The zoo plot meets the swampland: mutual (in)consistency of single-field inflation, string conjectures, and cosmological data

TL;DR

This work tests string-theory swampland conjectures against observational constraints on single-field inflation, focusing on concave potentials. By mapping the SC2 and its refined version SC2r onto the $n_S$–$r$ plane and comparing with Planck and BICEP2/Keck data, the authors derive tight bounds $M_{ m Pl}V_{\phi}/V \lesssim 0.1$ and $M_{ m Pl}^2V_{\phi\phi}/V \lesssim 0.02$ (and $c'\sim0.01$–$0.02$), in strong tension with the expectation $c\sim O(1)$. Extending to DBI and convex potentials does not substantially alleviate the conflict, with DBI yielding only $c<0.37$. The results imply that the simplest single-field slow-roll inflationary models are inconsistent with the basic swampland conjectures under current cosmological data, challenging the compatibility of these conjectures with early-Universe observations.

Abstract

We consider single-field inflation in light of string-motivated "swampland" conjectures suggesting that effective scalar field theories with a consistent UV completion must have field excursion $Δφ\lesssim M_{\rm Pl}$, in combination with a sufficiently steep potential, $M_{\rm Pl} V_φ/V \gtrsim {\cal O}(1)$. Here, we show that the swampland conjectures are inconsistent with existing observational constraints on single-field inflation. Focusing on the observationally favoured class of concave potentials, we map the allowed swampland region onto the $n_S$-$r$ "zoo plot" of inflationary models, and find that consistency with the Planck satellite and BICEP2/Keck Array requires $M_{\rm Pl} V_φ/V \lesssim 0.1$ and $-0.02 \lesssim M_{\rm Pl}^2 V_{φφ}/V < 0$, in strong tension with swampland conjectures. Extension to non-canonical models such as DBI Inflation does not significantly weaken the bound.

Figures (1)

• Figure 1: Regions in the $n_S$-$r$ plane allowed by data (red) and the swampland conjectures (blue) for various values of the parameter $c$ and with $c' = 0$. In particular, the red contours denote two-dimensional probability contours at 68% (dark red) and 95% C.L. (light red) in light of measurements of temperature and polarization anisotropies from Planck and measurements of degree-scale B-mode polarization from BICEP2/Keck Array. The region in the blue shaded contours is the region of parameter space allowed for single-field slow-roll inflation by the swampland conjectures, for various values of the parameter $c$ appearing in Eq. (\ref{['sc2']}). For definiteness we have focused on concave inflationary potentials ($V_{\phi\phi}<0$), whose parameter space lies below the gray shaded region. It is clear that $c \lesssim {\cal O}(0.1)$ is required for the predictions of single-field slow-roll inflation to be consistent with data, violating the string-based expectation that $c$ should be of order unity (the pivot scale plotted is $k_* = 0.05\, h\,\mathrm{Mpc}^{-1}$, and the calculated quantities $n_S$ and $r$ have been rescaled from $k_* = 0.002\, h\,\mathrm{Mpc}^{-1}$). The dashed lines show contours for different values of the second slow roll parameter $\eta = M_{\rm Pl}^2 V_{\phi\phi}/V$: the region below the dashed lines is constrained by the refined swampland conjecture, Eq. \ref{['sc2r']}, with $c' = 0.01$ and $c' = 0.02$, respectively.