  Transformation of CMB photons into light pseudoscalar particles at 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 CMB
spectral distortion and temperature anisotropy, the constraints on the coupling
constant of axion like particles to photons, $ g_{\phi\gamma} B \lesssim
(10^{-15} - 10^{-12}) \textrm{nG}\times \textrm{GeV}^{-1}$, are found for the
axion like particle mass in the interval $10^{-25}$ eV $\lesssim
m_{\phi}\lesssim 10^{-5}$ 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 axion like particle mass range $10^{-25}$
eV $\lesssim m_{\phi}\lesssim 10^{-14}$ eV, weaker limits, by at least 2 orders
of magnitude $g_{\phi\gamma} B \lesssim 10^{-11}\textrm{nG}\times
\textrm{GeV}^{-1}$, are obtained in comparison with the wave function
approximation. In the mass range $10^{-14}$ eV $\lesssim m_{\phi}\lesssim
10^{-5}$ 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 $\Delta T/T$
found by COBE and expected sensitivities by PIXIE/PRISM.
