Why are the cosmological constant, electroweak and Planck scales so different? This “double hierarchy” problem, where Λ ≪ M² _EW ≪ M² _p , is one of the most pressing in fundamental physics. We show that in a theory of N randomly coupled massive gravitons at the electroweak scale, these scales are linked precisely by such a double hierarchy for large N, with intriguing cosmological consequences. Surprisingly, in all the physical scales, only one massless graviton emerges which is also, effectively, the only one that is coupled to matter, giving rise to standard Einstein gravity, with M_p ²G_μν= T_μν at large N. In addition there is a tower of massive gravitons, the lightest of which can drive late-time acceleration. In this scenario, the observed empirical relation Λ M_p ² ∼ M_EW ⁴ as well as the double hierarchy, arise naturally since Λ ∼ M² _EW/√(N) and M² _p ∼ √(N)M_EW ² .

为什么宇宙常数、电弱和普朗克尺度如此不同？这个“双层次”问题，其中 Λ ≪ M ² _EW ≪ M ² _p ，是基础物理学中最紧迫的问题之一。我们表明，在电弱尺度上N随机耦合的大质量引力子的理论中，这些尺度通过大N的这种双重层次结构精确地联系在一起，具有有趣的宇宙学后果。令人惊讶的是，在所有物理尺度中，只出现了一个无质量引力子，它实际上也是唯一一个与物质耦合的引力子，产生了标准的爱因斯坦引力，M _p ² G _μν = T _μν 在大N处。此外还有一个巨大的引力子塔，其中最轻的可以驱动后期加速。在这种情况下，观察到的经验关系 Λ M _p ² ∼ M _EW ⁴ 以及双层次结构，自然产生自 Λ ∼ M ² _EW /√(N)和M ² _p ∼ √(N)M _EW ² 。