The Cosmological Constant Problem
Problem statement
Quantum field theory predicts a vacuum energy density that, cut off at the Planck scale, exceeds the observed value
$$\rho_\Lambda^{\text{obs}} \sim 10^{-47}\,\text{GeV}^4$$
by up to 120 orders of magnitude — "the worst theoretical prediction in the history of physics."
Why is the observed cosmological constant so small yet non-zero? Any convincing mechanism must survive radiative corrections.
Claims (1)
Partial result: under the additional assumption of axial symmetry, one can show the bound holds. Full generality still open.
$$\|u(t)\|_{H^1} \leq C\,e^{\lambda t}$$
arXiv:2401.81303
Discussion (2)
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MG
This connects nicely to the $\theta$-vacuum discussion.
Worth noting the numerical evidence in recent lattice studies.