Physics of Trans-Planckian Gravity

TL;DR

This paper argues that ghost-free theories of gravity cannot weaken below Einstein's General Relativity in the IR, implying trans-Planckian quantum degrees of freedom are non-physical and that gravity is UV self-complete without Wilsonian UV completion.

Contribution

It demonstrates that ghost-free gravity theories cannot become weaker than GR in the IR and proposes that trans-Planckian degrees of freedom are classical states, challenging Wilsonian UV completion.

Findings

Trans-Planckian quantum degrees of freedom do not exist in ghost-free theories.

Gravity is UV self-complete and not Wilsonian.

No energy domain exists where gravity becomes asymptotically weak or safe.

Abstract

We study the field theoretical description of a generic theory of gravity flowing to Einstein General Relativity in IR. We prove that, if ghost-free, in the weakly coupled regime such a theory can never become weaker than General Relativity. Using this fact, as a byproduct, we suggest that in a ghost-free theory of gravity trans-Planckian propagating quantum degrees of freedom cannot exist. The only physical meaning of a trans-Planckian pole is the one of a classical state (Black Hole) which is described by the light IR quantum degrees of freedom and gives exponentially-suppressed contributions to virtual processes. In this picture Einstein gravity is UV self-complete, although not Wilsonian, and sub-Planckian distances are unobservable in any healthy theory of gravity. We then finally show that this UV/IR correspondence puts a severe constraint on any attempt of conventional Wilsonian UV-completion of trans-Planckian gravity. Specifically, there is no well-defined energy domain in which gravity could become asymptotically weak or safe.