A very comprehensive review article has appeared on arXiv with the title Hitchhiker’s Guide to the Swampland: The Cosmologist’s Handbook to the string-theoretical Swampland Programme by Kay Lehnert (who just happens to be my PhD student). The paper is 170 pages long and contains over 1,800 references, which gives some idea of what a large field this is and how much work Kay has put into writing it!
The abstract reads
String theory has strong implications for cosmology: it tells us that we cannot have a cosmological constant, that single-field slow-roll inflation is ruled out, and that black holes decay. We elucidate the origin of these statements within the string-theoretical swampland programme. The swampland programme is generating a growing body of insights that have yet to be incorporated into cosmological models. Taking a cosmologist’s perspective, we highlight the relevance of swampland conjectures to black holes, dark matter, dark energy, and inflation, including their implications for scalar fields such as quintessence and axions. Our goal is to inspire cosmological model builders to examine the compatibility of effective field theories with quantum gravitational UV completions and to address outstanding cosmological tensions such as the Hubble tension. This comprehensive literature review presents clear definitions, cosmological implications, and the current status – including evidence and counterexamples – of the following swampland conjectures: the anti-de Sitter distance conjecture (AdSDC), the completeness conjecture (CC), the cobordism conjecture, the de Sitter conjecture (dSC), the swampland distance conjecture (SDC), the emergence proposal (EP), the Festina Lente Bound (FLB), the finite number of massless fields conjecture (or finite flux vacua conjecture (FFV)), the no global symmetries conjecture, the no non-supersymmetric theories conjecture, the non-negative null energy condition conjecture, the positive Gauss-Bonnet term conjecture, the species scale conjecture, the gravitino swampland conjecture (GSC), the tadpole conjecture, the tameness conjecture, the trans-Planckian censorship conjecture (tPCC/TCC), the unique geodesic conjecture, and the weak gravity conjecture (WGC), including the repulsive force conjecture (RFC).
This is essentially the literature review part of Kay’s thesis; the aim of his research is to study the implications of the string-theoretical swampland programme for cosmology. He’s particularly interested in the predictions string theory makes regarding inflation, dark energy, and dark matter, and the impact this has on the Hubble tension. The point of writing this review was to suggest projects that might be undertaken to bring string theory into the realm of testability, thus suppling material for the rest of Kay’s thesis, but I think it is also a very good guide for cosmologists of all types to what the swampland conjectures are and what they do and do not say about the Universe we actually live in.
In the Dark 