We define “third-derivative” general relativity by promoting the integration measure in Einstein-Hilbert action to be an arbitrary 4-form field strength. We project out its local fluctuations by coupling it to another 4-form field strength. This ensures that the gravitational sector contains only the usual massless helicity-2 propagating modes. Adding the charges to these 4-forms allows for discrete variations of the coupling parameters of conventional general relativity: $G_N,\mathrm{\Lambda },H_0$, and even $⟨\mathsf{Higgs}⟩$ are all variables which can change by jumps. Hence, de Sitter spacetime is unstable to membrane nucleation. Using this instability, we explain how the cosmological constant problem can be solved. The scenario utilizes the idea behind the irrational axion, but instead of an axion it requires one more 4-form field strength and corresponding charged membranes. When the membrane charges satisfy the constraint $\frac{2{\kappa }_{\mathsf{eff}}^2{\kappa }^2|{\mathcal{Q}}_i|}{3{\mathcal{T}}_i^2}<1$, the theory which ensues exponentially favors a huge hierarchy $\mathrm{\Lambda }/M_{\mathrm{Pl}}^4\ll 1$ instead of $\mathrm{\Lambda }/M_{\mathrm{Pl}}^4\simeq 1$. The discharges produce the distribution of the values of $\mathrm{\Lambda }$ described by the saddle point approximation of the Euclidean path integral.

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关于多元宇宙和自然等级的广义相对论

我们通过将 Einstein-Hilbert 作用中的积分度量提升为任意 4 形场强来定义“三阶导数”广义相对论。我们通过将其耦合到另一个 4-form 场强来预测其局部波动。这确保了引力扇区仅包含通常的无质量 helicity-2 传播模式。将电荷添加到这 4 种形式允许传统广义相对论的耦合参数的离散变化：$G_{ñ},\mathrm{\Lambda },H_0$， 乃至$⟨\mathsf{希格斯}⟩$都是可以通过跳跃改变的变量。因此，德西特时空对膜成核是不稳定的。利用这种不稳定性，我们解释了如何解决宇宙常数问题。该方案利用了非理性轴子背后的想法，但它需要一个多 4 型场强和相应的带电膜，而不是轴子。当膜电荷满足约束时$\frac{2{\kappa }_{\mathsf{效果}}^2{\kappa }^2|{\mathcal{问}}_{\mathrm{一世}}|}{3{\mathcal{吨}}_{\mathrm{一世}}^2}<1$, 随之而来的理论以指数方式支持巨大的等级制度$\mathrm{\Lambda }/{米}_{\mathrm{PL}}^4\ll 1$代替$\mathrm{\Lambda }/{米}_{\mathrm{PL}}^4\simeq 1$. 排放产生的值的分布$\mathrm{\Lambda }$由欧几里得路径积分的鞍点近似描述。