论宇宙学停滞的普遍性与持续性
On the Generality and Persistence of Cosmological Stasis
AI总结：
本文利用机器学习在完整参数空间中证明宇宙学停滞的普遍性，并提出衰变率与丰度随物种指数呈指数变化的新模型，该模型可实现与物种数成正比的暴胀级e-fold数，优于幂律模型的对数标度。
摘要：
N种物质向辐射的分层衰变可能与哈勃膨胀相平衡，从而产生停滞（stasis），这是一种物质和辐射丰度保持恒定的宇宙学演化新阶段。我们在衰变率和丰度的完整2N维空间上，运用多种机器学习技术分析停滞，这些衰变率和丰度作为控制动力学的玻尔兹曼方程组的输入。我们构建了一个可微分的玻尔兹曼求解器，以最大化停滞e-fold数𝒩。通过梯度上升获得的高停滞构型促使我们采用对数均匀分布来描述衰变率和丰度，以补充先前工作中的幂律分布。我们证明，从这些分布族中随机抽取的构型通常表现出许多e-fold的停滞。此外，我们将这些分布作为贝叶斯分析中以停滞为条件的先验，使用带归一化流的随机变分推断来建模后验。所有三项数值分析都证明了停滞的普遍性，并指向一个新模型，其中衰变率和丰度随物种指数呈指数变化。我们证明该指数模型满足精确的停滞方程，是一个吸引子，并满足𝒩∝N，在物种数量相对较少的情况下展现出暴胀级别的e-fold数。这与幂律模型的𝒩∝log(N)标度形成对比。最后，我们讨论了对涌现弦猜想和弦轴子景观的影响。
英文摘要：
Hierarchical decays of $N$ matter species to radiation may balance against Hubble expansion to yield stasis, a new phase of cosmological evolution with constant matter and radiation abundances. We analyze stasis with various machine learning techniques on the full $2N$-dimensional space of decay rates and abundances, which serve as inputs to the system of Boltzmann equations that governs the dynamics. We construct a differentiable Boltzmann solver to maximize the number of stasis $e$-folds $\mathcal{N}$. High-stasis configurations obtained by gradient ascent motivate log-uniform distributions on rates and abundances to accompany power-law distributions of previous works. We demonstrate that random configurations drawn from these families of distributions regularly exhibit many $e$-folds of stasis. We additionally use them as priors in a Bayesian analysis conditioned on stasis, using stochastic variational inference with normalizing flows to model the posterior. All three numerical analyses demonstrate the generality of stasis and point to a new model in which the rates and abundances are exponential in the species index. We show that the exponential model solves the exact stasis equations, is an attractor, and satisfies $\mathcal{N}\propto N$, exhibiting inflation-level $e$-folding with a relatively low number of species. This is contrasted with the $\mathcal{N}\propto \log(N)$ scaling of power-law models. Finally, we discuss implications for the emergent string conjecture and string axiverse.
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