The species scale and the refined TCC bound in time-dependent backgrounds of string theory

TL;DR

This work addresses how the trans-Planckian censorship conjecture (TCC) behaves when the natural quantum-gravity cutoff is the species scale rather than the Planck scale, within time-dependent string-theory backgrounds. It proposes the refined TCC and tests it across a suite of string compactifications with one or two moduli, using explicit FRW cosmologies in the Einstein frame and analyzing dilaton- and modulus-driven dynamics. Across superstring, heterotic, Type II, Type I, and multi-moduli scenarios, the refined TCC is consistently satisfied, it predicts a shorter de Sitter lifetime, and it yields a nontrivial bound on the cosmological constant, while supporting no-singularity cosmologies (e.g., string gas cosmology). The results suggest a coherent picture where the string scale governs the ultimate quantum-gravity cutoff, tying together swampland constraints, cosmological bounds, and finite-temperature string thermodynamics (e.g., the Hagedorn limit) to favor regular cosmologies with controlled moduli evolution.

Abstract

The species scale is the energy scale at which quantum corrections to Einstein's theory of gravity become significant. In many cases, this scale corresponds to the string mass scale, which can be much lower than the Planck scale in the weak coupling limit. In this note, we explore a variant of the TCC conjecture, which we refer to as the refined TCC. This version is related to the species scale as a new cutoff in quantum gravity, and we study whether stringy modes remain stringy and never exceed the Hubble horizon. The refined TCC predicts a shorter lifetime for de-Sitter spacetime and imposes a bound on the cosmological constant. We present supporting evidence for the refined TCC from cosmological solutions of different compactifications of various string theories. Furthermore, it is argued that both the TCC and the refined TCC are incompatible with the big-bang singularity. Therefore, if the TCC and the refined TCC hold, the big bang singularity must be ruled out. In scenarios such as string gas cosmology, where the TCC is realized, the spacetime background remains completely regular.

Figures (5)

• Figure 1: The string coupling in $D=4.$
• Figure 2: The refined TCC for $D=4$. We have chosen $\tau_i=0.01$ and $K=5$.
• Figure 3: The string coupling $g_s$ in $D=4$. We have chosen $d_1$ and $d_2$ in such away that $e^{\sqrt{\frac{3}{2}}\kappa_D d_1+\frac{1}{\sqrt{2}}\kappa_D d_2}=0.1$.
• Figure 4: The warp factor.
• Figure 5: The refined TCC for two moduli solution in $O(16)\times O(16)$ string theory. We have set $\tau_i=-1$.