Dark Matter Interactions, Helium, and the Cosmic Microwave Background

The cosmic microwave background (CMB) places a variety of model-independent constraints on the strength interactions of the dominant component of dark matter with the standard model. Percent-level subcomponents of the dark matter can evade the most stringent CMB bounds by mimicking the behavior of baryons, allowing for larger couplings and novel experimental signatures. However, in this Letter, we will show that such tightly coupled subcomponents leave a measurable imprint on the CMB that is well approximated by a change to the helium fraction, $Y_{\mathrm{He}}$. Using the existing CMB constraint on $Y_{\mathrm{He}}$, we derive a new upper limit on the fraction of tightly coupled dark matter, $f_{\mathrm{TCDM}}$, of $f_{\mathrm{TCDM}}<0.006$ (95% C.I.). We show that future CMB experiments can reach $f_{\mathrm{TCDM}}<0.001$ (95% C.I.) and confirm that the bounds derived in this way agree with the results of a complete analysis. These bounds provide an example of how CMB constraints on $Y_{\mathrm{He}}$ have applications beyond studying big bang nucleosynthesis, since tightly coupled dark matter plays no direct role in the formation of light nuclei. We briefly comment on the implications for model building, including millicharged dark matter.

Figure 1

Changes to the ionization fraction resulting from an increase of 0.02 to $Y_{\mathrm{He}}$ and to $F_{\mathrm{TCDM}}$. The dominant effects around hydrogen recombination are almost identical for both parameters. First and second helium recombination are visible in the orange curve as rapid changes in $x_e(z)$ around $z\simeq 6000$ and 1800 and likewise for helium reionization around $z\simeq 3$. These features are easily visible when we change $Y_{\mathrm{He}}$ but are not affected by changes to $F_{\mathrm{TCDM}}$.

Figure 2

Relative changes to the temperature (top) and $E$-mode polarization (bottom) power spectra resulting from an increase of 0.02 to $Y_{\mathrm{He}}$ and $F_{\mathrm{TCDM}}$.

Figure 3

Difference in $k_d^{-2}(a)$ [see Eq. (4)] between models where $Y_{\mathrm{He}}$ and $F_{\mathrm{TCDM}}$ are increased by 0.02 relative to the difference in $k_d^{-2}(a_{\star })$ between a model with $Y_{\mathrm{He}}$ increased by 0.02 and the fiducial model, where $a_{\star }$ is the scale factor at last scattering. It is clear that the difference in the damping scale accumulates during the very early times when helium has not yet recombined and the value of the ionization fraction $x_e(z)$ differs between the two models. The difference reaches a constant 8% offset after helium recombination.

Figure 4

Forecasts for $1\sigma$ constraints on $Y_{\mathrm{He}}$ in $\mathrm{\Lambda }\mathrm{CDM}+Y_{\mathrm{He}}$ compared to constraints on $f_{\mathrm{TCDM}}$ in $\mathrm{\Lambda }\mathrm{CDM}+f_{\mathrm{TCDM}}$ for a range of noise levels, assuming a 1.5 arc min beam. Our forecasts show that to a very good approximation the direct constraints on tightly coupled dark matter can be obtained from rescaling constraints using Eq. (10).