论文标题
早期宇宙的经典性的宇宙常数下限
Lower bound on the cosmological constant from the classicality of the Early Universe
论文作者
论文摘要
我们使用量子非模块性重力理论来关联宇宙常数，$λ$的价值以及宇宙学经典出现的能量量表。 $λ$和单型时间是互补的量子变量的事实，意味着长期量子宇宙应为$λ$为零（或实际上是在任何值中固定的）。同样，$λ$的较小度在其不确定性上构成了上限，因此在单峰时钟的不确定性或宇宙时期出现经典性的时间。古典性远非普朗克量表，而观察到的$λ$的$ 7 \ times 10^{11} $ gev的出现，并将经典区域视为我们的哈勃音量。我们通过直接评估单模型理论的连接表示中的宇宙波函数来确认这一论点。我们的论点是强大的，唯一的余地是我们的宇宙学经典斑块的共同量，这应该比观察到的最后散射表面大。如果认为它是整个封闭的宇宙，那么约束在$ω_k$：对于$-Ω_k<10^{ - 3} $的情况下，以$> 4 \ times 10^{12} $ gev达到了classicality。如果它是无限的，那么这种能量量表是无限的，并且宇宙在Minisuperspace近似中始终是经典的。这是一个了不起的巧合，即在普朗克量表以下的宇宙经典的唯一方法是将经典补丁的大小定义为红色光谱的非线性尺度，而观察到的频谱索引$ n_s = 0.967（4）$（约为$ 10^{11}} $ times当前的轮胎尺寸）。在全息宇宙学的背景下，我们可以将这种大小解释为双3D量子场理论中的限制规模，该理论可以通过未来的宇宙学调查（直接或间接）进行探测。
We use the quantum unimodular theory of gravity to relate the value of the cosmological constant, $Λ$, and the energy scale for the emergence of cosmological classicality. The fact that $Λ$ and unimodular time are complementary quantum variables implies a perennially quantum Universe should $Λ$ be zero (or, indeed, fixed at any value). Likewise, the smallness of $Λ$ puts an upper bound on its uncertainty, and so a lower bound on the unimodular clock's uncertainty or the cosmic time for the emergence of classicality. Far from being the Planck scale, classicality arises at around $7 \times 10^{11}$ GeV for the observed $Λ$, and taking the region of classicality to be our Hubble volume. We confirm this argument with a direct evaluation of the wavefunction of the Universe in the connection representation for unimodular theory. Our argument is robust, with the only leeway being in the comoving volume of our cosmological classical patch, which should be bigger than that of the observed last scattering surface. Should it be taken to be the whole of a closed Universe, then the constraint depends weakly on $Ω_k$: for $-Ω_k < 10^{-3}$ classicality is reached at $ > 4 \times 10^{12}$ GeV. If it is infinite, then this energy scale is infinite, and the Universe is always classical within the minisuperspace approximation. It is a remarkable coincidence that the only way to render the Universe classical just below the Planck scale is to define the size of the classical patch as the scale of non-linearity for a red spectrum with the observed spectral index $n_s = 0.967(4)$ (about $10^{11}$ times the size of the current Hubble volume). In the context of holographic cosmology, we may interpret this size as the scale of confinement in the dual 3D quantum field theory, which may be probed (directly or indirectly) with future cosmological surveys.
