Massimo Giovannini
The temperature and polarization inhomogeneities of the Cosmic Microwave Background might bear the mark of pre-decoupling magnetism. The parameters of a putative magnetized background are hereby estimated from the observed temperature autocorrelation as well as from the measured temperature-polarization cross-correlation.
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Detection of relic gravitational waves, through their imprint in the cosmic microwave background radiation, is one of the most important tasks for the planned CMBPol mission. In the simplest viable theoretical models the gravitational wave 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 potential observations of the CMBPol mission, which is expected to detect the relic gravitational waves if $r\gtrsim0.001$. The influence…
The tensor contribution to the $V$-mode polarization induced by a magnetized plasma at last scattering vanishes exactly. Conversely a polarized background of relic gravitons cannot generate a $V$-mode polarization. The reported results suggest that, in the magnetized $Λ$CDM paradigm, the dominant source of circular dichroism stems from the large-scale fluctuations of the spatial curvature.
We study the most general effects of relic vector fields on the inflationary background and density perturbations. Such effects are observable if the number of inflationary e-folds is close to the minimum requirement to solve the horizon problem. We show that this can potentially explain two CMB large scale anomalies: the quadrupole-octopole alignment and the quadrupole power suppression. We discuss its effect on the parity anomaly. We also provide analytical template for more detailed data comparison.
We investigate the effects of the presence of relic classical superhorizon inhomogeneities during inflation. This superhorizon inhomogeneity appears as a gradient locally and picks out a preferred direction. Quantum fluctuations on this slightly inhomogeneous background are generally statistical anisotropic. We find a quadrupole modification to the ordinary isotropic spectrum. Moreover, this deviation from statistical isotropy is scale-dependent, with a $\sim -1/k^2$ factor. This result implies that the statistical anisotropy mainly appears on large scales, while the spectrum on small scales r…
Analyzing the imprint of relic gravitational waves (RGWs) on the cosmic microwave background (CMB) power spectra provides a way to determine the signal of RGWs. In this Letter, we discuss a statistical bias, which could exist in the data analysis and has the tendency to overlook the RGWs. We also explain why this bias exists, and how to avoid it.
String Theory and Supergravity allow, in principle, to follow the transition of the inflaton from pre-inflationary fast roll to slow roll. This introduces an infrared depression in the primordial power spectrum that might have left an imprint in the CMB anisotropy, if it occurred at accessible wavelengths. We model the effect extending $Λ$CDM with a scale $Δ$ related to the infrared depression and explore the constraints allowed by {\sc Planck} data, employing also more conservative, wider Galactic masks in the low resolution CMB likelihood. In an extended mask with $f_{sky}=39\%$, we thus fin…
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 $\ell_t^*$…
In this talk we elaborate on a mechanism to generate local contributions to the curvature perturbation in isolated patches of the Cosmic Microwave Background (CMB). The mechanism, based on the generation of an out-of-equilibrium configuration in fluctuating scalar fields of mass $m\sim H$ during a sustained stage of fast-roll inflation, has been recently shown to be capable of accounting for some of the most robust large-angle anomalies detected in the CMB. In this talk, we show in detail how the embedding of the mechanism into models including vector fields can result in the breaking of stati…
In this paper, we discuss the constraint on the relic gravitational waves by both temperature and polarization anisotropies power spectra of cosmic microwave background radiation. Taking into account the instrumental noises of Planck satellite, we calculate the signal-to-noise ratio $S/N$ by the simulation and the analytic approximation methods. We find that, comparing with the $BB$ channel, the value of $S/N$ is much improved in the case where all the power spectra, $TT$, $TE$, $EE$ and $BB$, are considered. If the noise power spectra of Planck satellite increase for some reasons, the value o…
The B-mode polarization of the cosmic microwave background (CMB) radiation is an excellent information channel for the detection of relic gravitational waves. However, the detection is contaminated by the B-mode polarization generated by some other effects. In this paper, we discuss the contaminations caused by the cosmological birefringence, which converts the CMB E-mode to the B-mode, and forms the effective noise for the detection of gravitational waves. We find that this contamination is significant, if the rotation angle is large. However, this kind of B-mode can be properly de-rotated, a…
Light thermal relics of the hot big bang, often quantified by the parameter $N_\mathrm{eff}$, are one of the primary targets of cosmological measurements. At present, the energy density in such relics is constrained to be less than ten percent of the total energy density in radiation. Upcoming cosmic microwave background (CMB) experiments, however, have the potential to measure the radiation density at the one-percent level, which is close to well-motivated theoretical targets. In this paper, we explore to what degree the CMB observations can be enhanced by future large-scale structure surveys…
Constraining UV freeze-in of light relics with current and next-generation CMB observations
本研究针对早期宇宙轻遗迹紫外冻结产生场景，计算多类BSM基准模型在新参数空间的$ΔN_{\rm eff}$贡献，分析表明下一代CMB实验可补充或超越现有手段对轻遗迹与SM耦合的约束。
According to the CMB observations, Mielczarek (\cite{Mielczarek}) evaluated the reheating temperature, which could help to determine the history of the Universe. In this paper, we recalculate the reheating temperature using the new data from WMAP 7 observations. Based on that, we list the approximate solutions of relic gravitational waves (RGWs) for various frequency bands. With the combination of the quantum normalization of RGWs when they are produced and the CMB observations, we obtain the relation between the tensor-to-scalar ratio $r$ and the inflation index $β$ for a given scalar spectra…
A thermal gravitational wave background can be produced in the early Universe if a radiation dominated epoch precedes the usual inflationary stage. This background provides a unique way to study the initial state of the Universe. We discuss the imprint of this thermal spectra of gravitons on the cosmic microwave background (CMB) power spectra, and its possible detection by CMB observations. Assuming the inflationary stage is a pure de Sitter expansion we find that, if the number of e-folds of inflation is smaller than 65, the signal of this thermal spectrum can be detected by the observations …
The forthcoming release of data from the Planck mission, and possibly from the next round of Wilkinson Microwave Anisotropy Probe (WMAP) observations, make it necessary to revise the evaluations of relic gravitational waves in the existing data and, at the same time, to refine the assumptions and data analysis techniques in preparation for the arrival of new data. We reconsider with the help of the commonly used CosmoMC numerical package the previously found indications of relic gravitational waves in the 7-year (WMAP7) data. The CosmoMC approach reduces the confidence of these indications fro…
We compare the detection abilities for the relic gravitational waves by two kinds of forthcoming cosmic microwave background radiation (CMB) experiments, space-based Planck satellite and the various ground-based experiments. Comparing with the ground-based experiments, Planck satellite can observe all the CMB power spectra in all the multipole range, but having much larger instrumental noises. We find that, for the uncertainty of the tensor-to-scalar ratio $Δr$, PolarBear (II) as a typical ground-based experiment can give much smaller value than Planck satellite. However, for the uncertainty o…
Relic gravitational waves (RGWs) leave well-understood imprints on the anisotropies in the temperature and polarization of cosmic microwave background (CMB) radiation. In the TT and TE information channels, which have been well observed by WMAP and Planck missions, RGWs compete with density perturbations mainly at low multipoles. It is dangerous to include high-multipole CMB data in the search for gravitational waves, as the spectral indices may not be constants. In this paper, we repeat our previous work [W.Zhao & L.P.Grishchuk, Phys.Rev.D {\bf 82}, 123008 (2010)] by utilizing the Planck TT a…
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…
A fully QED/relativistic theory of light pressure of CMB radiation and Fokker-Planck equation for electron distribution combined with cosmologic relation for CMB temperature, T, yields analytic results for the evolution of the distribution over large span of time and energies. A strong imprint of CMB on electrons transpires via formation of "frozen non-equilibrium" state of electrons in current epoch, and possible existence of cutoff and narrow spectral lines as remnants of high-T sources.
We calculate how the relic density of dark matter particles is altered when their annihilation is enhanced by the Sommerfeld mechanism due to a Yukawa interaction between the annihilating particles. Maintaining a dark matter abundance consistent with current observational bounds requires the normalization of the s-wave annihilation cross section to be decreased compared to a model without enhancement. The level of suppression depends on the specific parameters of the particle model, with the kinetic decoupling temperature having the most effect. We find that the cross section can be reduced by…
One of the primary targets of current and future cosmological observations are light thermal relics of the hot big bang. Within the Standard Model of particle physics, an important thermal relic are cosmic neutrinos, while interesting extensions predict new light particles which are even more weakly coupled to ordinary matter. These elusive particles may nonetheless be produced efficiently in the early universe and their gravitational influence could be detectable in cosmological observables. In this thesis, we describe how measurements of the cosmic microwave background (CMB) and the large-sc…
We investigate constraints on the abundance of primordial black holes (PBHs) in the mass range 10^{15}-10^{17} g using data from the Cosmic Microwave Background (CMB) and MeV extragalactic gamma-ray background (EGB). Hawking radiation from PBHs with lifetime greater than the age of the universe leaves an imprint on the CMB through modification of the ionization history and the damping of CMB anisotropies. Using a model for redshift dependent energy injection efficiencies, we show that a combination of temperature and polarization data from Planck provides the strongest constraint on the abunda…
A massive particle decaying into neutrinos in the early Universe is known to be less constrained than if it was decaying into other standard model particles. However, even if the decay proceeds into neutrinos, the latter still inevitably emit secondary particles undergoing electromagnetic interactions that can be probed. We analyse in details how sensitive various cosmological probes are to such secondary particles, namely CMB anisotropies, CMB spectral distortions, and Big Bang Nucleosynthesis. For relics whose lifetime is shorter than the age of the Universe, this leads to original and strin…
Scaling Transformations and the Origins of Light Relics Constraints from Cosmic Microwave Background Observations
本文通过标度变换解析CMB对轻遗迹的约束来源，提出参考模型以区分约束成因，为构建规避CMB轻遗迹约束的宇宙学模型提供理论支持。
The existence and cosmological signatures of a relic background of very weakly interacting sub-eV particles (WISPs), produced by photon-WISP oscillations is reviewed.
It is argued that large scale angle correlations of the Cosmic Microwave Background Radiation (CMBR) temperature fluctuations measured by Wilkinson Microwave Anisotropy Probe (WMAP) mission may have a trace of discrete symmetries of quantum gravity
The cosmological birefringence caused by the coupling between the cosmic scalar field and the cosmic microwave background (CMB) photons through the Chern-Simons term can rotate the polarization planes of the photons, and mix the CMB E-mode and B-mode polarizations. The rotation angle induced by the dynamical scalar field can be separated into the isotropic background part and the anisotropic fluctuations. The effect of the background part has been be studied in the previous work (Zhao & Li, arXiv:1402.4324). In this paper, we focus on the influence of the anisotropies of the rotation angle. We…
Forecasting Constraints on Non-Thermal Light Massive Relics from Future CMB Experiments (CMB-S4/Simons Observatory)
本文通过Fisher预测分析了非热轻质量残余物模型对未来CMB实验的约束，并比较了不同分布模型的参数相关性与不确定性。
Sensitivity of Next-Generation CMB Surveys to Neutrinos and Other Light Relics
本研究利用DRAFT工具对CMB-S4不同巡天配置的$N_\mathrm{eff}$测量灵敏度做Fisher矩阵预测，给出精度结果并探讨其对早期宇宙物理研究的意义。
In the standard $Λ$CDM model, neutrinos are treated as radiation, with their masses and possible degeneracy ignored. In this paper, we compute the impact of a finite relic neutrino degeneracy $ξ$ on the CMB angular power spectra, and obtain constraints on $ξ$ using current cosmological data sets. We find that $ξ\approx O(1)$ is still allowed. We also study the correlations between $ξ$, the Hubble parameter $H_0$, and the spectral index $n_s$. Due to these correlations, the CMB constraints on inflation models are loosened when $ξ$ is fitted together with other cosmological parameters, such that…
Rapid Methods for Modeling Overdensities of Massive Neutrinos and Other Non-Cold Relics
提出一种基于 N-1-body 模拟的高效数值框架，可快速计算平坦 FRW 宇宙中球对称暗物质晕附近的中微子密度剖面，并支持灵活参数扫描与新物理整合。
Distinct signatures of spinning PBH domination and evaporation: doubly peaked gravitational waves, dark relics and CMB complementarity
本文扩展了旋转超低质量原初黑洞（PBH）的研究，探讨其蒸发产生的暗辐射与暗物质特征，发现诱导引力波背景与CMB测量存在互补性，未来实验可借此约束PBH参数空间并揭示早期宇宙膨胀历史。
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…
Interacting light thermal-relic dark matter: self-consistent cosmological bounds
本文利用CMB数据自洽约束轻量热遗迹暗物质的质量、DM-重子散射及湮灭截面，揭示参数简并并给出偶极矩暗物质模型的新宇宙学界限。
Relic gravitational waves (RGWs) , a background originated during inflation, would give imprints on the pulsar timing residuals. This makes RGWs be one of important sources for detection using the method of pulsar timing. In this paper, we discuss the effects of RGWs on the single pulsar timing, and give quantitively the timing residuals caused by RGWs with different model parameters. In principle, if the RGWs are strong enough today, they can be detected by timing a single millisecond pulsar with high precision after the intrinsic red noise in pulsar timing residuals were understood, even tho…
A number of theoretically well-motivated additions to the standard cosmological model predict weak signatures in the form of spatially localized sources embedded in the cosmic microwave background (CMB) fluctuations. We present a hierarchical Bayesian statistical formalism and a complete data analysis pipeline for testing such scenarios. We derive an accurate approximation to the full posterior probability distribution over the parameters defining any theory that predicts sources embedded in the CMB, and perform an extensive set of tests in order to establish its validity. The approximation is…
We examine the vector-portal inelastic dark matter (DM) model with DM mass $m_χ$ and dark photon mass $m_{A'}$, in the `forbidden dark matter' regime where $1 \lesssim m_{A'}/m_χ\lesssim 2$, carefully tracking the dark sector temperature throughout freezeout. The inelastic nature of the dark sector relaxes the stringent cosmic microwave background (CMB) and self-interaction constraints compared to symmetric DM models. We determine the CMB limits on both annihilations involving excited states and annihilation into $e^+e^-$ through initial-state-radiation of an $A'$, as well as limits on the DM …
Probing light relics through cosmic dawn
研究表明，将SKA等宇宙黎明21厘米巡测与CMB-S4等实验结合，可显著提升$N_{\rm eff}$约束，从而探测多种轻粒子模型。
We present an approximate, analytical calculation of the reionized spectra $C_l^{XX}$ of cosmic microwave background radiation (CMB) anisotropies and polarizations generated by relic gravitational waves (RGWs). Three simple models of reionization are explored, whose visibility functions are fitted by gaussian type of functions as approximations. We have derived the analytical polarization $β_l$ and temperature anisotropies $α_l$, both consisting of two terms proportional to RGWs at the decoupling and at the reionization as well. The explicit dependence of $β_l$ and $α_l$ upon the reionization …
Many scenarios of physics beyond the standard model predict new light, weakly coupled degrees of freedom, populated in the early universe and remaining as cosmic relics today. Due to their high abundances, these relics can significantly affect the evolution of the universe. For instance, massless relics produce a shift $ΔN_{\rm eff}$ to the cosmic expectation of the effective number of active neutrinos. Massive relics, on the other hand, additionally become part of the cosmological dark matter in the later universe, though their light nature allows them to freely stream out of potential wells.…
The presence of light thermally coupled dark matter affects early expansion history and production of light elements during the Big Bang Nucleosynthesis. Specifically, dark matter that annihilates into Standard Model particles can modify the effective number of light species in the universe $N_\mathrm{eff}$, as well as the abundance of light elements created buring BBN. These quantities in turn affect the cosmic microwave background (CMB) anisotropy. We present the first joint analysis of small-scale temperature and polarization CMB anisotropy from Atacama Cosmology Telescope (ACT) and South P…
Generation of the B-mode of CMB polarization by background of relic gravitational wave is discussed in connection with the BICEP2 measurements. Description of the polarization maps in terms of the eigenvectors of the polarization matrix is considered.
Thermal effects on Dark Matter production during cosmic reheating
研究宇宙再加热期间热历史对暗物质 relic abundance 的影响，结合 CMB 观测预测碰撞实验结果。
Many attempts to solve the Hubble tension with extended cosmological models combine an enhanced relic radiation density, acting at the level of background cosmology, with new physical ingredients affecting the evolution of cosmological perturbations. Several authors have pointed out the ability of combined Baryon Acoustic Oscillation (BAO) and Big Bang Nucleosynthesis (BBN) data to probe the background cosmological history independently of both CMB maps and supernovae data. Using state-of-the-art assumptions on BBN, we confirm that combined BAO, deuterium, and helium data are in tension with t…
Hunting Thermal Relics in the DESI DR1 Ly$α$ Forest
本研究利用DESI DR1莱曼-α森林功率谱结合CMB和BAO数据，约束额外相对论性粒子和热无菌中微子，未发现显著证据，并给出N_eff<3.41及m_s^eff<0.061 eV的严格上限。
We study signatures in the Cosmic Microwave Background (CMB) induced by the presence of strong spatial curvature prior to the epoch of inflation which generated our present universe. If inflation does not last sufficiently long to drive the large-scale spatial curvature to zero, then presently observable scales may have left the horizon while spatial slices could not be approximated by a flat, Euclidean geometry. We compute corrections to the power spectrum and non-gaussianity of the CMB temperature anisotropy in this scenario. The power spectrum does not receive significant corrections and is…
Cosmologies with Light Massive Relics (LiMRs) as a subdominant component of the dark sector are well-motivated from a particle physics perspective, and can also have implications for the $σ_8$ tension between early and late time probes of matter clustering. The effects of LiMRs on the Cosmic Microwave Background (CMB) and structure formation on large (linear) scales have been investigated extensively. In this paper, we initiate a systematic study of the effects of LiMRs on smaller, nonlinear scales using cosmological $N$-body simulations; focusing on quantities relevant for photometric galaxy …
The formalism of solid state physics has been applied to provide an additional tool for the research of cosmological problems. It is demonstrated how this new approach could be useful in the analysis of the Cosmic Microwave Background (CMB) data. After a transformation of the anisotropy spectrum of relict radiation into a special two-fold reciprocal space it was possible to propose a simple and general description of the interaction of relict photons with the matter by a "relict radiation factor". This factor enabled us to process the transformed CMB anisotropy spectrum by a Fourier transform …
We discuss a method to constrain the fraction density $f$ of the relativistic gas in the radiation dominant stage, by their impacts on a relic gravitational waves and the cosmic microwave background (CMB) $B$ polarization power spectrum. We find that the uncertainty of $f$ strongly depends on the noise power spectra of the CMB experiments and the amplitude of the gravitational waves. Taking into account of the CMBPol instrumental noises, an uncertainty $Δf=0.046$ is obtained for the model with tensor-to scalar ratio $r=0.1$. For an ideal experiment with only the reduced cosmic lensing as the c…
Rayleigh scattering of the cosmic microwave background (CMB) by neutral hydrogen shortly after recombination leaves frequency-dependent imprints on intensity and polarization fluctuations. High signal-to-noise observations of CMB Rayleigh scattering would provide additional insight into the physics of recombination, including greater constraining power for parameters like the primordial helium fraction, the light relic density, and the sum of neutrino masses. However, such a measurement of CMB Rayleigh scattering is challenging due to the presence of astrophysical foregrounds, which are more i…
The products of primordial nucleosynthesis and the cosmic microwave background (CMB) photons are relics from the early evolution of the Universe whose observations probe the standard model of cosmology and provide windows on new physics beyond the standard models of cosmology and of particle physics. In the standard, hot big bang cosmology, long before any stars have formed a significant fraction (~25%) of the baryonic mass in the Universe should be in the form of helium-4 nuclei. Since current 4He observations are restricted to low redshift regions where stellar nucleosynthesis has occurred, …
Might the radiation era extend back to the Big Bang? On dark matter production and the relic graviton background in quadratic gravity
本文在二次引力框架下重新审视辐射纪元回溯至大爆炸的后果，发现暗物质质量与引力子耦合系数的新关系，并提出暗物质引力产生机制，同时指出遗迹引力子背景可约束理论参数。
PUREPath: A Deep Latent Variational Model for Estimating CMB Posterior over Large Angular Scales of the Sky
PUREPath提出了一种结合贝叶斯统计与变分方法的嵌套概率多模态U-Net架构，用于估计CMB信号后验密度，有效降低前景污染，并提供逐像素的不确定性度量以提升宇宙学参数测量精度。
Perhaps the most controversial idea in modern cosmology is that our observable universe is contained within one bubble among many, all inhabiting the eternally inflating multiverse. One of the few way to test this idea is to look for evidence of the relic inhomogeneities left by the collisions between other bubbles and our own. Such relic inhomogeneities induces a coherent bulk flow over gigaparsec scales. Therefore, bubble collisions leave unique imprints in the cosmic microwave background (CMB) through the kinetic Sunyaev Zel'dovich (kSZ) effect, temperature anisotropies induced by the scatt…
Mild, unavoidable deviations from circular-symmetry of instrumental beams along with scan strategy can give rise to measurable Statistical Isotropy (SI) violation in Cosmic Microwave Background (CMB) experiments. If not accounted properly, this spurious signal can complicate the extraction of other SI violation signals (if any) in the data. However, estimation of this effect through exact numerical simulation is computationally intensive and time consuming. A generalized analytical formalism not only provides a quick way of estimating this signal, but also gives a detailed understanding connec…
The nonlinear interaction between one graviton and two scalars is enhanced in specific inflationary models, potentially leading to distinguishable signatures in the bispectrum of the cosmic microwave background (CMB) anisotropies. We develop the tools to examine such bispectrum signatures, and show a first application using WMAP temperature data. We consider several $\ell$-ranges, estimating the $g_{tss}$ amplitude parameter, by means of the so-called separable modal methodology. We do not find any evidence of a tensor-scalar-scalar signal at any scale. Our tightest bound on the size of the te…
Abundance and properties of dark radiation from the cosmic microwave background
本文通过总辐射丰度与自由流动比例重新表述轻遗迹粒子的宇宙学效应，并利用最新CMB、透镜和重子声学振荡数据约束暗辐射场景，发现强相互作用轻遗迹粒子存在边缘探测迹象。
We investigate for viable models of inflation that can successfully produce dark matter (DM) from inflaton decay process, satisfying all the constraints from Cosmic Microwave Background (CMB) and from some other observations. In particular, we analyze near-inflection-point small field inflationary scenario with non-thermal production of fermionic DM from the decaying inflaton field during the reheating era. To this end, we propose two different models of inflation with polynomial potential. The potential of Model I contains terms proportional to linear, quadratic, and quartic in inflaton; wher…
The equation of state (EOS), $w(z)$, is the most important parameter of dark energy. We reconstruct the evolution of this EOS in a model-independent way using the latest cosmic microwave background (CMB) data from Planck and other observations, such as type Ia supernovae (SNe Ia), the baryonic acoustic oscillation measurements (SDSS, 6dF, BOSS, and WiggleZ), and the Hubble parameter value $H(z)$. The results show that the EOS is consistent with the cosmological constant at the $2σ$ confidence level, not preferring a dynamical dark energy. The uncorrelated EOS of dark energy constraints from Pl…
Future Cosmic Microwave Background (CMB) satellite missions aim to use the $B$ mode polarization to measure the tensor-to-scalar ratio $r$ with a sensitivity of about $10^{-3}$. Achieving this goal will not only require sufficient detector array sensitivity but also unprecedented control of all systematic errors inherent to CMB polarization measurements. Since polarization measurements derive from differences between observations at different times and from different sensors, detector response mismatches introduce leakages from intensity to polarization and thus lead to a spurious $B$ mode sig…
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