Trans-Planckian Censorship Conjecture (TCC)

Establish the Trans-Planckian Censorship Conjecture by showing that any Friedmann–Robertson–Walker (FRW) phase of accelerated expansion with scale factor a and Hubble parameter H must obey (a_f/a_i) l_P ≤ 1/H_f, where i and f denote the initial and final times.

Background

The Trans-Planckian Censorship Conjecture (TCC) posits that accelerated expansion cannot stretch sub-Planckian modes to become super-horizon, thereby imposing strong bounds on cosmological dynamics and inflationary model-building. It is closely tied to holographic consistency and the existence of well-defined boundary observables.

In this work, the authors present holographic arguments that enforce TCC for classical scalar cosmologies under natural assumptions (e.g., validity of the EFT in the future vacuum). While they establish special cases and derive constraints consistent with TCC, the conjecture remains central as an explicit open statement with broad implications for positive potentials and plateau-like regions in moduli space.