# Swampland Distance Conjecture, Inflation and $\alpha$-attractors

## TL;DR

This paper explores how the Swampland Distance Conjecture constrains inflationary models, especially $oldsymbol{ extalpha}$-attractors, revealing a universal upper bound on inflaton excursions and implications for string theory realizations.

## Contribution

It demonstrates that the Swampland Distance Conjecture suggests inflation as an infinite distance phenomenon with $oldsymbol{ extalpha}$-attractor-like kinetic structures, and analyzes constraints on these models within string theory.

## Key findings

- SDC imposes an upper bound on inflaton excursion based on tensor-to-scalar ratio.
- Inflation in $ extalpha$-attractors can be compatible with SDC constraints.
- String theory realizations of these models should occur near infinite field distance singularities.

## Abstract

The Swampland Distance Conjecture (SDC) constraints the dynamics emerging at infinite distances in field space of any effective field theory consistent with quantum gravity. It provides a relation between the cut-off in energies and the field range which, as we show, in the context of inflation it yields a universal upper bound on the inflaton excursion in terms of the tensor-to-scalar ratio, measured at typical CMB scales. In this note, we investigate the interplay between the SDC and the emergent inflationary physics around infinite distances singularities in string theory, with a special look at its significance for the $\alpha$-attractor scenario of inflation. We show that the conjecture itself suggests that inflation may arise as an infinite distance phenomenon with the asymptotic kinetic structure typical of $\alpha$-attractors. Furthermore, we argue that a proper string realisation of these cosmological models in Calabi-Yau manifolds should occur around infinite field distance singularities. However, such constructions typically imply that inflation should not take place in the limit where the inflaton kinetic term develops a pole but rather in the opposite regime. Finally, we study the constraints that the SDC poses on $\alpha$-attractors and show that they still leave considerable room for compatibility with observations.