Investigating Baryon Acoustic Oscillations in Non-Trivial Curvature Cosmological Models

The study of baryon acoustic oscillations (BAO) is crucial in observational cosmology. BAO features arise from sound waves in the early universe, leading to a characteristic scale in the distribution of baryons. This scale is expected to be visible in the current matter distribution. The Lambda Cold Dark Matter (ΛCDM) model predicts these features, which have been confirmed through various galaxy surveys. The detection of BAO has been pivotal in understanding the universe's expansion and structure. However, the ΛCDM model faces challenges, including the presence of dark energy and matter, which constitute a significant portion of the universe's content. These unresolved issues prompt the exploration of alternative cosmological models. The document emphasizes the need for improved data precision to distinguish between these models effectively. The advent of next-generation surveys will provide the necessary data to refine our understanding of cosmic structures and dynamics.

The theoretical foundation of this research involves generalizing the comoving distance definition to accommodate non-FLRW space-times. This approach allows for the investigation of cosmological models that exhibit non-trivial spatial curvature. The document discusses various models, including Lemaître-Tolman-Bondi models and modified gravity cosmologies. These models challenge the traditional flat universe assumption and offer insights into the universe's complex structure. The Alcock-Paczyński effect is also examined, highlighting its significance in measuring cosmic distances and understanding the anisotropic nature of the universe. The timescape model is presented as a notable example of a non-FLRW cosmology, which provides different predictions compared to the ΛCDM model. This section underscores the importance of theoretical advancements in interpreting observational data and refining cosmological models.

The methodology section outlines the empirical models developed for extracting the BAO characteristic scale from galaxy surveys. The authors propose a fitting procedure that does not rely on specific cosmological assumptions, allowing for broader applicability across various models. The document details the application of these methods to the Baryon Oscillation Spectroscopic Survey (BOSS) dataset, focusing on the CMASS and LOWZ galaxy surveys. The analysis involves measuring correlation functions and identifying BAO features within the data. The authors validate their methods using ΛCDM mocks, ensuring robustness and reliability. This innovative approach to data analysis is significant as it enables the extraction of BAO features without the constraints of traditional models, paving the way for new insights into cosmic structure and evolution.

The results indicate that the correlation functions derived from both the ΛCDM and timescape models exhibit pronounced BAO features. The analysis reveals that the anisotropic Alcock-Paczyński distortion parameter is consistent with zero, suggesting that different spatial curvature evolutions can explain the observed relative positions of the tangential and radial BAO scales. This finding is crucial as it implies that models with varying curvature can still yield similar observational outcomes. The discussion emphasizes the implications of these results for future cosmological studies. The ability to apply the developed methods to a wide range of models enhances the understanding of cosmic structures and their evolution. The document concludes by highlighting the necessity for continued exploration of alternative cosmological models to address the unresolved mysteries of the universe.