The non-thermal secondary CMB anisotropies from a cosmic distribution of radio galaxy lobes

Current and upcoming high angular resolution and multifrequency experiments are well poised to explore the rich landscape of secondary cosmic microwave background (CMB) anisotropies. In this context, we compute, for the first time, the power spectrum of CMB fluctuations from a cosmological distribution of evolving lobes of giant radio galaxies. We also explicitly take into account the non-thermal electron distribution, which has important implications for the inference of the CMB angular power spectrum. We calculate the mean global non-thermal y-distortion, ⟨y⟩_NT. For observationally reasonable distribution of the jet luminosities in the range of 10⁴⁵-10⁴⁷ erg s^-1, we find ⟨y⟩_NT to be less than 10^-5, and hence not violating the cosmic background explorer limit as previously claimed. Using the unique spectral dependence of the non-thermal Sunyaev-Zeldovich (SZ), we show that a detection of ⟨y⟩_NT can be within reach at the level of ≳5σ from a future Primordial Inflation Explorer (PIXIE)-like experiment provided we understand the foregrounds precisely. The total non-thermal SZ power spectrum, $C^{\mathrm{ NT}}_\ell$, from the radio lobes peaks at ℓ ~ 3000 with an amplitude $\sim 1{{\ \rm per\ cent}}$ of thermal SZ power spectrum from galaxy clusters. A detection of the $C^{\mathrm{ NT}}_\ell$, with a PIXIE-like sensitivity experiment, can lead to ~5σ constraint on the mass dependence of the jet luminosity with the constraint becoming at least ten times better for the proposed more ambitious CMB-HD survey. This will further lead to the tightest constraint on the central black hole mass-to-host halo mass scaling relations.