Cosmology without the cosmological principle
Fecha
2025
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Universidad de Valparaíso
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Facultad
Facultad de Ciencias
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Instituto de Física y Astronomía
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Nota general
Doctor en Astrofísica. Universidad de Valparaíso. 2025.
Resumen
Recent studies strongly suggest that the ΛCDM model may no longer serve as the definitive standard model in cosmology, given the increasing tensions between different cosmological observables. Some researchers have described this situation as a ”crisis in cosmology.” The ΛCDM model relies on two fundamental assumptions: the isotropy of the universe (supported by observational evidence) and the Copernican principle (a philosophical postulate). Together, these assumptions lead to the well-known Cosmological Principle, with the homogeneity of the universe emerging as a direct consequence. In this thesis, I review the cosmological consequences of relaxing some of these assumptions, exploring inhomogeneous and anisotropic universe models, as well as tilted cosmologies, which consider observers in motion relative to the Hubble flow. We examine methods to study these effects using existing cosmological data. First, we explore a variety of models that describe inhomogeneous and anisotropic universes, including different metric theories, perturbative analyses, averaging effects, tilted scenarios, and cosmographic approaches. We then apply this theoretical framework to analyze SNIA data and the local peculiar velocity field, aiming to constrain key parameters.
On large scales, baryonic matter in the universe tends to cluster into structures known as the cosmic web, which exhibits fractal behavior. The impact of this inhomogeneous large-scale structure on cosmology is an active area of research, spanning from its description through various metrics derived from Einstein’s field equations to more complex challenges, such as the back-reaction problem related to the aver- aging of general relativity. In this work, we investigate the local fractal structure of the universe using luminosity distance relations derived from fractal-like matter distributions in LTB inhomogeneous models, analyzed against SNIA data. Our find- ings suggest that while a fractal distribution of matter cannot fully account for the cosmic acceleration, it remains a valuable tool for studying the fractality of the local universe, provided the background cosmology is known. It is important to note, however, that this remains a simplified model, and the inclusion of a true fractal distribution of matter in the field equations is an ongoing research challenge involving complex, non-differentiable mathematics.
The effects of general relativity on the evolution of the local large-scale structure remain poorly understood. Some studies indicate that the growth of density contrasts and peculiar velocities accelerates over time when using the covariant formalism of general relativity, as compared to the standard Newtonian or semi-Newtonian ap- proaches. Additionally, the back-reaction problem in cosmology addresses the challenge of averaging cosmological quantities such as matter density, a task complicated by the non-linearity and complexity of the governing equations. Tilted cosmologies, which apply the covariant formalism to study the universe from the perspective of observers moving with peculiar velocities relative to the Hubble expansion, offer significant insights. Theoretical analyses suggest that the deceleration parameter measured by such observers could be negative, even if the background universe is not accelerating, provided the observers are located within a contracting bulk flow extending over large scales. In this work, we take a step toward observing these effects by extracting the volume scalar of the local peculiar velocity field via velocity reconstructions, confirming that the local peculiar velocity field is indeed contracting. Recent blind analyses of SNIA data and independent velocity field reconstructions support this conclusion, further highlighting the importance of studying tilted cosmologies and the relativistic effects on large-scale structure evolution. In this context, we use the covariant formulation to develop a connection between the enhanced growth rate of peculiar velocities in relativistic physics and the semi-Newtonian approach. This effect is strongly linked to the neglect of additional gravitational sources, such as the flux of energy, in Newtonian gravity.
From an observational standpoint, we adopt a phenomenological approach, performing a statistical analysis on the most recent SNIA compilation, Pantheon+, using the cosmographic luminosity distance. We extract the deceleration parameter for different portions of the universe by dividing the data into redshift bins and hemispheres. Our analysis reveals that the deceleration parameters are not consistent across the binned groups, which contradicts the assumption of a homogeneous universe. Statistical tests indicate a trend of increasing deceleration parameters, a result consistent with recent studies. It is also worth noting that very nearby supernovae (at z ≤ 0.008) appear to be unsuitable for cosmological analysis, as they are contaminated by the velocity dispersion of the local peculiar velocity field, yielding values that do not align with background cosmological parameters. Various corrections using differ- ent models have been attempted to improve this data, but they have not yielded the desired results, while other studies opt to analyze the raw SNIA redshift data directly.
In conclusion, the possibility of explaining the apparent accelerated expansion of the universe without invoking dark energy remains a compelling alternative. Models such as tilted cosmologies continue to hold potential, supported by current observa- tional data that challenge the cosmological principle. If dark energy and the acceleration of the universe are indeed real, a deeper understanding of the local structure in cosmological observations is crucial for constraining the physical parameters involved. This highlights the importance of further research into the fractal structure of matter, the physical properties of the bulk flow we inhabit, and the still poorly understood general relativistic effects on the evolution of the large-scale structure. The thesis presents several avenues for future research that could expand our scientific understanding in these areas.
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