The non-thermal secondary CMB anisotropies from radio galaxy lobes
  Current and upcoming high angular resolution and multi-frequency experiments
are well poised to explore the rich landscape of secondary CMB anisotropies. In
this context, we compute for the first time, the power spectrum of CMB
fluctuations from plasma in a cosmological distribution of evolving lobes of
giant radio galaxies. We, also, explicitly take into account the non-thermal
electron distribution, as opposed to thermal distribution, which has important
implications for the inference of the CMB angular power spectrum. The
relativistic particles are fed from the central supermassive blackholes via
radio jets leading to radio lobes expanding to megaparsec scales into the
intergalactic medium. Using a model of radio galaxy, we model the energetics
and the pressure of the non-thermal electrons. We calculate the mean global
non-thermal y-distortion, \ynt. For observationally reasonable distribution of
the jet luminosities in the range of $10^{45}-10^{47}$ ergs$^{-1}$, we find
\ynt to be less than $10^{-5}$, and hence not violating the COBE limit as
previously claimed. Using the unique spectral dependence of the non-thermal SZ,
we show that a detection of \ynt can be within reach at the level of $\gtrsim
5\sigma$ from a future PIXIE-like experiment. The total non-thermal SZ power
spectrum, $C^{NT}_\ell$, from the radio lobes is shown to peak at $\ell \sim
3000$ with an amplitude $\sim 1\%$ of thermal SZ power spectrum from galaxy
clusters, and is also within the reach for a PIXIE like experiment. Finally, we
show that a detection of the $C^{NT}_\ell$ with a PIXIE-like experiment can
lead to $\sim 5\sigma$ 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.
