In previous works, we have derived a Running Vacuum Model (RVM) for a string Universe, which provides an effective description of the evolution of 4-dimensional string-inspired cosmologies from inflation till the present epoch. In the context of this “stringy RVM” version, it is assumed that the early Universe is characterised by purely gravitational degrees of freedom, from the massless gravitational string multiplet, including the antisymmetric tensor field. The latter plays an important role, since its dual gives rise to a ‘stiff’ gravitational axion “matter”, which in turn couples to the gravitational anomaly terms, assumed to be non-trivial at early epochs. In the presence of primordial gravitational wave (GW) perturbations, such anomalous couplings lead to an RVM-like dynamical inflation, without external inflatons. We review here this framework and discuss potential scenarios for the generation of such primordial GW, among which the formation of unstable domain walls, which eventually collapse in a non-spherical-symmetric manner, giving rise to GW. We also remark that the same type of “stiff” axionic matter could provide, upon the generation of appropriate potentials during the post-inflationary eras, (part of) the Dark Matter (DM) in the Universe, which could well be ultralight, depending on the parameters of the string-inspired model. All in all, the new (stringy) mechanism for RVM inflation preserves the basic structure of the original (and more phenomenological) RVM, as well as its main advantages: namely, a mechanism for graceful exit and for generating a huge amount of entropy capable of explaining the horizon problem. It also predicts axionic DM and the existence of mild dynamical Dark Energy (DE) of quintessence type in the present universe, both being “living fossils” of the inflationary stages of the cosmic evolution. Altogether the modern RVM appears to be a theoretically sound (string-based) approach to cosmology with a variety of phenomenologically testable consequences.

在之前的工作中，我们为弦宇宙推导出了一个运行真空模型 (RVM)，它提供了对 4 维弦启发宇宙学从暴胀到现在的演化的有效描述。在这个“stringy RVM”版本的背景下，假设早期宇宙的特征是纯粹的引力自由度，来自无质量的引力弦多重态，包括反对称张量场。后者起着重要的作用，因为它的对偶产生了一个“僵硬的”引力轴子“物质”，这反过来又耦合到引力异常项，在早期被认为是非平凡的。在存在原始引力波 (GW) 扰动的情况下，这种异常耦合会导致类似 RVM 的动态膨胀，而没有外部膨胀子。我们在这里回顾了这个框架并讨论了产生这种原始 GW 的潜在场景，其中不稳定畴壁的形成，最终以非球对称的方式坍塌，从而产生了 GW。我们还注意到，在暴胀后时代产生适当的电位后，同类型的“硬”轴子物质可以提供宇宙中的（部分）暗物质（DM），它很可能是超轻的，具体取决于关于字符串启发模型的参数。总而言之，RVM 膨胀的新（字符串）机制保留了原始（和更多现象学）RVM 的基本结构，以及它的主要优点：即优雅退出和生成大量熵的机制来解释地平线问题。它还预测了当前宇宙中存在轴子DM和典型类型的温和动力暗能量（DE），两者都是宇宙演化暴胀阶段的“活化石”。总而言之，现代 RVM 似乎是一种理论上合理的（基于字符串的）宇宙学方法，具有各种现象学可检验的结果。