Small-scale CMB anisotropies induced by the primordial magnetic fields

The primordial magnetic fields (PMFs) produced in the early universe are expected to be origin of large-scale cosmic fields. PMFs considered leave a footprint on microwave background (CMB) anisotropies due both electromagnetic force and gravitational interaction. In this paper, we investigate how affect CMB smaller scales than mean-free-path photons. We solve baryon Euler equation with Lorentz PMFs, show that vector-type perturbations from induce below Silk scale as $\ell>3000$. Based our calculations, put constraint combined temperature obtained by Planck South Pole Telescope (SPT). have found highly-resolved SPT 2017 bandpowers at $\ell \lesssim 8000$ favor PMF model small scale-dependence. As result, SPT's joint-analysis puts spectral index $n_B<-1.14$ 95% confidence level (C.L.), is more stringent compared Planck-only $n_B<-0.28$. strength normalized co-moving 1 Mpc also tightly constrained $B_{1\mathrm{Mpc}}<1.5$ nG C.L., while $B_{1\mathrm{Mpc}}<3.2$ only data C.L. discuss effects cosmological parameter estimate when including induced PMFs.