Draining the Swampland

Abstract

We discuss some implications of the recently suggested Swampland conjecture $\frac{|\nabla V|}{V}\gtrsim c\sim 1$, together with a previous one $\Delta \varphi \lesssim 1$. We list some implications for particle phenomenology and the Early Universe. The most intriguing implication of the conjecture could be a significant shift in allowed inflationary models, if not ruling out slow-roll (single field) inflation altogether. The tension of inflation and the conjecture does not only regard the amplitude of the tensor spectrum, but also its tilt, as $c\gtrsim 1$ implies both a yet unobserved tensor to scalar ratio, and an enhancement of the observed scalar power spectrum on large scales in discord with current data that favors a suppression on these scales. Scalar fields are abundant in theories of quantum gravity. Considering a second scalar field, its dynamics are dictated by the relation between its mass, $m$, and the Hubble parameter, $H$, at different epochs in the history of the Universe. This scalar field, a drainon, fulfills the conjecture draining up the swampland. For Inflation, this drainon requires a modest hierarchy compared to the inflaton. For the rest of the thermal history of the Universe, the drainon can be a coherently oscillating scalar field strengthening the case of Dark Matter candidates of that sort.

Added discussion about logarithmic potentials in string theory and supergravity. Matches the published version

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