Diluting Cosmological Constant In Infinite Volume Extra Dimensions

TL;DR

The paper proposes a brane-world model with infinite-volume extra dimensions in which vacuum energy primarily curves the extra space, not our 4D spacetime, thereby softening gravity in the IR. An induced Einstein-Hilbert term on the brane yields 4D gravity up to a crossover scale r_c, while a continuum of light bulk KK modes and unbroken bulk SUSY evade traditional no-go theorems. The model predicts a reversed Hubble-energy relation for N>2, enabling a small observed H0 even for large E4, with M_* ~ 1e-3 eV and r_c ~ H0^-1, and it forecasts observable signatures such as sub-mm and Hubble-scale gravity modifications and TeV-scale Regge states. The approach offers a principled route to a small cosmological constant with distinct experimental and cosmological implications, while requiring careful UV completion to ensure background softness.

Abstract

We argue that the cosmological constant problem can be solved in a braneworld model with infinite-volume extra dimensions, avoiding no-go arguments applicable to theories that are four-dimensional in the infrared. Gravity on the brane becomes higher-dimensional at super-Hubble distances, which entails that the relation between the acceleration rate and vacuum energy density flips upside down compared to the conventional one. The acceleration rate decreases with increasing the energy density. The experimentally acceptable rate is obtained for the energy density larger than (1 TeV)$^4$. The results are stable under quantum corrections because supersymmetry is broken only on the brane and stays exact in the bulk of infinite volume extra space. Consistency of 4D gravity and cosmology on the brane requires the quantum gravity scale to be around $10^{-3}$ eV. Testable predictions emerging within this approach are: (i) simultaneous modifications of gravity at sub-millimeter and the Hubble scales; (ii) Hagedorn-type saturation in TeV energy collisions due to the Regge spectrum with the spacing equal to $10^{-3}$ eV.

Figures (1)

• Figure 1: (A) The worldvolume vacuum diagram of the SM fields that renormalizes the brane tension (i.e., the 4D cosmological constant). These contributions are protected by ${\cal N}=1$ worldvolume supersymmetry. Therefore, they are cutoff by the worldvolume SUSY breaking scale $M_{\rm susy}$. (B) The worldvolume two-point diagram that renormalizes (induces) the EH term on the brane. These contributions are not protected by ${\cal N}=1$ supersymmetry. They can only be protected by conformal invariance which in our model is broken at the scale $M_{\rm SM}$ that is close to $M_{\rm Pl}$. Hence, there can be a hierarchy between (B) and (A). (C) The bulk vacuum diagram. Only the bulk particles (which do not include the SM particles) are running in this loop (bulk particles are denoted by double lines). This diagram is protected by unbroken bulk SUSY. Therefore, the cosmological constant in the bulk is zero. (D) The bulk two-point diagram which renormalizes the bulk EH term. As in (C), only the bulk particles are running in the loop. This diagram is cutoff by the bulk scale $M_*$. Therefore, the natural value of the constant in front of the bulk EH term is $M_*^{2+N}$; there is huge hierarchy between this coefficient and that of the worldvolume EH term coming from (B).