String Cosmology: New Tools to connect String Theory with Cosmological Observations

宇宙学研究宇宙的起源，以及迄今为止宇宙演化的主要特征。宇宙膨胀主要是由引力控制的，这是爱因斯坦的广义相对论所描述的力。这一理论在描述远距离发生的引力现象方面极为成功。然而，当试图描述发生在小尺度上的现象时，广义相对论显然失败了。事实上，我们所拥有的描述短距离物理的最好理论是基于量子力学的。但它的原理在应用于遵循广义相对论规则的引力现象时，会导致不一致的结果。这个问题与宇宙学有关，在试图研究宇宙非常年轻，然后非常小的时期时，量子力学效应是重要的。例如，在我们宇宙的早期，人们认为宇宙膨胀经历了一个极快的加速阶段，称为暴涨。在这个时期，量子效应决定了在时空结构中产生微小的不均匀，这在随后的宇宙演化中孕育了大规模的结构。广义相对论和量子力学的一致共轭目标是推动弦理论发展的主要目标。这一理论引入了非常不寻常的概念：它的一致性要求我们的宇宙比观察到的维度多六个维度，这些维度包裹在一个很小的空间里，日常经验无法观察到。此外，它还预测了在更高维度的背景中波动的膜物体的存在，在那里构成我们宇宙的粒子可以被局部化。然而，为了检验这些美丽的想法，我们需要探索发生在极小范围内的现象。我发现所有这些想法都非常令人兴奋，所以我决定研究弦理论和宇宙学之间的关系，主要目的是找到通过宇宙学观察来检验弦理论的新方法。正如前面所解释的，在宇宙非常小的早期，发生的现象受到短距离物理的影响，然后可能受到弦理论的影响。暴胀就是最重要的例子：它是一个在观测到的CMB辐射模式上留下明显印记的过程，并提供了影响宇宙随后演化的初始条件。出于这些原因，我的部分研究致力于研究弦理论中的膨胀模型。它们可以具有特殊的性质，因为它们使用了该理论提供的许多成分。因此，对弦膨胀模型的研究为揭示弦理论特有的效应提供了独特的机会，并允许通过宇宙学观察来检验其观点。更具体地说，我的研究活动的主要目标可以概括为以下内容。首先，我计划开发理论工具，以便将观测结果与弦激励的宇宙学模型进行比较。这是一个广泛的课题，需要详细阐述旨在分析宇宙涨落演化的现有技术，以便将它们应用于弦激励的宇宙学模型。然后，我将尝试个性化最有希望的基于弦理论的宇宙学模型，这些模型提供了最好的机会，可以用未来的宇宙学观测进行验证。一旦这一点完成，我将努力阐述这些模型，以便从理论上使它们完全令人满意，并详细研究它们对将通过观测检验的宇宙量的预测。

Cosmology studies the origin of the Universe, and the main features of its evolution until today. The Universe expansion is mainly controlled by gravity, the force described by Einstein's General Relativity. This theory is extremely successful for describing gravitational phenomena that occur at large distances. However, when attempting to describe phenomena occurring at small scales, General Relativity apparently fails. Indeed, the best theories we have to describe short distance physics are based on Quantum Mechanics. But its principles lead to inconsistent results, when applied to gravitational phenomena following the rules of General Relativity. This problem is relevant for Cosmology, when trying to investigate epochs in which the Universe was very young, and then very small, in which quantum mechanical effects are important. For example, in the early epochs of our Universe, it is believed that cosmological expansion has experienced a phase of extremely fast acceleration, called Inflation. During this epoch, quantum effects are decisive to produce small inhomogeneities in the structure of the space-time, that seed large scale structures in the subsequent evolution of the Universe. The aim of consistently conjugate General Relativity with Quantum Mechanics is the main goal that motivated the development of String Theory. This theory introduces very unusual concepts: its consistency requires that our Universe has six dimensions more than the observed ones, that are wrapped on a small space, and unobservable by everyday experience. Also, it predicts the existence of membrane objects, fluctuating in a higher dimensional background, where the particle constituting our Universe can be localized. In order to check these beautiful ideas, however, we need to probe phenomena happening at extremely small scales. I find all these ideas extremely exciting, so I decided to study the relation between string theory and cosmology, with the main aim to find new ways to test string theory by cosmological observations. As explained before, phenomena occurring at early epochs, when the Universe was extremely small, are affected by short distance physics, and then possibly by String Theory. Inflation is the most important example: it is a process that leaves clear imprints in the pattern of the observed CMB radiation, and provides initial conditions affecting the subsequent evolution of the Universe. For these reasons part of my research is devoted to study models of inflation in String Theory. They can have peculiar properties, since they use many of the ingredients that the theory offers. The study of string models of inflation, then, offers unique opportunities to reveal effects that are characteristic of String Theory, and allows to test its ideas by means of cosmological observations. More specifically, the main objectives of my research activity can by summarized in the following. First, I plan to develop the theoretical tools allowing to compare observational results with string motivated cosmological models. This is a broad subject that requires the elaboration of existing techniques aimed to analyze the evolution of cosmological fluctuations, in order to apply them to string motivated cosmological models. Then, I will try to individuate the most promising cosmological models, based on string theory, that offer the best opportunities for being testable with future cosmological observations. Once this has been done, I will try to elaborate those models, in order to render them fully satisfactory from a theoretical point of view, and study in detail their predictions for cosmological quantities that will be tested by observations.