A Tip for Landscape Riders: Multi-Field Inflation Can Fulfill the Swampland Distance Conjecture

Understand

We study how both the swampland distance conjecture and the Lyth bound affect the parameter space of multi-field models of inflation.

• A generic feature of multi-field inflation is that the geodesic distance $\left[\Delta\phi\right]_\text{G}$ separating any two points laying along the inflationary trajectory differs from the non-geodesic distance $\left[\Delta\phi\right]_\text{NG}$ traversed by the inflaton between those points.
• These distances must respect a relation of the form $\left[\Delta\phi\right]_\text{G} = f\left(\left[\Delta\phi\right]_\text{NG}\right) \leq \left[\Delta\phi\right]_\text{NG}$, where $f$ is a function determined by the specific multi-field model under scrutiny.
• We show that this relation leads to important constraints on the parameter space characterizing the multi-field dynamics.