The Swampland Conjecture Bound Conjecture

TL;DR

This paper proposes an upper bound on the number of swampland conjectures based on entropy considerations, compares it to the growth of conjecture research, and discusses implications for the multiverse and string landscape exploration.

Contribution

It introduces a novel entropy-based upper bound on swampland conjectures and connects it to the growth rate of research and multiverse properties.

Findings

Upper bound of approximately 10^117 conjectures based on entropy constraints.

Projected saturation of conjecture growth bound within 10^-8 H_0^-1.

Lower bound of about 10^263 Hubble volumes needed for full string landscape exploration.

Abstract

I conjecture an upper bound on the number of possible swampland conjectures by comparing the entropy required by the conjectures themselves to the Beckenstein-Hawking entropy of the cosmological horizon. Assuming of order 100 kilobits of entropy per conjecture, this places an upper bound of order $10^{117}$ on the number of conjectures. I estimate the rate of production of swampland conjectures by the number of papers listed on INSPIRE with the word "swampland" in the title or abstract, which has been showing approximately exponential growth since 2014. At the current rate of growth, the entropy bound on the number of swampland conjectures can be projected to be saturated on a timescale of order $10^{-8} H_0^{-1}$. I compare the upper bound from the Swampland Conjecture Bound Conjecture (SCBC) to the estimated number of vacua in the string landscape. Employing the duality suggested by AdS/CFT between the quantum complexity of a holographic state and the volume of a Wheeler-Dewitt spacetime patch, I place a conservative lower bound of order $\mathcal{N}_H > 10^{263}$ on the number of Hubble volumes in the multiverse which must be driven to heat death to fully explore the string landscape via conjectural methods.