Is cosmic birefringence due to dark energy or dark matter? A tomographic approach

A pseudoscalar “axionlike” field, $\varphi$, may explain the $3\sigma$ hint of cosmic birefringence observed in the $EB$ power spectrum of the cosmic microwave background polarization data. Is $\varphi$ dark energy or dark matter? A tomographic approach can answer this question. The effective mass of dark energy field responsible for the accelerated expansion of the Universe today must be smaller than $m_{\varphi }\simeq {10}^{-33}\mathrm{eV}$. If $m_{\varphi }\gtrsim {10}^{-32}\mathrm{eV}$, $\varphi$ starts evolving before the epoch of reionization and we should observe different amounts of birefringence from the $EB$ power spectrum at low ($l\lesssim 10$) and high multipoles. Such an observation, which requires a full-sky satellite mission, would rule out $\varphi$ being dark energy. If $m_{\varphi }\gtrsim {10}^{-28}\mathrm{eV}$, $\varphi$ starts oscillating during the epoch of recombination, leaving a distinct signature in the $EB$ power spectrum at high multipoles, which can be measured precisely by ground-based cosmic microwave background observations. Our tomographic approach relies on the shape of the $EB$ power spectrum and is less sensitive to miscalibration of polarization angles.

Figure 1

The visibility function as a function of redshift $z$. The orange and blue regions show the recombination and reionization epochs, respectively. The reionization is included using the tanh model with $z_{\mathrm{rei}}=7.82$ [42, 46].

Figure 2

Evolution of $\varphi$ for $m_{\varphi }={10}^{-28.0}$ (green), ${10}^{-30.3}$ (blue), ${10}^{-31.2}$ (red), and ${10}^{-32.3}\mathrm{eV}$ (black). The shaded regions show recombination and reionization epochs as in Fig. 1.

Figure 3

The $EB$ power spectrum from piecewise constant angles given in Eq. (13): $\beta ={\beta }_{\mathrm{rec}}$ for $z>10$ and $\beta ={\beta }_{\mathrm{rei}}$ for $z\le 10$. The top and bottom panels show $l(l+1)C_l^{EB}/(2\pi )$ and the effective angles given in Eq. (16), respectively.

Figure 4

Same as Fig. 3, but for axion dynamics shown in Fig. 2.

Figure 5

Ratio of the effective cosmic birefringence angles from reionization and recombination defined in Eq. (17). The ratio is sensitive to the change in the axion mass over ${10}^{-32}\mathrm{eV}\lesssim m_{\varphi }\lesssim {10}^{-31}\mathrm{eV}$.

Figure 6

The $EB$ power spectrum for large $m_{\varphi }$. The left panel shows $l(l+1)C_l^{EB}/(2\pi )$ for $m_{\varphi }={10}^{-28.8}$ (black), ${10}^{-27.9}$ (red), ${10}^{-27.8}$ (blue), and ${10}^{-27.7}\mathrm{eV}$ (green). The dotted vertical lines show the positions of the third peak. The right panel shows axion dynamics for each $m_{\varphi }$. The shaded region shows the recombination epoch as in Fig. 1.

Figure 7

The effective rotation angles from the Boltzmann equation (wiggly lines) and $⟨\beta ⟩$ given in Eq. (18) (horizontal lines) for $m_{\varphi }={10}^{-27.9}$ (top) and ${10}^{-27.8}\mathrm{eV}$ (bottom).

Figure 8

The expected $1\sigma$ error contours in the two-dimensional parameter space ($\alpha$ and $g{\varphi }_{\mathrm{in}}/2$ in units of degrees). The axion masses are $m_{\varphi }={10}^{-32}$ (top) and ${10}^{-30}\mathrm{eV}$ (bottom). We show the results from the full $l$ range (black), reionization bump ($2\le l\le 20$; orange dashed), and high multipoles ($21\le l\le 500$; green dot-dashed). We assume a LiteBIRD-like experiment without delensing. The black and green contours overlap in the top panel.

Figure 9

The expected $1\sigma$ and $2\sigma$ error contours on ${\log }_{10}{m}_{\varphi }$ and $|g{\varphi }_{\mathrm{in}}/2|$ (in units of degrees) for $m_{\varphi ,\mathrm{fid}}={10}^{-30}\mathrm{eV}$. The miscalibration angle is marginalized over using a Gaussian prior with ${\sigma }_{\alpha }=0.5°$ (top) and 0.1° (bottom). The fiducial value of $g{\varphi }_{\mathrm{in}}/2$ is chosen to give ${\beta }_{\mathrm{rec}}=0.35°$ (red dots). The black dashed lines show $|g{\varphi }_{\mathrm{in}}/2|$ for ${\beta }_{\mathrm{rec}}=0.35°$ at each $m_{\varphi }$. We assume a LiteBIRD-like experiment.

Figure 10

Same as Fig. 9 but for $m_{\varphi ,\mathrm{fid}}={10}^{-28}\mathrm{eV}$.

Figure 11

Same as Fig. 10 but for an SO-like experiment.

Figure 12

Same as the top panel of Fig. 11 but for a CMB-S4-like experiment. The result for ${\sigma }_{\alpha }=0.1°$ is similar.