Constraining long-lived dark sector particles with CMB and Lyman-$α$

TL;DR

This work investigates constraints on long-lived, metastable dark sector particles whose decays inject energy into the intergalactic medium (IGM). The authors compute redshift-dependent energy-deposition efficiencies $f_c(z)$ for decays to $e^+e^-$ and $\gamma\gamma$, including backreaction effects, by modifying the DarkHistory code, and apply these to Ly$\alpha$ forest temperature measurements to constrain the DS parameter space $(\tau_{\rm DS}, f_{\rm DS})$. They also revisit Planck 2018 optical-depth bounds using the same deposition functions, enabling a consistent comparison between Ly$\alpha$ and CMB constraints across lifetimes $\tau_{\rm DS} \gtrsim 10^{14}$ s. The results show that Ly$\alpha$ bounds are competitive with Planck 2015 and, in some long-lifetime regimes, stronger than earlier CMB bounds, with explicit exclusions such as $f_{\rm DS} \sim 8\times10^{-9}$ at $\tau_{\rm DS} \sim 5\times10^{16}$ s for $e^+e^-$ decays and sub-keV masses for $\gamma\gamma$ channels. They project sizable gains from 21-cm cosmology and illustrate translations to evaporating PBH scenarios, highlighting the complementarity of late-time probes for hidden-sector physics.

Abstract

We use measurements of the intergalactic medium (IGM) temperature from the Lyman-$α$ forest to place new limits on models in which long-lived dark sector (DS) particles, with lifetimes longer than $10^{16}$ s, deposit energy into the IGM through their decays. Such DS decays into Standard Model (SM) states can modify the late-time thermal history of the IGM, making Lyman-$α$ data a sensitive probe of hidden sectors with cosmologically long lifetimes. Our analysis demonstrates that constraints from late-time IGM heating offer a complementary window to those from the Cosmic Microwave Background (CMB), in constraining dark sector parameter space. We further revisit limits on such decaying DS models from Planck's measurements of the optical depth to reionization and provide updates relevant for DS lifetimes longer than $10^{14}$ s. The model-independent constraints on the DS parameter space we derive in this work can be reinterpreted for a wide range of decaying hidden-sector scenarios, including evaporating primordial black holes and SM-coupled dark photons.

Figures (7)

• Figure 1: Computed $f_{\rm Hion}(z)$ (top row) and $f_{\rm heat}(z)$ (bottom row) as a function of redshift of deposition and initial kinetic energy of the injected particles, without backreaction, obtained using a modified version of DarkHistory code for DS particle $\chi$ decaying into $e^+e^-$ for DS lifetime $\tau_{\rm DS} = 10^{13}$ s (first column), $10^{15}$ s (second column) and $10^{17}$ s (third column).
• Figure 2: Left: Ionization history showing the free electron fraction as a function of redshift for energy injections from the decays of DS of mass $m_{\rm DS} =$ 500 MeV, into $e^+e^-$. The solid red curve represents the tanh model for free electron fraction reproducing the $\textit{Planck 2018}$ constraints on $\tau_{\rm reion}$Planck:2018vyg. The DS parameters used for the three ionization histories are: $\tau_{\rm DS} = 10^{13}$ s, $f_{\rm DS} = 4 \times 10^{-9},$ (solid blue); $\tau_{\rm DS} = 10^{15}$ s, $f_{\rm DS} = 4 \times 10^{-11}$ (yellow dot dashed); and $\tau_{\rm DS} = 10^{17}$ s, $f_{\rm DS} = 1.3 \times 10^{-10}$ (dotted), with the ionization level set to the tanh one at low redshifts. Right: IGM temperature $T_{\rm m}$ as a function of redshift for two DS decay scenarios with $m_{\rm DS}=100\,\mathrm{MeV}$ and decay to $e^+e^-$. The dashed yellow curve corresponds to a case that overheats the IGM relative to Ly$\alpha$--inferred temperatures Walther:2018pnnGaikwad:2020art and is therefore excluded, while the solid blue curve remains under-heated and is consistent with the data. The Ly$\alpha$ measurements of $T_{\rm m}$ (shown in teal) constitute the fiducial dataset Liu:2020wqz used in this analysis. The ionization history is fixed to a tanh parametrization at low redshifts for $T_{\rm m}$ evolution with redshift.
• Figure 3: Left: Constraints on DS parameter space obtained using CMB estimates based on the evaluation of the optical depth to reionization (see main text) for DS particle $\chi$ decaying to $e^+e^-$. The blue and yellow regions are the most stringent limits we obtain in this work using the reported values of $\tau_{\rm reion}$ in Planck 2015Planck:2015fie and Planck 2018Planck:2018vyg datasets for DS mass $= 100$ MeV. We further compare our results with the strongest existing bounds on decaying dark sectors obtained in previous studies, derived from full CMB analyses of the Planck 2015 data by Poulin et al. Poulin:2016anj (dashed pink), and of the Planck 2018 data by Lucca et al. Lucca:2019rxf (dotted teal), where in the latter case, the authors have used a constant efficiency function $f_{\rm eff} = 1$ (see discussion in the main text). The vertical grey region indicates the region of $\tau_{\rm DS} \lesssim 10^{14}$ s where our CMB bounds based on optical depth reionization cannot constrain ionization level change (see discussion in main text). Our estimated CMB bounds using Eq. \ref{['eq:stima_xe']} are also shown for comparison as a dot-dashed line. Right: Constraints on DS parameter space obtained from IGM heating using Ly$\alpha$ temperature measurements for DS with mass $m_{\rm DS} = 10^{8.5}$eV, decaying to $e^+e^-$, where we have set the ionization free electron fraction for low redshifts to Planck's tanh model. Here the dashed red curve shows the bounds without backreaction [no BR] and solid red shows the stronger bounds with backreaction [BR] included. In pink dot-dashed curve, the estimated bound for Lyman$-\alpha$ using Eq. \ref{['eq:stima_Tm']} are shown.
• Figure 4: Left: Constraints derived in this work for DS decaying to $e^+e^-$ for the ionization history fixed to tanh model. The width of the bands correspond to the extreme assumptions on the DS mass from 1 TeV (weakest) to 316 MeV (strongest) for Ly$\alpha$ bounds and in the range 1 TeV - 100 MeV for the CMB bounds. The red band has been derived using Lyman-$\alpha$ IGM temperature measurements, whereas the blue and yellow bands have been derived using CMB optical depth evaluation for the Planck 2015 and Planck 2018 measurements respectively. The vertical grey region indicates the region of $\tau_{\rm DS} \lesssim 10^{14}$ s where our CMB bounds based on optical depth reionization cannot constrain ionization level change (see discussion in main text). We additionally show the estimated bounds using Eq. \ref{['eq:stima_Tm']} that will be probed by 21-cm probes (dot-dashed). Right: Same constraints derived in this work for DS decaying to $\gamma \gamma$ where for the Lyman$-\alpha$ band (red), we vary the DS mass between 100 MeV (weakest) to 100 eV (strongest) and for the CMB constraint bands, between 1 TeV (weakest) and 39.8 eV (strongest).
• Figure 5: Constraints on DS parameter space obtained using CMB estimates based on the evaluation of the optical depth to reionization from Planck 2018 measurement of $\tau_{\rm reion}$ for DS decaying to $e^+e^-$(left) and for DS decaying to $\gamma \gamma$(right) final states for different DS mass values. For the $e^+e^-$ case, DS mass values in the range 30 - 300 MeV give some of the most competitive bounds, here we have shown the strongest that we obtain (for $m_{\rm DS}$ set to 100 MeV) to not crowd the plot. For $\gamma \gamma$ case, the strongest bounds are obtained for DS mass in the sub-keV range - the best we obtain is for DS mass close to 40 eV.