Self-tuning of the cosmological constant in brane-worlds with $P(X,\phi)$

TL;DR

This paper explores a brane-world model with a scalar field described by a general Lagrangian, demonstrating a self-tuning mechanism that can naturally lead to a flat universe without fine-tuning the vacuum energy.

Contribution

It introduces a self-tuning brane-world model with a general $P(X,\phi)$ scalar field, identifying a unique non-singular solution with an unconventional kinetic term that ensures a flat universe.

Findings

The model enforces a vanishing 4d curvature regardless of vacuum energy.

The solution accommodates any warp factor profile without bulk singularity.

Preliminary stability analysis shows no obvious instabilities.

Abstract

We revisit the idea of self-tuning the observed cosmological constant to a vanishing value and promote it to a selection criterion of brane-world models, in which our Universe is described by a 3-brane embedded in a 5d bulk. As a concrete setup, we consider a bulk scalar field $\phi$ described by a general Lagrangian $P(X,\phi)$ with $X=-(\partial\phi)^2/2$. By requiring that the model enforces the 4d curvature of the maximally symmetric 3-brane world-volume to vanish independently of the 4d effective vacuum energy, only two possibilities remain: one with a canonical bulk kinetic term and the other with an unconventional bulk kinetic term similar to a Cuscuton field. Further demanding the absence of bulk singularity, the latter is selected as a unique possibility within the class of models. At the background level, the solution can accommodate any warp factor profile free from bulk singularity and with a finite effective 4d Planck mass. In a cosmological context, our solution would describe our (almost) flat Universe at late times, with a bulk warp factor profile expected to be determined by the evolution of the Universe before dilution of the matter fields by cosmic expansion. Eventually, a simple analysis is performed in the bulk showing no obvious instability around the background solution. A full stability analysis taking into account brane bending modes is nevertheless necessary and left for future work.