Future CMB constraints on cosmic birefringence and implications for fundamental physics

The primary scientific target of the ground- and space-based cosmic microwave background (CMB) polarization experiments 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 midcost space mission PICO. We examine the detectability of both a stochastic anisotropic rotation field, as well as 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 $1\ensuremath{\sigma}$ bound on the isotropic CPR from the current value of 30 arcmin to 1.5 and 0.6 arcmin, respectively, while a CMB-S4-like experiment and PICO will reduce it to $\ensuremath{\sim}0.1\text{ }\text{ }\mathrm{arcmin}$. 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 potential implications for fundamental physics by interpreting the forecasted bounds on CPR in terms of the corresponding constraints on pseudoscalar fields coupled to electromagnetism, primordial magnetic fields (PMF), and violations of Lorentz invariance. We find that CMB-S4-like and PICO can reduce the $1\ensuremath{\sigma}$ bound on the amplitude of the scale-invariant PMF from 1 to 0.1 nG, while also probing the magnetic field of the Milky Way. The upcoming experiments will also tighten bounds on the axion-photon coupling, with SO improving the bound from ${f}_{a}\ensuremath{\gtrsim}50{H}_{I}$ at present, where ${H}_{I}$ is the energy scale of inflation, to ${f}_{a}\ensuremath{\gtrsim}500{H}_{I}$, and CMB-S4-like and PICO raising it to ${f}_{a}\ensuremath{\gtrsim}\mathrm{few}\ifmmode\times\else\texttimes\fi{}{10}^{3}{H}_{I}$, placing stringent constraints on the string theory axions.

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