Future CMB constraints on cosmic birefringence and implications for
  fundamental physics
  The primary scientific target of the CMB polarization experiments that are
currently being built and proposed is the detection of primordial tensor
perturbations. As a byproduct, these instruments will significantly improve
constraints on cosmic birefringence, or the rotation of the CMB polarization
plane. If convincingly detected, cosmic birefringence would be a dramatic
manifestation of physics beyond the standard models of particle physics and
cosmology. We forecast the bounds on the cosmic polarization rotation (CPR)
from the upcoming ground-based Simons Observatory (SO) and the space-based
LiteBIRD experiments, as well as a "fourth generation" ground-based CMB
experiment like CMB-S4 and the mid-cost space mission PICO. We examine the
detectability of both a stochastic anisotropic rotation field and an isotropic
rotation by a constant angle. CPR induces new correlations of CMB observables,
including spectra of parity-odd type in the case of isotropic CPR, and
mode-coupling correlations in the anisotropic rotation case. We find that
LiteBIRD and SO will reduce the 1$\sigma$ bound on the isotropic CPR from the
current value of 30 arcmin to 1.5 and 0.6 arcmin, respectively, while
CMB-S4-like and PICO will reduce it to $\sim 0.1$ arcmin. The bounds on the
amplitude of a scale-invariant CPR spectrum will be reduced by 1, 2 and 3
orders of magnitude by LiteBIRD, SO and CMB-S4-like/PICO, respectively. We
discuss implications of the forecasted CPR bounds for pseudoscalar fields,
primordial magnetic fields (PMF), and violations of Lorentz invariance. We find
that CMB-S4-like and PICO can reduce the 1$\sigma$ bound on the amplitude of
the scale-invariant PMF from 1 nG to 0.1 nG, while also probing the magnetic
field of the Milky Way. They will also significantly improve bounds on the
axion-photon coupling, placing stringent constraints on the string theory
axions.
