一个合理的非全息从头算宇宙学常数
A Reasonable Ab Initio Cosmological Constant Without Holography
摘要：
我们对暗能量的起源给出了一个很好的解释，声称它来自于即使在空的时空中也存在的小的残余负标量曲率。真空之所以有这种剩余曲率，是因为时空从根本上是离散的，而离散几何有更多的方法来具有负曲率而不是正曲率。我们在量子引力的{ \em动力学三角剖分}（DT）模型中计算了这一效应，得到的宇宙学常数$Λ$与观测结果一致.我们首先几乎完全描述了DT模型在三维空间中的真空能量。值得注意的是，状态之间的能隙以[Δ \mathcal{A} = \frac{\ell}{8\mathcal{V}} ]的自然单位递增，其中$\ell$是模型中的“普朗克长度”，$\mathcal{V}$是宇宙的体积。然后，仅使用$N$能级中最接近零的真空，其中$N$是以$\ell$为单位的宇宙半径，我们将我们的模型应用于当前共同移动的空间体积以获得$|Λ| \approx 10^{-123}$。这个结果有严格的证明，不依赖于任何全息原理或仔细调整的参数。我们唯一未知的是低能态的相对熵，它决定了$Λ$的符号。数值证据有力地表明，DT模型中的时空熵是标量曲率的递减函数，因此该模型也预测了$Λ$的正确符号。
英文摘要：
We give a well-motivated explanation for the origin of dark energy, claiming that it arises from a small residual negative scalar-curvature present even in empty spacetime. The vacuum has this residual curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect in the well-known {\em dynamical triangulations} (DT) model for quantum gravity and the predicted cosmological constant $Λ$ agrees with observation. We begin by almost completely characterizing the DT-model's vacuum energies in dimension three. Remarkably, the energy gap between states comes in increments of [Δ\mathcal{A} =\frac{\ell}{8\mathcal{V}}] in natural units, where $\ell$ is the "Planck length" in the model and $\mathcal{V}$ is the volume of the universe. Then, using only vacua in the $N$ energy levels nearest zero, where $N$ is the universe's radius in units of $\ell$, we apply our model to the current co-moving spatial volume to get $|Λ| \approx 10^{-123}$. This result comes with a rigorous proof and does not depend on any holographic principle or carefully tuned parameters. Our only unknown is the relative entropy of the low-energy states, which sets the sign of $Λ$. Numerical evidence strongly suggests that spacetime entropy in the DT-model is a decreasing function of scalar-curvature, so the model also predicts the correct sign for $Λ$.
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