Peering Beyond the Veil of Last Scattering: A View of the Universe with CMB Spectral Distortions

Author(s)

Cyr, Bryce, Aghanim, Nabila, Baker, Ethan, Battistelli, Elia Stefano, Battye, Richard, Bernal, José Luis, Chluba, Jens, Coulon, Xavier, Coulton, William, de Bernardis, Paolo, Di Valentino, Eleonora, Domènech, Guillem, Evangelista, Sara, Fabbian, Giulio, Finelli, Fabio, Hill, J. Colin, Khatri, Rishi, Kogut, Alan, Lagache, Guilaine, Liu, Hongwan, Maffei, Bruno, Majidi, Fereshteh, Maniyar, Abhishek S., Martins, C.J.A.P., Masi, Silvia, McMahon, Jeff, Paoletti, Daniela, Poulin, Vivian, Qin, Wenzer, Remazeilles, Mathieu, Rubiño-Martín, José Alberto, Sabyr, Alina, Rao, Mayuri Sathyanarayana, Sierra, Carlos, Singal, Jack, Slatyer, Tracy R., Teixeira, Elsa M., Thiele, Leander, Vacher, Léo, Watts, Duncan

Abstract

The frequency spectrum of the cosmic microwave background is the most precise blackbody ever measured in nature, with deviations constrained at the level of almost one part per million from the COBE satellite. Nevertheless, departures away from a perfect blackbody are present in standard $Λ$CDM cosmology, lurking just beneath the surface of our current observational bounds. These spectral distortions provide invaluable information on our thermal history in both the post- and pre-recombination epochs, allowing us to peer beyond last scattering and into the primordial Universe. Here, we present an overview of the underlying physics responsible for generating CMB spectral distortions at all epochs. As an illustration of this rich physics, we review a comprehensive set of mechanisms capable of generating distortions both within and beyond the standard $Λ$CDM paradigm. We also discuss the information that can be gleaned by going beyond the monopole (sky-averaged) spectrum and exploiting the spatial information present in anisotropic spectral distortions. To supplement our discussion of the diverse science of spectral distortions, we provide an overview of the upcoming and proposed experimental landscape. We highlight that the combination of the TMS, COSMO, and BISOU experiments will provide the first discovery of a monopole $y$-type distortion within the coming decade. From space, the proposed FOSSIL experiment is forecasted to improve upon the original COBE/FIRAS measurement by roughly three orders of magnitude in sensitivity, bringing with it the detection of the $Λ$CDM $μ$-type distortion sourced by the dissipation of small scale acoustic modes in the pre-recombination plasma. With transformational measurements on the horizon, CMB spectral distortions offer a uniquely sensitive probe of the thermal history of the Universe at redshifts $z \lesssim 2 \times 10^6$.

Figures

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An illustration of the various spectral distortion epochs within the wider context of the thermal history of the Universe. This figure was initially generated by ChatGPT and then post-processed.

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Left: Individual distortion shapes normalized to their total energy density $\Delta \rho_{\rm i} = \int \id x \,\,(\id \Delta \rho_{\rm i}/\id x)$. Right: Full spectral distortion shapes with greatly exaggerated distortion amplitudes, for illustration. Here the normalization is over the full distorted spectrum.

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Left: Individual distortion shapes normalized to their total energy density $\Delta \rho_{\rm i} = \int \id x \,\,(\id \Delta \rho_{\rm i}/\id x)$. Right: Full spectral distortion shapes with greatly exaggerated distortion amplitudes, for illustration. Here the normalization is over the full distorted spectrum.

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An extrapolation of the nearly scale-invariant spectrum of scalar perturbations to small scales. Forecasted constraints from \FOSSIL are given assuming no small-scale power except for a $\delta$-function spike at each wavenumber in order to be maximally conservative. Due to the integrated nature of the $\mu$-distortion, \FOSSIL/\PIXIE would have the sensitivity required to observe the standard model spectrum if it extends out to $k \simeq 10^4 \,\, {\rm Mpc}^{-1}$. Quantitative $\mu$ distortion forecasts are given on the right hand side of the plot to further stress the point that \FOSSIL has the reach to observe the diffusion damping signal.

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Benchmark models and limits on the primordial curvature power spectrum. The forecasted sensitivity of a future probe such as \FOSSIL is shown in the black dotted line~\cite{Cyr:2023pgw}. Limits come from CMB anisotropies~\cite{Planck:2018jri}, Lyman-$\alpha$ forest~\cite{Bird:2010mp}, \COBEF $\mu$-type~\cite{Pritchard:2025yda} and $y$-type~\cite{Cyr:2023pgw} distortions. To showcase the parameter space for PBHs, we reproduce the curves from Ref.~\cite{Pritchard:2025yda} in green, which show the level of power necessary to produce $f_\mathrm{PBH} = 10^{-5}$ in the cases of Gaussian enhancements and including cubic non-Gaussianity. The interesting parameter space that \FOSSIL will probe for PBHs is highlighted in the thick red contour. We also reproduce a benchmark model for NQPBHs from Ref.~\cite{Qin:2025ymc} in red, which is a narrow peak in the power spectrum that produces a significant population of SMBH seeds. Both these theoretical models for PBHs predict a spectral distortion which will be detected at high statistical significance by \FOSSIL.

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Indirect and direct probes of GWs with CMB spectral distortions, respectively, in the upper and lower panels. The bottom x-axis is the comoving scale, while the top x-axis shows the number of e-foldings from the end of inflation. The blue curve shows one example of primordial fluctuations that explain CMB anisotropies and the nHz GW background at PTAs, and which can be falsified by \FOSSIL \cite{Tagliazucchi:2023dai}. Upper panel: We show current constraints on the primordial power spectrum, in shaded gray regions, from CMB anisotropies \cite{Planck:2018vyg}, Lyman-$\alpha$ \cite{Bird:2010mp}, and \COBEF CMB spectral distortions. The purple-shaded region shows the many orders of magnitude by which \FOSSIL will improve, enabling it to probe models that connect CMB measurements with GWs at PTAs. The red shaded regions illustrate possible CMB B-mode contamination \cite{Cyr:2023pgw} (left red region) and possible SMBH seed formation \cite{Kawasaki:2012kn,Unal:2020mts,Hooper:2023nnl} (right red region). Lower panel: We show direct probes of the primordial GW background's amplitude. In shaded gray, we show current constraints from CMB anisotropies \cite{Planck:2018vyg}, and with gray violins, we show evidence for a nHz GW background at PTAs \cite{NANOGrav:2023gor}. The purple shaded regions show the expected GW sensitivity from the B-mode polarization survey LiteBIRD \cite{LiteBIRD2023,Cyr:2023pgw} and \FOSSIL. The solid orange line is a typical example of GWs generated during inflation, e.g., in spectator axion-U(1) \cite{Namba:2015gja} and axion-SU(2) inflation models \cite{Campeti:2020xwn} (see also Ref.~\cite{Putti:2024uyr}), which we parametrized using a broad log-normal bump. We thank Matteo Braglia for kindly providing this figure.

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Total primordial (pre-recombination) distortion signatures in new physics scenarios. Solid curves correspond to photon excess relative to a blackbody, while dashed curves are photon decrements. CS: Crit are superconducting string scenarios with equal amounts of energy injection into electromagnetic species and gravitational waves, while CS: RSB is the best-fit value of $I$ and $G\mu$ to the observed radio synchrotron background (RSB) \cite{Cyr:2023yvj}. Each of these scenarios provide distinct avenues for detection and model discrimination through their spectral variation away from $\Lambda$CDM.

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The cosmological recombination radiation (CRR) as obtained with {\tt CosmoSpec}. This {\it fingerprint} from the cosmological recombination process encodes valuable information about the time and duration of the {\it three} recombination epochs. The characteristic frequency pattern, extending over decades in frequency, is hard to mimic by foregrounds or instrumental effects and thus can principally be extracted using sensitive CMB spectrometer approaches \citep[e.g.,][]{Hart2020CRR}. Figure is taken from \citep{Chluba2016CosmoSpec}.

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Whisker plot of absolute CMB temperature measurements, showing FIRAS (1996, 2009) \cite{Fixsen:1996nj,Fixsen:2009ug} in blue, ARCADE (2011) \cite{Fixsen:2009xn, Seiffert:2011} in gray, and the \FOSSIL forecast in navy, with an improvement in the error of about one order of magnitude. Points denote monopole $T_0$ values with $1\sigma$ uncertainties. The blue band marks the FIRAS 2009 re-analysis point for reference.

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left panel: Estimated Fisher-matrix uncertainties for $\Omega_bh^2$ as a function of the maximum $\ell$, using lensed TT, TE, and EE power spectra under the assumption of the cosmic-variance limit. Errors on $T_0$ from FIRAS degrade the precision on $\Omega_bh^2$ by $50\%$ for future experiments. Right panel: correlation between $H_0$ and $T_0$ under $\Lambda$CDM when analyzing {\it Planck} data. Taken from Ref.~\cite{Wen:2020txi}.

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left panel: Estimated Fisher-matrix uncertainties for $\Omega_bh^2$ as a function of the maximum $\ell$, using lensed TT, TE, and EE power spectra under the assumption of the cosmic-variance limit. Errors on $T_0$ from FIRAS degrade the precision on $\Omega_bh^2$ by $50\%$ for future experiments. Right panel: correlation between $H_0$ and $T_0$ under $\Lambda$CDM when analyzing {\it Planck} data. Taken from Ref.~\cite{Wen:2020txi}.

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The frequency dependence of the relativistic thermal SZ signal (in Jy/sr) for a range of different electron temperatures.

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Top left: Predictions of $\tmono$, $\ymono$ based on the SIMBA galaxy formation model. Each points show results for a single simulation of the CAMELS suite color coded by values of the $A_{AGN2}$ parameter describing the velocity of AGN jets. The state of the art measurements from \cite{Fabbian_2025} are shown in red. As $\tmono$ is unconstrained by the data, we fix it to the median of the predictions. The excluded area at 95\% C.L. is shown in grey. Top right: Same as the left panel for the IllustrisTNG feedback model, which predicts weaker feedback effects compared to SIMBA. In both SIMBA and IllustrisTNG models, \FOSSIL will be able to pinpoint the physical mechanisms underlying feedback with high precision. Bottom: forecast for the matter power spectrum suppression as constrained by \FOSSIL measurements of $\ymono$ and $\tmono$ at 68\% C.L. (blue). We used the CAMELS IllustrisTNG as simulated data and show the allowed values currently constrained from DES cosmic shear alone (orange) and with kSZ data (purple). The fiducial suppression of the Illustris , IllustrisTNG-100 and IllustrisTNG- 300 simulations in solid lilac, green and red respectively. \FOSSIL will allow to set high-precision constrain on the baryon-induced suppression at high precision even for low-feedback model such as those implemented in IllustrisTNG.

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Top left: Predictions of $\tmono$, $\ymono$ based on the SIMBA galaxy formation model. Each points show results for a single simulation of the CAMELS suite color coded by values of the $A_{AGN2}$ parameter describing the velocity of AGN jets. The state of the art measurements from \cite{Fabbian_2025} are shown in red. As $\tmono$ is unconstrained by the data, we fix it to the median of the predictions. The excluded area at 95\% C.L. is shown in grey. Top right: Same as the left panel for the IllustrisTNG feedback model, which predicts weaker feedback effects compared to SIMBA. In both SIMBA and IllustrisTNG models, \FOSSIL will be able to pinpoint the physical mechanisms underlying feedback with high precision. Bottom: forecast for the matter power spectrum suppression as constrained by \FOSSIL measurements of $\ymono$ and $\tmono$ at 68\% C.L. (blue). We used the CAMELS IllustrisTNG as simulated data and show the allowed values currently constrained from DES cosmic shear alone (orange) and with kSZ data (purple). The fiducial suppression of the Illustris , IllustrisTNG-100 and IllustrisTNG- 300 simulations in solid lilac, green and red respectively. \FOSSIL will allow to set high-precision constrain on the baryon-induced suppression at high precision even for low-feedback model such as those implemented in IllustrisTNG.

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Contours of the relative differential contributions to the mean Compton-$y$ and mean electron temperature, $T_e$, as a function of halo mass and redshift. We compare the sensitivity of the ACT/SPT tSZ power spectrum $C_\ell^{yy}$ (at $\ell \sim 3000$) and DES weak lensing correlation function $\xi_-^{\kappa\kappa}$ as computed by \cite{Lucie-Smith-2025}.

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The response of the global 21cm brightness temperature in the presence of soft photon backgrounds. Case studies are shown with and without soft photon heating for free-free ($\gamma = 3.0$), synchrotron ($\gamma = 3.6$), and an intermediate type spectral tilt ($\gamma = 3.3$). Left: the response when the background is sourced pre-recombination ($z_{\rm inj} \simeq z_{\rm eq}$). Right: same, but for a post-recombination ($z_{\rm inj} = 100$) scenario, which showcases the need to propery account for this free-free heating effect. Figure adapted from \cite{CyrAcharyaChluba2024}.

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The response of the global 21cm brightness temperature in the presence of soft photon backgrounds. Case studies are shown with and without soft photon heating for free-free ($\gamma = 3.0$), synchrotron ($\gamma = 3.6$), and an intermediate type spectral tilt ($\gamma = 3.3$). Left: the response when the background is sourced pre-recombination ($z_{\rm inj} \simeq z_{\rm eq}$). Right: same, but for a post-recombination ($z_{\rm inj} = 100$) scenario, which showcases the need to propery account for this free-free heating effect. Figure adapted from \cite{CyrAcharyaChluba2024}.

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Ongoing and future LIM experiments, indicating the redshift coverage for each of the targeted (thick) and interloper (thin) spectral lines, and the survey sky area. A space-based spectroscopic mission could do a full-sky survey of millimeter and sub-millimeter lines across all these redshifts. Adapted and updated from Ref.~\cite{Bernal:2022jap}.

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Ongoing and future LIM experiments, indicating the redshift coverage for each of the targeted (thick) and interloper (thin) spectral lines, and the survey sky area. A space-based spectroscopic mission could do a full-sky survey of millimeter and sub-millimeter lines across all these redshifts. Adapted and updated from Ref.~\cite{Bernal:2022jap}.

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Main detectable spectral lines by a broad-band space-based spectrometer targeting absolute CMB spectral distortions. Inspired by Ref.~\cite{Silva:2019jbe} and updated using the models employed in Ref.~\cite{Bernal:2022jap}.

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Spectral distortion signatures computed using \texttt{DarkHistory} for the $\chi \rightarrow e^+e^-$ process. The variety of dark matter masses and lifetimes are chosen such that they saturate upper limits from CMB anisotropy studies \cite{Liu2023}. The sensitivities of \COBEF (red), BISOU (blue) and \FOSSIL (green) are also plotted.

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A variety of dark photon spectral distortions ($\gamma \rightarrow A'$). For resonant conversions occurring in the $\mu$-epoch (orange), during the $\mu$-y transition (green), and post-recombination (blue/red), we show parameter space points near the detection threshold of \FOSSIL. The ordered pairs are $(m,\epsilon)$, and each distortion is computed in the homogeneous limit.

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Left: Absolute values of the angular cross-power spectra between primordial spectral distortion anisotropies and primary CMB anisotropies for $\langle\mu\rangle =2\times 10^{-8}$, $\langle y\rangle =4\times 10^{-9}$, and $f_{\rm NL}^{\rm loc}=1$: $C_\ell^{\mu T}$ (red), $C_\ell^{yT}$ (purple), $C_\ell^{\mu E}$ (blue), and $C_\ell^{yE}$ (cyan). Solid (dashed) lines indicate positive (negative) values of the cross-spectra. The theoretical predictions are based on the calculations presented in \cite{Ravenni2017} and were recently refined in \citep{Chluba2026muT}. Right: Illustration of the $\mu T$ signals for a scenario with enhanced small-scale power (a factor of $\simeq 10^3$ in amplitude around $k_{\rm p}\simeq 10^2\,{\rm Mpc}^{-1}$). We then illustrate the $\ell$ dependence of the total signal for varying values of $f_{\rm NL}$, demonstrating how the spectro-spatial information can in principle be used to distinguish different models and break degeneracies. The figure is taken from \citep{Chluba2026muT}.

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Left: Absolute values of the angular cross-power spectra between primordial spectral distortion anisotropies and primary CMB anisotropies for $\langle\mu\rangle =2\times 10^{-8}$, $\langle y\rangle =4\times 10^{-9}$, and $f_{\rm NL}^{\rm loc}=1$: $C_\ell^{\mu T}$ (red), $C_\ell^{yT}$ (purple), $C_\ell^{\mu E}$ (blue), and $C_\ell^{yE}$ (cyan). Solid (dashed) lines indicate positive (negative) values of the cross-spectra. The theoretical predictions are based on the calculations presented in \cite{Ravenni2017} and were recently refined in \citep{Chluba2026muT}. Right: Illustration of the $\mu T$ signals for a scenario with enhanced small-scale power (a factor of $\simeq 10^3$ in amplitude around $k_{\rm p}\simeq 10^2\,{\rm Mpc}^{-1}$). We then illustrate the $\ell$ dependence of the total signal for varying values of $f_{\rm NL}$, demonstrating how the spectro-spatial information can in principle be used to distinguish different models and break degeneracies. The figure is taken from \citep{Chluba2026muT}.

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Reconstructed $\mu T$ (left) and $\mu E$ (right) cross-power spectra for a LiteBIRD-like mission, assuming $\langle\mu\rangle = 2\times10^{-8}$ and $f_{\rm NL}^{\rm loc}(k\simeq740\,{\rm Mpc}^{-1})=4500$ \citep{Remazeilles2022:mu}. After foreground mitigation and component separation using the Constrained ILC (CILC) method, the $\mu T$ and $\mu E$ correlations are recovered without significant bias over the multipole range $2\leq \ell \leq 500$. Combining the recovered modes over the multipoles, the joint $\mu T$ and $\mu E$ measurements yield a $5\sigma$ detection of $f_{\rm NL}^{\rm loc}=4500$ on scales $k\simeq740\,{\rm Mpc}^{-1}$ inaccessible to conventional CMB anisotropy or large-scale structure observables.

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Reconstructed $\mu T$ (left) and $\mu E$ (right) cross-power spectra for a LiteBIRD-like mission, assuming $\langle\mu\rangle = 2\times10^{-8}$ and $f_{\rm NL}^{\rm loc}(k\simeq740\,{\rm Mpc}^{-1})=4500$ \citep{Remazeilles2022:mu}. After foreground mitigation and component separation using the Constrained ILC (CILC) method, the $\mu T$ and $\mu E$ correlations are recovered without significant bias over the multipole range $2\leq \ell \leq 500$. Combining the recovered modes over the multipoles, the joint $\mu T$ and $\mu E$ measurements yield a $5\sigma$ detection of $f_{\rm NL}^{\rm loc}=4500$ on scales $k\simeq740\,{\rm Mpc}^{-1}$ inaccessible to conventional CMB anisotropy or large-scale structure observables.

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Cross correlation power spectra of the CMB temperature with the standard distortions $\mu$ and $y$. Two different generation mechanisms for SD anisotropies have been considered: on the left, photons converting into dark photons varying the number density, on the right, particles decaying and injecting heating into the CMB. For both scenarios, we considered three different values for the conversion redshift ($z_{\rm con}$) and decay rates ($\Gamma_X$ in ${\rm sec}^{-1}$), respectively, spanning both the $\mu$- and $y$-epoch before recombination.

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Cross correlation power spectra of the CMB temperature with the standard distortions $\mu$ and $y$. Two different generation mechanisms for SD anisotropies have been considered: on the left, photons converting into dark photons varying the number density, on the right, particles decaying and injecting heating into the CMB. For both scenarios, we considered three different values for the conversion redshift ($z_{\rm con}$) and decay rates ($\Gamma_X$ in ${\rm sec}^{-1}$), respectively, spanning both the $\mu$- and $y$-epoch before recombination.

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Left: Assembly of the TMS internal structure in the IAC integration clean room (June 2026). Center: TMS platform and supporting structure, installed at the Teide Observatory inside the TMS dome (November 2022). Right: TMS cold load (black-body internal calibrator), fabricated by INAF-OAS (Bologna, Italy).

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Left: rendering of the COSMO DFTS. All parts shown are inserted in a pulse-tube cooled cryostat at temperatures below 3K. Right: the COSMO DFTS in the laboratory during room temperature validation tests (June 2026).

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The Cosmological Recombintaion Radiation is 9 orders of magnitude fainter than the CMB blackbody spectrum. Though faint, it has a well predicted and rich spectral signature which is advantageous for signal detection. The APSERa band is highlighted in the shaded region. APSERa in its final phase will be an array of 128 cooled radiometers deployed in a high altitude radio quiet site, with a primary science goal of detecting the CRR. CRR signature from COSMOSPEC \cite{Chluba2016CosmoSpec}.

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A rending view of the BISOU instrument: the various sub-systems are mounted on the cold plate (gold) and inside the L-shaped dewar. The whole instrument is cooled down to 2.7 K using liquid helium, while the detectors are at about 100 mK. Image courtesy V. Sauvage.

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Sensitivity of the \FOSSIL mission (black) compared to the \COBEF sensitivity (purple). The $\mu$-distortion (green) and the CRR (red) spectra are also shown for reference. Solid curves indicate positive values, while dashed curves indicate negative values.

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A Super-\PIXIE mission with 3 FTS modules would tune the channel width and optical passband of each module to optimize the combined sensitivity to foregrounds and CMB spectral distortions.

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Sensitivities for the \textit{SPECTER} 16-band optimized (black circles) and the 34-band multichroic configurations (red rombs) assuming a full sky observation and one year of spectral distortion integration time. Total astrophysical foregrounds (dot-dashed orange), $\mu$-distortion (cyan), and $y$-distortion (dark blue) and its relativistic correction (light blue) are also shown. Note that the absolute values of the distortions are plotted with dashed lines corresponding to the negative values. \textit{COBE/FIRAS} sensitivity (grey crosses) and the scaled CMB blackbody emission (dotted green) are plotted for reference. Figure adapted from Ref.~\cite{specter}.

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A summary of various $\Lambda$CDM distortions and forecasted sensitivities from the most advanced experimental designs. The $\mu$ distortion is sourced by the damping of small scale power under the assumption of a nearly scale invariant spectrum of perturbations down to $k \simeq 10^{5} \, {\rm Mpc}^{-1}$. The $y$ distortion signatures are from the thermal (orange) Sunyaev-Zel'dovich effect and its relativistic corrections (red). Finally, the spectrum of cosmological recombination radiation (CRR) as computed by \texttt{CosmoSpec} is shown in blue.