The Swampland Conjecture Bound Conjecture
Abstract
I conjecture an upper bound on the number of possible swampland conjectures by comparing the entropy required by the conjectures themselves to the BeckensteinHawking 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 WheelerDewitt 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 arXiv:
 arXiv:2103.16583
 Bibcode:
 2021arXiv210316583K
 Keywords:

 High Energy Physics  Theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 5 pages, 1 figure, 394 references