Constraining $\mu$ and $y$ distortions in the Cosmic Microwave Background with COBE/FIRAS Data

This paper presents a novel approach to constrain the $\mu$- and y- distortions in the Cosmic Microwave Background (CMB) using the COBE/FIRAS data. The analysis draws from the concept of blackbody radiation inversion (BRI), a mathematical technique typically used to determine the temperature distribution from a radiated power spectrum. We study the deviations from the ideal blackbody spectrum or the spectral distortions by incorporating first a non-zero chemical potential $\mu$ via the Bose-Einstein distribution and then the Compton parameter $y$ while keeping the monopole temperature constant. We infer the results as probability distribution functions on these distortions. Finally, we derive $\mu =(8.913\pm 0.736)\times {10}^{-5}$ and $y=(1.532\pm 0.092)\times {10}^{-5}$ at a $68\mathrm{\%}$ confidence interval. The results are consistent with prior values and provide tighter constraints on the CMB spectral distortion and synergies of the primordial Universe.