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Cosmological Implications of Nonminimally-Coupled $f(R)$ Gravity and the Lagrangian of Cosmic Fluids

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.