Dimensional Reduction and (Anti) de Sitter Bounds

TL;DR

This paper uses dimensional reduction to analyze bounds on scalar potential gradients and light particle masses related to the cosmological constant, revealing implications for universe acceleration, supersymmetric vacua, and potential links between the cosmological constant and neutrino mass.

Contribution

It applies dimensional reduction to derive bounds on scalar potential gradients and light particle masses, clarifying their implications for cosmology and quantum gravity.

Findings

The bound | abla V|/V ; ; 4/(d-2) precludes accelerated expansion in Einstein-dilaton gravity.

The bound m b7 f; |a3|^{1/2} cannot be satisfied in our universe but is saturated in supersymmetric AdS vacua.

The bound m b7 f; |a3|^{1/d} may relate the cosmological constant to neutrino mass, linking the cosmological constant problem and the hierarchy problem.

Abstract

Dimensional reduction has proven to be a surprisingly powerful tool for delineating the boundary between the string landscape and the swampland. Bounds from the Weak Gravity Conjecture and the Repulsive Force Conjecture, for instance, are exactly preserved under dimensional reduction. Motivated by its success in these cases, we apply a similar dimensional reduction analysis to bounds on the gradient of the scalar field potential $V$ and the mass scale $m$ of a tower of light particles in terms of the cosmological constant $\Lambda$, which ideally may pin down ambiguous $O(1)$ constants appearing in the de Sitter Conjecture and the (Anti) de Sitter Distance Conjecture, respectively. We find that this analysis distinguishes the bounds $|\nabla V|/V \geq \sqrt{4/(d-2)}$, $m \lesssim |\Lambda|^{1/2}$, and $m \lesssim |\Lambda|^{1/d}$ in $d$-dimensional Planck units. The first of these bounds precludes accelerated expansion of the universe in Einstein-dilaton gravity and is almost certainly violated in our universe, though it may apply in asymptotic limits of scalar field space. The second bound cannot be satisfied in our universe, though it is saturated in supersymmetric AdS vacua with well-understood uplifts to 10d/11d supergravity. The third bound likely has a limited range of validity in quantum gravity as well, so it may or may not apply to our universe. However, if it does apply, it suggests a possible relation between the cosmological constant and the neutrino mass, which (by the see-saw mechanism) may further provide a relation between the cosmological constant problem and the hierarchy problem. We also work out the conditions for eternal inflation in general spacetime dimensions, and we comment on the behavior of these conditions under dimensional reduction.