3-form dark energy and cosmic birefringence

Abstract

3-forms are interesting fields to study in the cosmological context for numerous reasons, such as being candidates for explaining inflation and dark energy. The background evolution of a 3-form field is similar to but distinguishable from a scalar field in an expanding universe, and its tensorial structure allows for unique couplings that cannot be experienced by canonical scalars. In this work, we explore the possibility that 3-form dark energy can explain cosmic birefringence. We consider two EFT-inspired couplings between the 3-form and the photon, and compute the birefringence angle $\beta$. We find that a dimension-6 gauge-invariant operator necessitates an extremely large coupling to explain $\beta\sim0.3^\circ$, the value suggested by observations of recent cosmic microwave background radiation. Conversely, a dimension-4 operator can accommodate $\beta\sim0.3^\circ$ at the expense exciting the longitudinal mode of the photon. Interestingly, demanding a self-consistent decoupling limit implies the photon mass lies within a few orders of magnitude of $H_0$. We also derive `universal' profiles for $\beta(z)$, finding the $\beta$ from the dimension-4 operator is insensitive to the form of the 3-form potential but is sensitive to the initial conditions. Contrarily, the dimension-6 operator is highly sensitive to the form of the potential. We finally compare the universal profiles to that of axion-like particle (ALP) dark energy and an ultralight massive 3-form, the latter obtained from numerically integrated cosmological histories consistent with $\Lambda$CDM up to low redshift. Our results show that birefringence from 3-form dark energy can both mimic that from an ALP or be distinguishable, depending on the field configuration in the early universe.