论文标题
非微耦合$ f（r）$ gravity和cosmic液体的拉格朗日的宇宙学含义
Cosmological Implications of Nonminimally-Coupled $f(R)$ Gravity and the Lagrangian of Cosmic Fluids
论文作者
论文摘要
在宇宙学的标准模型中，宇宙的背景演变通常可以通过一般相对论以及均匀和各向同性度量的最小化与一系列完美的流体相结合来充分描述。这些流体通常由它们的能量量张量描述，这些量可以从流体的拉格朗日密度中得出。在一般相对论下，拉格朗日密度仅与特定完美流体产生正确的能量量张量有关。在物质字段和重力之间具有非最小耦合（NMC）的理论中，情况并非如此。在这种情况下，除了它们的能量弹药张量之外，在运动方程式中，物质场的壳拉格朗日密度明确出现在运动方程中。因此，确定正确的壳上的拉格朗日密度对特定流体的确定至关重要，以便对相应的宇宙学含义进行准确的描述。从本质上讲，这是本文解决的问题。 我们的目的是解决三个要点。我们介绍了有关宇宙流体的拉格朗日密度的文献中的一些结果，并消除了关于其选择自由（或缺乏其壳的自由）的一些误解，无论是在一般相对论还是具有NMC的理论中。此外，我们得出了由具有固定静止质量和结构的孤子颗粒组成的流体的正确的拉格朗日密度。其次，我们研究了这种类型的完美流体在重力和物质领域之间具有NMC的背景下的热力学行为。最后，我们使用这些结果来获得特定NMC重力模型的新型宇宙学约束，使用来自宇宙微波背景，大爆炸核合成，IA型超新星和巴里昂声学振荡观察的数据。
In the standard model of cosmology, the background evolution of the Universe can in general be adequately described by general relativity and a uniform and isotropic metric minimally coupled with a collection of perfect fluids. These fluids are usually described by their energy-momentum tensor, which can be derived from the fluid's Lagrangian density. Under general relativity, the Lagrangian density is only relevant to the extent that it results in the correct energy-momentum tensor for a specific perfect fluid. This is not the case in theories that feature a nonminimal coupling (NMC) between the matter fields and gravity. In such cases, the on-shell Lagrangian density of the matter fields appears explicitly in the equations of motion, in addition to their energy-momentum tensor. The determination of the correct on-shell Lagrangian density for a particular fluid is therefore of paramount importance in order to provide an accurate description of the corresponding cosmological implications. In essence, this is the problem tackled in this thesis. We have aimed at addressing three key points. We covered some of the results in the literature regarding the Lagrangian density of cosmic fluids, and cleared up some misunderstandings regarding the freedom of choice (or lack thereof) of its on-shell form, both in general relativity and in theories featuring an NMC. In addition, we derived the correct Lagrangian density for fluids composed of solitonic particles with fixed rest mass and structure. Secondly, we studied the thermodynamic behaviour of perfect fluids of this type in the context of theories featuring an NMC between gravity and the matter fields. Finally, we used these results to derive novel cosmological constraints on specific NMC gravity models, using data from cosmic microwave background, big-bang nucleosynthesis, type Ia supernovae and baryon acoustic oscillations observations.
