通过量子隧穿从涌现宇宙产生暴胀时期
Creation of an inflationary epoch from an Emergent Universe through quantum tunneling
AI总结：
该研究在双度量理论框架下，通过量子隧穿使静态涌现宇宙产生势垒，以WKB近似计算出接近1的幂律隧穿概率，从而形成暴胀时期。
AI中文摘要：
我们认为，极早期宇宙可由涌现宇宙（Emergent Universe）很好地描述，其几何结构为静态且经典稳定的爱因斯坦宇宙（Einstein Universe），这在某些双度量理论（Two Measures Theories，TMT）中是可能的。这些解没有大爆炸，而是延伸到任意早的时间。我们所考虑的TMT是具有自发破缺标度不变性的理论，包含一个标量场（dilatonic field），该场对实现标度不变性至关重要，在对称性破缺后会获得非平凡的有效势，我们在爱因斯坦框架（Einstein frame）中对其进行研究。利用与标量场相关的守恒量，我们将宇宙学演化重新表述为有效势V(φ̇)的形式，该势呈现出发散的势垒，将静态解与后续的膨胀演化分隔开。对对应的小超空间哈密顿量（minisuperspace Hamiltonian）进行量子化后，我们用WKB近似计算隧穿概率。一旦通过要求隧穿概率的一致半经典解释确定平方根的分支，隧穿作用量就有明确定义且有限。我们发现，势垒会对隧穿指数产生对数贡献，使得隧穿概率呈现幂律而非通常的指数依赖关系，对于所考虑的参数值，该概率接近1。宇宙因此以有限的尺度因子进入超暴胀阶段，进而发展为慢滚暴胀。这种暴胀宇宙的量子产生并不代表时空的量子产生，因为时空在隧穿之前就已存在。
英文摘要：
We consider that the very early Universe was well described by an Emergent Universe, whose geometry was that of a static and classically stable Einstein Universe, which is possible in certain Two Measures Theories (TMT). These solutions do not have a big bang, but rather they extend to arbitrarily early times. The TMT we consider are theories with spontaneously broken scale invariance and contain a dilaton field, crucial for the implementation of the scale invariance, that after the symmetry breaking acquires a nontrivial effective potential, which we study in the Einstein frame. Using the conserved quantity associated with the dilaton, we recast the cosmological evolution in terms of an effective potential $V(\dotϕ)$, which exhibits a divergent barrier separating the static solution from the subsequent expanding evolution. Quantizing the corresponding minisuperspace Hamiltonian, we evaluate the tunneling probability in the WKB approximation. The tunneling action is well defined and finite once the branch of the square root is fixed by requiring a consistent semiclassical interpretation of the tunneling probability. We find that the barrier gives rise to a logarithmic contribution to the tunneling exponent, yielding a power-law rather than the usual exponential dependence of the tunneling probability, which for the parameter values considered is close to unity. The Universe thus emerges with a finite scale factor into a superinflationary phase that develops into slow-roll inflation. This quantum creation of an inflationary Universe does not represent a quantum creation of spacetime, which exists before the tunneling.
