The role of gravity in naturalness versus consistency: strong- <i>CP</i> and dark energy

There is an ongoing debate on how seriously one should take the naturalness puzzles as the guidelines to new physics. In this debate gravity is often put aside, as an insignificant spectator force. However, this attitude misses the entire essence of the story. Through its [Formula: see text]-matrix formulation, gravity promotes certain puzzles, such as the cosmological constant and strong-[Formula: see text] problems, into the consistency issues. The respective consistency requirements make the theory highly predictive. In particular, the cosmological vacuum energy must be zero. This has fundamental implications both for strong-[Formula: see text] and for dark energy puzzles. QCD must include an axion as an intrinsic part of the gauge redundancy, without the need of any global symmetry. This gives [Formula: see text] to all orders in operator expansion. Applied to cosmology, the [Formula: see text]-matrix implies that the energy budget of the Universe cannot come from a constant. Correspondingly, the dark energy is an unambiguous signal of new physics around the Hubble scale. This article is part of the theme issue 'The particle-gravity frontier'.