Swampland conjectures and late-time cosmology

We discuss the cosmological implications of the string swampland conjectures for late-time cosmology, and test them against a wide range of state of the art cosmological observations. The refined de Sitter conjecture constrains either the minimal slope or the curvature of the scalar potential, and depends on two dimensionless constants. For constants of size one or larger, tension exists between observations, especially the Hubble constant, and the slope and curvature conjectures at a level of $4.5\sigma$ and $2.3\sigma$, respectively. Smaller values of the constants are permitted by observations, and we determine upper bounds at varying confidence levels. We also derive and constrain the relationship between cosmological observables and the scalar field excursion during the acceleration epoch, thereby testing the distance conjecture.

Figure 1

The marginalized probability distribution of the parameter $\lambda$ of the exponential potential relevant for the C1.1 dS conjecture and the joint marginalized distribution of $\lambda$ and total field excursion relevant for the C2 distance conjecture. The dashed line is the relation between these two parameters predicted by Eq. (9). The darker and lighter shades correspond respectively to the 68% C.L. and the 95% C.L. regions.

Figure 2

The marginalized probability distribution of the parameter $c$ of the cosine potential, relevant for the C1.2 dS conjecture, and the joint marginalized distribution of $c$ and total field excursion relevant for the C2 distance conjecture. The darker and lighter shades correspond respectively to the 68% C.L. and the 95% C.L. regions.

Figure 3

The marginalized probability distribution of ${\lambda }_{\mathrm{eff}}$ for both the exponential and cosine potentials together with its joint marginalized distribution with total field excursion for the ALL dataset. The dashed line is the relation between these two parameters predicted by Eq. (9). The darker and lighter shades correspond respectively to the 68% C.L. and the 95% C.L. regions.

Figure 4

The joint marginalized distribution of initial condition tuning and $c$ for the cosine potential and the ALL dataset. Models are cut based on their value of ${\lambda }_{\mathrm{eff}}$ at the 95% C.L. bound from the exponential potential, resulting in models shown with ${\lambda }_{\mathrm{eff}}<0.51$. The density of points is proportional to the joint PDF and the color represents the value of ${\lambda }_{\mathrm{eff}}$. The dashed line represents the amount of tuning needed to stabilize a given value of $c$ given by Eq. (14). The solid line represents the tuning cut that we enforce.