Using the CMB angular power spectrum to study Dark Matter-photon interactions

TL;DR

The paper addresses whether interactions between Dark Matter and photons leave detectable imprints on the CMB. It develops a DM–γ coupling framework by extending the Boltzmann equations with a momentum-exchange term and implements it in CLASS, enabling precise computation of TT and EE spectra under DM–γ coupling. Using Planck 1-year data (Planck+WP) and a constant cross section, the authors derive a stringent bound $\sigma_{DM-\gamma} \le 8 \times 10^{-31} (m_{DM}/\mathrm{GeV})$ cm$^2$ (68% CL), equivalent to $u \le 1.2 \times 10^{-4}$, while a $T^2$-dependent cross section yields $\sigma_{DM-\gamma} \le 6 \times 10^{-40} (m_{DM}/\mathrm{GeV})$ cm$^2$. These results show that DM–γ interactions, regardless of DM annihilation or decay properties, can be constrained by cosmological observations, and that future CMB polarization and high-$\\ell$ measurements could tighten these limits further, with complementary sensitivity from large-scale structure and Lyman-$\\alpha$ data. Overall, the work establishes CMB cosmology as a universal probe of dark-sector physics and motivates continued improvement in polarization and small-scale measurements.

Abstract

In this paper, we explore the impact of Dark Matter-photon interactions on the CMB angular power spectrum. Using the one-year data release of the Planck satellite, we derive an upper bound on the Dark Matter-photon elastic scattering cross section of sigma_{DM-photon} < 8 x 10^{-31} (m_DM/GeV) cm^2 (68% CL) if the cross section is constant and a present-day value of sigma_{DM-photon} < 6 x 10^{-40} (m_DM/GeV) cm^2 (68% CL) if it scales as the temperature squared. For such a limiting cross section, both the B-modes and the TT angular power spectrum are suppressed with respect to LCDM predictions for l > 500 and l > 3000 respectively, indicating that forthcoming data from CMB polarisation experiments and Planck could help to constrain and characterise the physics of the dark sector. This essentially initiates a new type of dark matter search that is independent of whether dark matter is annihilating, decaying or asymmetric. Thus, any CMB experiment with the ability to measure the temperature and/or polarisation power spectra at high l should be able to investigate the potential interactions of dark matter and contribute to our fundamental understanding of its nature.

Figures (5)

• Figure 1: The effect of DM--$\gamma$ interactions on the $TT$ (left) and $EE$ (right) components of the CMB angular power spectrum, where the strength of the interaction is characterised by $u \equiv \left[{\sigma_{\rm{DM}-\gamma}}/{\sigma_{\mathrm{Th}}} \right] \left[{m_{\rm{DM}}}/{100~\rm{GeV}} \right]^{- 1}$ ($u=0$ corresponds to zero DM--$\gamma$ coupling) and $\sigma_{\rm{DM}-\gamma}$ is constant. For all the curves, we consider a flat $\Lambda$CDM model with $H_0 = 70~\mathrm{km}~{\mathrm{s}}^{-1}~{\mathrm{Mpc}}^{-1}$ ($h = 0.7$), $\Omega_{\Lambda} = 0.7$, $\Omega_{\mathrm{m}} = 0.3$ and $\Omega_{\mathrm{b}} = 0.05$, where $u$ is the only additional parameter. The new coupling has two main effects: i) a suppression of the small-scale peaks due to a combination of collisional damping and a delayed photon decoupling, and ii) a shift in the peaks to larger $\ell$ due to a decrease in the sound speed of the thermal plasma. (Note that $u = 10^{-4}$ is difficult to distinguish from $u = 0$ at this scale).
• Figure 2: Triangle plot showing the one and two-dimensional posterior distributions of the cosmological parameters set by Planck, with $u \equiv \left[{\sigma_{\rm{DM}-\gamma}}/{\sigma_{\mathrm{Th}}} \right] \left[{m_{\rm{DM}}}/{100~\rm{GeV}} \right]^{- 1}$ as a free parameter and a constant $\sigma_{\rm{DM}-\gamma}$. The contours correspond to the 68% and 95% confidence levels. $\Omega_{\rm{b}} h^2$ is the baryon energy density, $\Omega_{\rm{DM}} h^2$ is the dark matter energy density, $h$ is the reduced Hubble parameter, $A_s$ is the primordial spectrum amplitude, $n_s$ is the spectral index and $z_{\rm{reio}}$ is the reionisation redshift.
• Figure 3: A comparison between the $TT$ angular power spectra for the maximally allowed (constant) DM--$\gamma$ cross section ($u \simeq 10^{-4}$), and the 9-year WMAP Hinshaw:2012aka and one-year Planck Ade:2013zuv best-fit data. Also plotted are the full 3-year data from the SPT and ACT experiments Calabrese:2013jyk. On the left, we see a suppression of power with respect to WMAP-9 and Planck for $\ell \gtrsim 3000$ and on the right, we give our prediction for the $TT$ component of the angular power spectrum at high $\ell$.
• Figure 4: The effect of DM--$\gamma$ interactions on the $B$-modes of the angular power spectrum, where the strength of the interaction is characterised by $u \equiv \left[{\sigma_{\rm{DM}-\gamma}}/{\sigma_{\mathrm{Th}}} \right] \left[{m_{\rm{DM}}}/{100~\rm{GeV}} \right]^{- 1}$ (with a constant $\sigma_{\rm{DM}-\gamma}$) and we use the ' Planck + WP' best-fit parameters from Ref. Ade:2013zuv. The data points are the recent $B$-mode polarisation measurements from the SPT experiment, where SPTpol 1, SPTpol 2 and SPTpol 3 refer to $({\hat{\rm{E}}}^{150}{\hat{\phi}}^{\rm{CIB}}) \times {\hat{\rm{B}}}^{150}$, $({\hat{\rm{E}}}^{95}{\hat{\phi}}^{\rm{CIB}}) \times {\hat{\rm{B}}}^{150}$ and $({\hat{\rm{E}}}^{150}{\hat{\phi}}^{\rm{CIB}}) \times {\hat{\rm{B}}}_{\chi}^{150}$ respectively in Ref. Hanson:2013hsb. For the maximally allowed (constant) DM--$\gamma$ cross section ($u \simeq 10^{-4}$), we see a deviation from the Planck best-fit $\Lambda$CDM model for $\ell \gtrsim 500$ and a significant suppression of power for larger $\ell$.
• Figure 5: The influence of DM--$\gamma$ interactions on the matter power spectrum, where the strength of the interaction is characterised by $u \equiv \left[{\sigma_{\rm{DM}-\gamma}}/{\sigma_{\mathrm{Th}}} \right] \left[{m_{\rm{DM}}}/{100~\rm{GeV}} \right]^{- 1}$ (with a constant $\sigma_{\rm{DM}-\gamma}$) and we use the ' Planck + WP' best-fit parameters from Ref. Ade:2013zuv. The new coupling produces (power-law) damped oscillations at large scales, reducing the number of small-scale structures, thus allowing the cross section to be constrained. For allowed (constant) DM--$\gamma$ cross sections ($u \lesssim 10^{-4}$), significant damping effects are restricted to the non-linear regime ($k \gtrsim 0.2~h~{\rm{Mpc}}^{-1}$).