosmic microwave background allow us to detect clusters and groups of galaxies, filaments of hot gas and the non-uniformities in the warm hot intergalactic medium. Several CMB experiments (on small areas of sky) and theoretical groups (for full sky) have recently published y-type distortion maps. We propose to search for two artificial hot spots in such y-type maps resulting from the incomplete subtraction of the effect of the motion induced dipole on the cosmic microwave background sky. This dipole introduces, at second order, additional temperature and y-di…
We examine the impact of different anisotropic relics on inflation, in particular the predictions on the density perturbations. These relics can be the source of the large scale anomalies in the cosmic microwave background. There are two different types of background relics, one from the matter sector and the other purely from the metric. Although the angular-dependence of the statistical anisotropy in both cases are degenerate, the scale-dependence are observationally distinctive. In addition, we demonstrate that non-Bunch-Davies vacuum states can extend the statistical anisotropy to much sho…
We measure the skewness power spectrum of the Cosmic Microwave Background (CMB) anisotropies optimized for a detection of the secondary bispectrum generated by the correlation of the CMB lensing potential with integrated Sachs-Wolfe effect and the Sunyaev-Zel'dovich effect. The covariance of our measurements is generated by Monte-Carlo simulations of Gaussian CMB fields with noise properties consistent with Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data. When interpreting multi-frequency measurements we also take into account the confusion resulting from unresolved radio point sources…
We constrain the rotation angle $α$ of the linear polarization of CMB photons using the large angular scale (up to $\sim 4^\circ$) signal in WMAP 7 year data. At these scales, the CMB polarization pattern probes mostly the reionization era. A genuine rotation may be interpreted as cosmological birefringence, which is a well known tracer of new physics, through the breakdown of fundamental symmetries. Our analysis provides $α= -1.6^{\circ} \pm 1.7^{\circ} (3.4^{\circ})$ at 68% (95%) C.L. for the multipoles range $Δ\ell = 2-47$ not including an instrumental systematic uncertainty that the WMAP t…
We explore the microwave anisotropies at large angular scales produced by the emission from cold and large dust grains, expected to exist in the outer parts of the Solar System, using a simple toy model for this diuse emission. Its amplitude is constrained in the Far-IR by the COBE data and is compatible with simulations found in the literature. We analyze the templates derived after subtracting our model from the WMAP ILC 7 yr maps and investigate on the cosmological implications of such a possible foreground. The anomalies related to the low quadrupole of the angular power spectrum, the two-…
We investigate the weak lensing corrections to the CMB temperature and polarization anisotropies. We consider all the effects beyond the leading order: post-Born corrections, LSS corrections and, for the polarization anisotropies, the correction due to the rotation of the polarization direction between the emission at the source and the detection at the observer. We show that the full next-to-leading order correction to the B-mode polarization is not negligible on small scales and is dominated by the contribution from the rotation, this is a new effect not taken in account in previous works. C…
