论文标题
早期宇宙的扩张速度如何？
How Slowly can the Early Universe Expand?
论文作者
论文摘要
当宇宙的扩展由状态参数方程$ w $和声音速度$ c_s $满足$ W = C_S^2 \ le 1 $的完美流体主导时，Hubble参数$ h $和时间$ t $满足限制的$ ht $ ht $ ht \ ge ge 1/3 $。最近，人们对具有$ ht <1/3 $的“超慢”扩展法（有时被描述为“快速扩展”模型）。我们研究了可以产生超慢膨胀的各种模型：具有负电势的标量场，正压流体，Braneworld模型或早期宇宙中的游荡阶段。超慢扩展的标量现场模型和正压模型在前一种情况下对$ W = 1 $或$ W \ rightarrow \ infty $的进化不稳定，而在后一种情况下，$ w \ rightarrow \ rightarrow \ infty $。 Braneworld模型可以产生超慢的扩展，但需要超出标准Friedman方程的扩展定律。游荡的早期宇宙模型可以在早期宇宙中产生准静态膨胀阶段，但需要外来的负密度分量。这些结果表明，应谨慎对待早期宇宙中超慢扩张阶段的吸引力，尽管游荡的早期宇宙可能值得进一步研究。这些结果不适用于超慢的收缩模型。
When the expansion of the universe is dominated by a perfect fluid with equation of state parameter $w$ and a sound speed $c_s$ satisfying $w = c_s^2 \le 1$, the Hubble parameter $H$ and time $t$ satisfy the bound $Ht \ge 1/3$. There has been recent interest in "ultra-slow" expansion laws with $Ht < 1/3$ (sometimes described as "fast expanding" models). We examine various models that can produce ultra-slow expansion: scalar fields with negative potentials, barotropic fluids, braneworld models, or a loitering phase in the early universe. Scalar field models and barotropic models for ultra-slow expansion are unstable to evolution toward $w = 1$ or $w \rightarrow \infty$ in the former case and $w \rightarrow \infty$ in the latter case. Braneworld models can yield ultra-slow expansion but require an expansion law beyond the standard Friedman equation. Loitering early universe models can produce a quasi-static expansion phase in the early universe but require an exotic negative-density component. These results suggest that appeals to an ultra-slow expansion phase in the early universe should be approached with some caution, although the loitering early universe may be worthy of further investigation. These results do not apply to ultra-slow contracting models.
