arXiv 2004.010672020-04hep-thgr-qc

大- $N$随机矩阵引力与双层次问题

Large-$N$ Random Matrix Gravity and the Double Hierarchy Problem

Nima Khosravi

备注：: the arguments became more clear. comments are welcome!
DOI：: 10.1088/1475-7516/2021/05/065

摘要：

为什么宇宙学常数、电弱和普朗克尺度如此不同？这个"双重层次”问题，其中$Λ\ll M^2_{EW} \ll M^2_p$，是基础物理学中最紧迫的问题之一。我们表明，在一个理论的$N$随机耦合的大质量引力子在电弱尺度，这些规模是精确地连接这样一个双层次的大$N$，有趣的宇宙学后果。令人惊讶的是，在所有的物理尺度中，只出现了一个无质量的引力子，它也是唯一一个有效地与物质耦合的引力子，从而产生了标准的爱因斯坦引力，而$M_p^2\, G_{μν}= T_{μν}$则是大的$N$。此外，还有一座巨大的引力子塔，其中最轻的引力子可以驱动晚期加速。在这种情况下，观察到的经验关系$Λ\, M_p^2 \sim M_{EW}^4$以及双层次，自然出现，因为$Λ\sim M^2_{EW}/\sqrt{N}$和$M^2_p \sim \sqrt{N}M_{EW}^2$。

英文摘要：

Why are the cosmological constant, electroweak and Planck scales so different? This ``double hierarchy" problem, where $Λ\ll M^2_{EW} \ll M^2_p$, 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 $M_p^2\, G_{μν}= T_{μν}$ 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 $Λ\, M_p^2 \sim M_{EW}^4$ as well as the double hierarchy, arise naturally since $Λ\sim M^2_{EW}/\sqrt{N}$ and $M^2_p \sim \sqrt{N}M_{EW}^2$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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