The energy spectrum of the cosmic microwave background (CMB) allows constraining episodes of energy release in the early Universe. In this paper we revisit and refine the computations of the cosmological thermalization problem. For this purpose a new code, called CosmoTherm, was developed that allows solving the coupled photon-electron Boltzmann equation in the expanding, isotropic Universe for small spectral distortion in the CMB. We explicitly compute the shape of the spectral distortions caused by energy release due to (i) annihilating dark matter; (ii) decaying relict particles; (iii) dissipation of acoustic waves; and (iv) quasi-instantaneous heating. We also demonstrate that (v) the continuous interaction of CMB photons with adiabatically cooling non-relativistic electrons and baryons causes a negative mu-type CMB spectral distortion of DI_nu/I_nu ~ 10^{-8} in the GHz spectral band. We solve the thermalization problem including improved approximations for the double Compton and Bremsstrahlung emissivities, as well as the latest treatment of the cosmological recombination process. At redshifts z <~ 10^3 the matter starts to cool significantly below the temperature of the CMB so that at very low frequencies free-free absorption alters the shape of primordial distortions significantly. In addition, the cooling electrons down-scatter CMB photons introducing a small late negative y-type distortion at high frequencies. We also discuss our results in the light of the recently proposed CMB experiment Pixie, for which CosmoTherm should allow detailed forecasting. Our current computations show that for energy injection because of (ii) and (iv) Pixie should allow to improve existing limits, while the CMB distortions caused by the other processes seem to remain unobservable with the currently proposed sensitivities and spectral bands of Pixie.
Accurate computations of spectral distortions of the cosmic microwave background (CMB) are required for constraining energy release scenarios at redshifts $z\gtrsim 10^3$. The existing literature focuses on distortions that are small perturbations to the background blackbody spectrum. At high redshifts ($z\gtrsim 10^6$), this assumption can be violated, and the CMB spectrum can be significantly distorted at least during part of its cosmic evolution. In this paper, we carry out accurate thermalization computations, evolving the distorted CMB spectrum in a general, fully non-linear way, consiste…
We consider the distortions of the cosmic microwave background (CMB) dipole anisotropy related to the primordial recombination radiation (PRR) and primordial $y$- and $μ$-distortions. The signals arise due to our motion relative to the CMB restframe and appear as a frequency-dependent distortion of the CMB temperature dipole. To leading order, the expected relative distortion of the CMB dipole does not depend on the particular observation directions and reaches the level of $10^{-6}$ for the PRR- and $μ$-distortions and $10^{-5}$ for the $y$-distortion in the frequency range 1 -- 700 GHz. The …
CMB spectral distortions from small-scale isocurvature fluctuations
在小尺度下，原始扰动的衰减引起了宇宙微波背景（CMB）的畸变。在这里，依赖于不同类型的宇宙学初始条件的失真进行了探讨，包括绝热，重子/冷暗物质等曲率，中微子密度/速度等曲率模式和一些混合物。确定每个模式的辐射传递函数，然后用于计算耗散加热速率和光谱失真签名，利用热化代码CosmoTherm的分析估计和数值结果。在此基础上，导出了共形牛顿规范下流体模的早期超视界行为，并给出了紧耦合传递函数近似。由不同扰动模式引起的CMB光谱失真可以使用这里提供的简单的k空间窗口函数来估计。中微子带走了一部分原始扰动功率，引入了取决于扰动类型的总效率因子。结果表明，未来对CMB频谱的测量有可能在非常小的尺度上探测不同的扰动模式（对应于波数1 Mpc^{-1} < k < few x 10^4 Mpc^{-1}）。这些约束是在大尺度上获得的补充，因此为早期宇宙物理学提供了一个令人兴奋的新窗口。
Probing correlations among short and long-wavelength cosmological fluctuations is known to be decisive for deepening the current understanding of inflation at the microphysical level. Spectral distortions of the CMB can be caused by dissipation of cosmological perturbations when they re-enter Hubble after inflation. Correlating spectral distortions with temperature anisotropies will thus provide the opportunity to greatly enlarge the range of scales over which squeezed limits can be tested, opening up a new window on inflation complementing the ones currently probed with CMB and LSS. In this p…
We propose using the upcoming Cosmic Microwave Background (CMB) ground based experiments to detect the signal of ALPs (Axion like particles) interacting with magnetic fields in galaxy clusters. The conversion between CMB photons and ALPs in the presence of the cluster magnetic field can cause a polarized spectral distortion in the CMB around a galaxy cluster. The strength of the signal depends upon the redshift of the galaxy cluster and will exhibit a distinctive spatial profile around it depending upon the structure of electron density and magnetic field. This distortion produces a different …
CMB spectral distortions are induced by Compton collisions with electrons. We review the various schemes to characterize the anisotropic CMB with a non-Planckian spectrum. We advocate using logarithmically averaged temperature moments as the preferred language to describe these spectral distortions, both for theoretical modeling and observations. Numerical modeling is simpler, the moments are frame-independent, and in terms of scattering the mode truncation is exact.
Although the Cosmic Microwave Background agrees with a perfect blackbody spectrum within the current experimental limits, it is expected to exhibit certain spectral distortions with known spectral properties. We propose a new method, Frequency Space Differential (FSD) to measure the spectral distortions in the CMB spectrum by using the inter-frequency differences of the brightness temperature. The difference between the observed CMB temperature at different frequencies must agree with the frequency derivative of the blackbody spectrum, in the absence of any distortion. However, in the presence…
Primordial bubbles that possibly nucleate through quantum tunneling during inflation in a multidimensional potential might have left some relic detectable at the present time. These bubbles turn into black holes during the radiation era, which may account for the LIGO black holes, supermassive black holes, and may play an important role in dark matter. Typically, these black holes are surrounded by an energy deficit in the form of a spherical sound wave packet propagating outwards. In this work we study how this perturbation of the cosmic plasma dissipates before the time of recombination, lea…
If the large scale structure of the Universe was created, even partially, via Zeldovich pancakes, than the fluctuations of the CMB radiation should be formed due to bulk comptonization of black body spectrum on the contracting pancake. Approximate formulas for the CMB energy spectrum after bulk comptonization are obtained. The difference between comptonized energy spectra of the CMB due to thermal and bulk comptonization may be estimated by comparison of the plots for the spectra in these two cases.
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…
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…
In this work we consider CMB spectral distortions as a probe of dark matter microphysics in the early universe. We demonstrate that future experiments such as PRISM have the potential to distinguish between scenarios which offer solutions to the small-scale problems of CDM cosmology.
Although both early and late-time modifications of the $Λ$CDM model have been proposed to address the Hubble tension, compelling arguments suggest that for a solution to be successful it needs to modify the expansion history of the universe prior to recombination. This greatly increases the importance of precise CMB observations, and in this letter we make the argument for CMB spectral distortions, highlighting their potential role in constraining models that introduce significant shifts in the standard $Λ$CDM parameters, such as the scalar spectral index, in attempt to solve the Hubble tensio…
Current constraints on energy injection in the form of energetic particles before the epoch of recombination using CMB spectral distortions assume that all energy goes into $y$ and $μ$-type distortions. We revisit these constraints with exact calculations of the spectral distortions by evolving the electromagnetic cascades. The actual spectral distortion differs in shape and amplitude from the $y$-type distortion and depends on the energy and nature of injected particles. The constraints on the energy injection processes such as dark matter decay can be relaxed by as much as a factor of 5.
In multiple inflation scenario having two inflations with an intermediate matter-dominated phase, the power spectrum is estimated to be enhanced on scales smaller than the horizon size at the beginning of the second inflation, $k > k_{\rm b}$. We require $k_{\rm b} > 10 {\rm Mpc}^{-1}$ to make sure that the enhanced power spectrum is consistent with large scale observation of cosmic microwave background (CMB). We consider the CMB spectral distortions generated by the dissipation of acoustic waves to constrain the power spectrum. The $μ$-distortion value can be $10$ times larger than the expect…
Prior to recombination, Silk damping causes the dissipation of energy from acoustic waves into the monopole of the Cosmic Microwave Background (CMB), resulting in spectral distortions. These can be used to probe the primordial scalar power spectrum on smaller scales than it is possible with CMB anisotropies. An enhancement of power on these scales is nevertheless required for the resulting distortions to be detectable by future experiments like PIXIE. In this paper, we examine all 49 single-field inflation models listed by Martin et al. in the Encyclopaedia Inflationaris [1] and find that only…
Distortions to the cosmic microwave background~(CMB) blackbody spectrum are calculated in the framework of cosmological perturbation theory. The second order Boltzmann equation is explicitly solved, with the spectral $y$ distortion and the frequency independent second order temperature perturbation. We also solve higher order Boltzmann equations systematically and find new type spectral distortions in the low energy limit of electrons. As an example, we concretely construct a solution to the cubic order Boltzmann equation and show that it can be characterized by three parameters: a cubic order…
Forecasts for CMB μ- and i-type spectral distortion constraints on the primordial power spectrum on scales 8 < k < 10^4 Mpc^-1 with the future Pixie-like experiments
红移为1.5 x 10^4 < z < 2 x 10^6的丝绸阻尼消除了对应于同向波数8 < k < 10^4 Mpc^-1（10^5 < \ell < 10^8）尺度上的CMB各向异性。这种耗散的能量被CMB吸收，在μ型和i型CMB光谱中产生黑体畸变。我们研究，使用Fisher矩阵，我们可以从测量这些频谱失真的原始功率谱从未来的实验，如Pixie的约束，以及这些约束如何改变，因为我们改变的频率分辨率和灵敏度的实验。我们表明，额外的信息的形状的$i$型失真，结合μ型失真，使我们能够打破这些尺度上的功率谱的幅度和谱指数之间的简并性，并导致更严格的约束。考虑到y型畸变的部分简并度和CMB黑体部分的温度，我们量化了μ型畸变和i型畸变中包含的信息。我们还计算了原始功率谱的约束时，光谱失真的信息相结合的CMB各向异性测量的WMAP，SPT，ACT和普朗克实验。
We consider the Stokes parameters' frequency spectral distortions arising due to Compton scattering of the anisotropic cosmic microwave background (CMB) radiation, the Sunyaev-Zel' dovich effect (SZ), towards clusters of galaxies. We single out a very special type of such distortions and find simple analytical formulas for them. We show that this kind of distortion has a very distinctive spectral shape and can be separated from other kinds of contaminants. We demonstrate that this effect gives us an opportunity for an independent estimation of the low-multipole angular CMB anisotropies, such a…
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 improve previous calculations of the CMB spectral distortions due to the decay of primordial magnetic fields. We focus our studies on causally generated magnetic fields at the electroweak and QCD phase transitions. We also consider the decay of helical magnetic fields. We show that the decay of non-helical magnetic fields generated at either the electroweak or QCD scale produce $μ$ and $y$-type distortions below $10^{-8}$ which are probably not detectable by a future PIXIE-like experiment. We show that magnetic fields generated at the electroweak scale must have a helicity fraction $f_*>10^…
Measurements of the cosmic microwave background (CMB) spectral $y$-distortion anisotropy offer a test for the statistical isotropy of the primordial density perturbations on $0.01\lesssim k{\rm Mpc}\lesssim 1$. We compute the 1-point ensemble averages of the $y$-distortion anisotropies which vanish for the statistically isotropic perturbations. For the quadrupole statistical anisotropy, we find $4π\langle y_{2m}\rangle=-6.8A_2\times 10^{-9}Y_{2m}(\mathbf d )$ with the quadruple Legendre coefficient of the anisotropic powerspectrum $A_2$ and the $\ell=2$ spherical harmonics $Y_{2m}(\mathbf d )$…
We show that the cumulative CO emission from galaxies throughout cosmic history distorts the spectrum of the cosmic microwave background (CMB) at a level that is well above the detection limit of future instruments, such as the Primordial Inflation Explorer (PIXIE). The modeled CO signal has a prominent bump in the frequency interval 100-200 GHz, with a characteristic peak intensity of ~ 2$\times$10$^{-23}$ W m$^{-2}$ Hz$^{-1}$ sr$^{-1}$. Most of the CO foreground originates from modest redshifts, z ~ 2-5, and needs to be efficiently removed for more subtle distortions from the earlier univers…
We discuss mixed inflaton and spectator field models where both the fields are responsible for the observed density fluctuations. We use the current CMB data to constrain both the general mixed model as well as some specific representative scenarios, and collate the results with the model predictions for the CMB spectral $μ$ distortion. We find the posterior distribution of $μ$ using MCMC chains and demonstrate that the standard single-field inflaton model typically predicts $μ\sim 10^{-8}$ with a relatively narrow distribution, whereas for the mixed models, the distribution turns out to be mu…
Heliosheath Synchrotron Radiation As A Possible Source For The Arcade 2 CMB Distortions
这份简短的笔记推测，最近报道的残留CMB信号[Seiffert et al 2009]可能起源于太阳的日鞘。导出了一个与Seiffert等人的拟合函数具有相同幂律形式的温度谱函数。特别地，隐含了+2的谱指数。厚度约为1AU的光学薄辐射壳可以匹配所需的1K度幂律振幅。基于Alfven的日球电流模型，以相对论电子的嵌入双层为能量源，讨论了日鞘磁场的可能机制。
Since the measurements of COBE/FIRAS in the mid-90's we know that the energy spectrum of the cosmic microwave background (CMB) is extremely close to that of a perfect blackbody at an average temperature T0~2.726K. However, a number of early-universe processes are expected to create CMB spectral distortions - departures of the average CMB energy spectrum from a blackbody - at a level that is within reach of present-day technology. This provides strong motivation to study the physics of CMB spectral distortions and ask what these small signals might be able to tell us about the Universe we live …
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…
It is generally assumed that for energy injection before recombination, all of the injected energy is dissipated as heat in the baryon-photon plasma, giving rise to the $y$-type, $i$-type, and $μ$-type distortions in the CMB spectrum. We show that this assumption is incorrect when the energy is injected in the form of energetic (i.e. energy much greater than the background CMB temperature) particles. We evolve the electromagnetic cascades, from the injection of high energy particles, in the expanding Universe and follow the non-thermal component of CMB spectral distortions resulting from the i…
Cosmic Microwave Background (CMB) experiments, such as WMAP and Planck, measure intensity anisotropies and build maps using a linearized formula for relating them to the temperature blackbody fluctuations. However, this procedure also generates a signal in the maps in the form of y-type distortions which is degenerate with the thermal Sunyaev Zel'dovich (tSZ) effect. These are small effects that arise at second-order in the temperature fluctuations not from primordial physics but from such a limitation of the map-making procedure. They constitute a contaminant for measurements of: our peculiar…
We present a general framework for accurate spectral modeling of the low multipoles of the cosmic microwave background (CMB) as observed in a boosted frame. In particular, we demonstrate how spectral measurements of the low multipoles can be used to separate the motion-induced dipole of the CMB from a possible intrinsic dipole component. In a moving frame, the leakage of an intrinsic dipole moment into the CMB monopole and quadrupole induces spectral distortions with distinct frequency functions that respectively peak at 337 GHz and 276 GHz. The leakage into the quadrupole moment also induces …
Unavoidable CMB spectral features and blackbody photosphere of our Universe
宇宙微波背景辐射能谱中的光谱特征包含了大量关于宇宙早期物理过程的信息，z < 2 x 10^6。宇宙微波背景辐射的光谱畸变与其他宇宙学探测是互补的。事实上，CMB频谱中包含的大部分信息是无法通过任何其他方式获取的。这篇评论概述了宇宙历史上CMB光谱特征背后的主要物理学，集中在不可避免的扭曲上，并且必须存在于下一代拟议的CMB实验可观察到的水平。这里考虑的光谱畸变包括来自宇宙学复合的光谱特征，再电离过程中CMB被金属共振散射的光谱特征，这使我们能够测量它们的丰度，再电离过程中和之后的y型畸变，以及在红移z > 1.5 x 10^4时产生的μ型和i型（介于μ和y之间）畸变。
We present a novel mathematical formalism that allows to easily compute the expected kinetic Sunyaev Zeldovich (kSZ) signal in intensity and polarization due to an anisotropic primordial Cosmic Microwave Background (CMB). We derive the expected intensity and polarization distortions in the direction of non-moving galaxy clusters and then we generalize our calculations for non-zero peculiar velocity. We show that, in the direction of moving clusters, low CMB multipoles impose intensity and polarization spectral distortions with different frequency dependences. The polarization signal primarily …
We show that inflationary models with broken rotational invariance generate testable off-diagonal signatures in the correlation between the $μ$-type distortion and temperature fluctuations of the cosmic microwave background. More precisely, scenarios with a quadrupolar bispectrum asymmetry, usually generated by fluctuations of primordial vector fields, produce a nonvanishing $μ$-$T$ correlation when $|\ell_1-\ell_2|=2$. Since spectral distortions are sensitive to primordial fluctuations up to very small scales, a cosmic variance limited spectral distortion experiment can detect such effects wi…
We study the E and B mode polarisation of the cosmic microwave background (CMB) originating from the transverse peculiar velocity of free electrons, at second order in perturbation theory, during the reionisation and post-reionisation eras. Interestingly, the spectrum of this polarised kinetic Sunyaev-Zeldovich (SZ) effect can be decomposed into a blackbody part and a y-type distortion. The y-distortion part is distinguishable from the primary E and B modes and also the lensing B modes. Furthermore, it is also differentiable from the other y-type signals, such as the thermal SZ effect, which a…
We revisit the cosmological constraints on resonant and non-resonant conversion of photons to axions in the cosmological magnetic fields. We find that the constraints on photon-axion coupling and primordial magnetic fields are much weaker than previously claimed for low mass axion like particles with masses $m_{\rm a} \lesssim 5\times 10^{-13}\,\text{eV}$. In particular we find that the axion mass range $10^{-14}\,\text{eV} \le m_{\rm a} \le 5\times 10^{-13}\,\text{eV}$ is not excluded by the CMB data contrary to the previous claims. We also examine the photon-axion conversion in the Galactic …
A variety of beyond the standard model scenarios contain very light hidden sector U(1) gauge bosons undergoing kinetic mixing with the photon. The resulting oscillation between ordinary and hidden photons leads to spectral distortions of the cosmic microwave background. We update the bounds on the mixing parameter $χ_0$ and the mass of the hidden photon $m_{γ'}$ for future experiments measuring CMB spectral distortions, such as PIXIE and PRISM/COrE. For $10^{-14}\;{\rm eV}\lesssim m_{γ'}\lesssim 10^{-13}\;{\rm eV}$, we find the kinetic mixing angle $χ_0$ has to be less than $10^{-8}$ at 95\% C…
This paper proposes a new approach to separate the $μ$ spectral distortions of the cosmic microwave background from foregrounds with poorly defined spectral shapes. The idea is based on finding the optimal response to the observed signal. This response is weakly sensitive to foregrounds with parameters that are within some certain limits of their possible variations and, at the same time, very sensitive to the amplitude of $μ$ distortion. The algorithm described in this paper is stable, easy to implement, and simultaneously minimizes the response to foregrounds and photon noise.
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 …
