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Chern-Simons Gravity and Neutrino Self-Interactions

Dynamical Chern-Simons gravity (dCS) is a four-dimensional parity-violating extension of general relativity. Current models predict the effect of this extension to be negligible due to large decay constants $f$ close to the scale of grand unified theories. Here, we present a construction of dCS allowing for much smaller decay constants, ranging from sub-eV to Planck scales. Specifically, we show that if there exists a fermion species with strong self-interactions, the short-wavelength fermion modes form a bound state. This bound state can then undergo dynamical symmetry breaking and the resulting pseudoscalar develops Yukawa interactions with the remaining long-wavelength fermion modes. Due to this new interaction, loop corrections with gravitons then realize a linear coupling between the pseudoscalar and the gravitational Chern-Simons term. The strength of this coupling is set by the Yukawa coupling constant divided by the fermion mass. Therefore, since self-interacting fermions with small masses are ideal, we identify neutrinos as promising candidates. For example, if a neutrino has a mass $m_ν\lesssim {\rm meV}$ and the Yukawa coupling is order unity, the dCS decay constant can be as small as $f \sim 10^3 m_ν\lesssim {\rm eV}$. We discuss other potential choices for fermions.