  The evidence for a non-vanishing isotropic cosmic birefringence in recent
analyses of the CMB data provides a tantalizing hint for new physics. Domain
wall (DW) networks have recently been shown to generate an isotropic
birefringence signal in the ballpark of the measured value when coupled to
photons. In this work, we explore the axionic defects hypothesis in more detail
and extending previous results to annihilating and late-forming networks, and
by pointing out other smoking-gun signatures of the network in the CMB spectrum
such as the anisotropic birefringent spectrum and B-modes. We also argue that
the presence of cosmic strings in the network does not hinder a large isotropic
birefringence signal because of an intrinsic environmental contribution coming
from low redshifts thus leaving open the possibility that axionic defects can
explain the signal. Regarding the remaining CMB signatures, with the help of
dedicated 3D numerical simulations of DW networks, that we took as a proxy for
the axionic defects, we show how the anisotropic birefringence spectrum
combined with a tomographic approach can be used to infer the formation and
annihilation time of the network. From the numerical simulations, we also
computed the spectrum of gravitational waves (GWs) generated by the network in
the post-recombination epoch and use previous searches for stochastic GW
backgrounds in the CMB to derive for the first time a bound on the tension and
abundance of networks with DWs that annihilate after recombination. Our bounds
extend to the case where the network survives until the present time and
improve over previous bounds by roughly one order of magnitude. Finally, we
show the interesting prospects for detecting B-modes of DW origin with future
CMB experiments.
