CMB constraints on mass and coupling constant of light pseudoscalar particles

Transformation of cosmic microwave background photons into light pseudoscalar particles at the post-big-bang-nucleosynthesis epoch is considered. Using the present day value of a large scale magnetic field to estimate it at earlier cosmological epochs, the oscillation probability of photons into light pseudoscalar particles with an account of coherence breaking in cosmological plasma is calculated. Demanding that the photon transformation does not lead to an exceedingly large cosmic microwave background spectral distortion and temperature anisotropy, the constraints on the coupling constant of axionlike particles to photons, $g_{\varphi \gamma }B\lesssim (10^{-15}–10^{-12})\mathrm{nG}\times {\mathrm{GeV}}^{-1}$, are found for the axionlike particle mass in the interval $10^{-25}\mathrm{eV}\lesssim m_{\varphi }\lesssim 10^{-5}\mathrm{eV}$, where $B$ is the strength of the large scale magnetic field at the present time. Our results update the previously obtained ones since we use the density matrix formalism which is more accurate than the wave function approximation for the description of oscillations with an essential coherence breaking. In the axionlike particle mass range $10^{-25}\mathrm{eV}\lesssim m_{\varphi }\lesssim 10^{-14}\mathrm{eV}$, weaker limits, by at least 2 orders of magnitude $g_{\varphi \gamma }B\lesssim 10^{-11}\mathrm{nG}\times {\mathrm{GeV}}^{-1}$, are obtained in comparison with the wave function approximation. In the mass range $10^{-14}\mathrm{eV}\lesssim m_{\varphi }\lesssim 10^{-5}\mathrm{eV}$, on the other hand, limits that are stronger, by more than an order of magnitude, are obtained. Our results are derived by using upper limits on spectral distortion parameter $\mu$ and temperature anisotropy $\mathrm{\Delta }T/T$ found by COBE and expected sensitivities found by PIXIE/PRISM.

Figure 1

Plot of the hydrogen ionization fraction $X_e(T)$ as a function of temperature $T$ for ${\mathrm{\Omega }}_B{h}_0^2=0.022$ and ${\mathrm{\Omega }}_M{h}_0^2=0.12$.

Figure 2

Log-Log plot of $m_i=\{m_{\mathrm{pla}},m_{\mathrm{QED}},m_a\}$ as a function of temperature $T$ in Kelvin in the CMB energy range: $1.2\le x\le 11.3$ (colored regions). The QED terms, $m_{\mathrm{QED}}$ (in green upper region and in black lower region) for $B=2\times 10^3\mathrm{nG}$ and $B=1\mathrm{nG}$ and plasma term $m_{\mathrm{pla}}$ (in red), are respectively shown. The term $m_a$ (in blue or in black) for fixed values of $m_{\varphi }=10^5\mathrm{eV}$ (top region) and $m_{\varphi }=10^{-14}\mathrm{eV}$ (bottom region) is shown. The term $m_a$ and plasma term $m_{\mathrm{pla}}$ do not depend on $B$.

Figure 3

Exclusion/sensitivity plot for the ALP parameter space $g_{\varphi \gamma }B-x$ due to $\mu$-distortions for magnetic field $B=1\mathrm{nG}$, $m_{\varphi }=1\times 10^{-11}–5\times 10^{-6}\mathrm{eV}$ for (a) COBE upper limits on $\mu$ and (b) PIXIE expected sensitivity on $\mu$. We can see that tighter limits on $g_{\varphi \gamma }B$ are obtained at the highest energy point, $x=11.3$.

Figure 4

Resonance mass ${\overline{m}}_{\varphi }$ as a function of the temperature $T$ in Kelvin for $B=1\mathrm{nG}$. The resonance mass is presented for two values of the photon energy, $x=1.2$ (dot dashed curve) and $x=11.3$ (continuous curve), but the curves are indistinguishable indicating that the resonance does not depend on $x$ in the energy interval considered here. Panel (b) is the same as panel (a) but in a reduced temperature interval. The resonant mass regions which contribute to $\mu$-distortion and temperature anisotropy, as well as the region where the multiple resonances are excited (within the solid lines in the lower part of the graph) are presented there.

Figure 5

Exclusion plot based on the COBE data for the ALP parameter space $g_{\varphi \gamma }B-m_{\varphi }$ for magnetic field $B=1\mathrm{nG}$ and $x=11.3$ in the resonant case. In panel (a) the exclusion plot is deduced from upper limit on $\mu$ and in panel (b) the exclusion plot is derived from the COBE sensitivity on the temperature anisotropy $\delta T/T\sim 10^{-5}$ . In panel (b) the bounds are presented for the mass in the resonant mass range: $1.6\times 10^{-14}\mathrm{eV}\le m_{\varphi }\le 6.18\times 10^{-13}\mathrm{eV}$.

Figure 6

Exclusion plot for the ALP parameter space, $g_{\varphi \gamma }B-m_{\varphi }$ in the case of COBE (region above solid line) and sensitivity of PIXIE (region above dot dashed line), based on the combined limits on $\mu$-distortion and temperature anisotropy for magnetic field $B=1\mathrm{nG}$ and $x=11.3$. We can see that at the transition points ($m_{\varphi }=1.6\times 10^{-14}\mathrm{eV}$, $m_{\varphi }=2\times 10^{-10}\mathrm{eV}$, and $2.45\times 10^{-6}\mathrm{eV}$) from the resonant region to the nonresonant region there is an extremely sharp increase in $g_{\varphi \gamma }B$, by more than an order of magnitude. This is a consequence of the fast varying solutions at the transition points. Using the logarithmic scale and wide range of ALP masses slightly magnifies this effect. In the ALP mass range $m_{\varphi }\le 2\times 10^{-10}\mathrm{eV}$, the exclusion plot of COBE and sensitivity of PIXIE have been obtained from CMB temperature anisotropy. For $2\times 10^{-10}<m_{\varphi }\le 10^{-5}$ both the exclusion plot and sensitivity of PIXIE have been obtained from $\mu$-distortion. In the mass range $m_{\varphi }\le 2\times 10^{-10}\mathrm{eV}$, temperature anisotropy gives more stringent limits with respect to $\mu$-distortion while for $m_{\varphi }>2\times 10^{-10}\mathrm{eV}$, $\mu$-distortion gives tighter limits in comparison with temperature anisotropy.