Is a massive graviton with cosmological mass a consistent theory?
In plain words
Giving the graviton a tiny mass, comparable to the inverse age of the universe, changes gravity at the largest distances. Versions without unstable ghost modes exist, but they may violate causality or lack any consistent high-energy completion.
Precise statement
For ghost-free (de Rham-Gabadadze-Tolley) massive gravity and bigravity with $m_g \sim \hbar H_0/c^2$, approximately $10^{-33}\,\mathrm{eV}/c^2$, the strong-coupling scale $\Lambda_3 = (m_g^2 M_P)^{(1/3)}$ corresponds to a length of roughly $10^3\,\mathrm{km}$. Determine whether the theory admits a Lorentz-invariant, unitary, causal UV completion compatible with S-matrix positivity bounds. An answer is an explicit completion or a no-go theorem.
What would settle it
A positivity-bound or causality theorem that excludes the parameter space, or an explicit UV completion.
Status in the literature
Positivity analyses (2016-2023) leave a narrow or empty allowed region; gravitational-wave dispersion bounds $m_g$ below about $10^{-23}\,\mathrm{eV}/c^2$ (2021).