⚛️ general relativity

Cosmology without the cosmological principle: A study of the large-scale structure effects in the background universe

This thesis investigates the cosmological consequences of relaxing the Cosmological Principle by reviewing and applying various inhomogeneous, anisotropic, and tilted universe models to existing observational data, such as supernovae and peculiar velocities, in response to growing tensions within the standard $\Lambda$ CDM framework.

Original authors: Erick Pastén

Published 2026-08-18

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Erick Pastén

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For most of the last century, astronomers have operated under a comforting assumption: that the universe, when viewed from a great enough distance, looks the same everywhere and in every direction. This idea, known as the cosmological principle, suggests that our position in the cosmos is not special. It implies that if you were to travel to a distant galaxy and look back at the universe, you would see the same vast, uniform distribution of matter that we see from Earth. This principle is the foundation of our standard model of cosmology, a framework that explains how the universe expands and evolves. However, this model relies on the existence of a mysterious, invisible force called dark energy to explain why the expansion of the universe is speeding up. As observations have become more precise, cracks have begun to appear in this picture. Different ways of measuring the universe's expansion rate yield conflicting results, and strange patterns in the distribution of galaxies suggest that the universe might not be as uniform as we thought. If the universe is not perfectly smooth, or if our local neighborhood is moving in a unique way, the standard model might be missing a crucial piece of the puzzle.

A doctoral thesis by Erick Pastén, completed at the University of Valparaíso in Chile, takes a hard look at these cracks. Instead of accepting the standard model as the final word, Pastén explores what happens if we relax the assumption that the universe is perfectly uniform. He investigates whether the strange behavior we see in the data—specifically the apparent acceleration of the universe—could be an illusion caused by the local structure of the cosmos or the way we are moving through it. The work combines theoretical physics with a deep dive into the latest data from Type Ia supernovae, which are exploding stars used as cosmic mile markers to measure distances across the universe.

One of the first avenues Pastén explored was the idea that matter in the universe is arranged in a fractal pattern, similar to the branching of a tree or the jagged edge of a coastline, where the same patterns repeat at different scales. If the distribution of galaxies follows such a pattern rather than a smooth, even spread, it could change how we calculate the universe's expansion. To test this, Pastén built a mathematical model that allowed for a transition from a fractal-like distribution of matter in our local neighborhood to a smooth, uniform distribution further out. He then compared the predictions of this model against the light from over a thousand supernovae. The results were clear: while a fractal distribution of matter is an interesting concept, it cannot fully explain the observed acceleration of the universe. The model failed to fit the data unless it made unrealistic assumptions, such as the universe beginning at different times in different places. This suggests that while the local universe is indeed clumpy and complex, this clumpiness alone is not the secret behind cosmic acceleration.

The thesis then turned its attention to a more subtle effect: the motion of our own galaxy and the local group of galaxies relative to the general expansion of the universe. Imagine the universe as a vast, expanding ocean. While the water flows outward, a boat might be drifting in a specific current. If the boat is moving with the current, the water seems to flow smoothly past it. But if the boat is moving against a converging current, the water might appear to rush toward it, creating a false impression of the ocean's behavior. In cosmology, this is known as a "tilted" scenario. Pastén examined whether we live in a region where the flow of matter is contracting, pulling galaxies together rather than letting them drift apart. Using sophisticated reconstructions of the local velocity field based on the positions and movements of millions of galaxies, he found that the local flow of matter is indeed contracting on average. This contraction creates a local effect that can mimic the signs of acceleration. If an observer is inside a contracting flow, the universe can appear to be speeding up, even if the universe as a whole is not. This finding supports the idea that the "dark energy" driving acceleration might be a local illusion created by our specific location and motion, rather than a universal force.

To verify these ideas without relying on a pre-existing model of the universe, Pastén performed a statistical analysis of the supernova data, breaking the observations into different distance ranges and different directions in the sky. He looked for inconsistencies that would violate the cosmological principle. The analysis revealed that the measured rate of deceleration or acceleration is not consistent across the universe. When the data was split into different slices of distance, the results varied significantly, suggesting that the universe does not look the same at all scales. Furthermore, when the data was divided into two halves of the sky based on the direction of our motion relative to the cosmic background, the results showed a tension between the two sides. Most notably, the very closest supernovae, those within a few hundred million light-years, showed behavior that was completely different from the rest of the sample. These nearby stars are heavily influenced by the chaotic, local movements of galaxies, making them unreliable for measuring the smooth expansion of the universe. When these nearby outliers were removed, the inconsistencies in the data became even more pronounced, suggesting that the standard model might be missing something fundamental about how the universe evolves on large scales.

The study concludes that the effects of the local large-scale structure on our measurements are likely greater than previously assumed. It suggests that the standard model of cosmology, which assumes a perfectly smooth and uniform universe, may be underestimating the complexity of the real cosmos. The apparent acceleration of the universe could be a combination of local effects, such as the contraction of our immediate cosmic neighborhood, and the limitations of our current mathematical tools. Pastén's work does not prove that dark energy does not exist, but it strongly suggests that we cannot ignore the messy, clumpy, and moving nature of the universe when we try to understand it. The thesis argues that to truly understand the cosmos, we must stop assuming we are in a special, average place and start accounting for the specific, peculiar motion of our local environment. By doing so, we may find that the universe is more dynamic and less uniform than our textbooks have led us to believe, and that the key to solving the mystery of cosmic acceleration lies in understanding the intricate dance of matter in our own cosmic backyard.

Technical Summary: Cosmology without the Cosmological Principle

Problem Statement
The standard $\Lambda$ CDM cosmological model, while successful in matching many observations, faces increasing theoretical and observational tensions, including the Hubble tension, the $\sigma_8$ discrepancy, and anomalies in the Cosmic Microwave Background (CMB) and Type Ia Supernova (SNIA) data. These models rely heavily on the Cosmological Principle (CP), which assumes the universe is globally homogeneous and isotropic. This thesis investigates the consequences of relaxing the CP, specifically exploring whether inhomogeneous and anisotropic structures, peculiar velocities, and relativistic effects can explain observed cosmological phenomena—such as apparent cosmic acceleration—without invoking Dark Energy. The central hypothesis is that local large-scale structure (LLSS) effects and the motion of observers relative to the Hubble flow (tilted cosmologies) may be underestimated or misinterpreted in standard analyses.

Methodology
The research employs a multi-faceted approach combining theoretical modeling, covariant formalism, and statistical analysis of observational data:

Theoretical Frameworks:
- Inhomogeneous Metrics: The study reviews and utilizes Lemaitre-Tolman-Bondi (LTB) models to describe radially inhomogeneous universes. It specifically tests models where matter distribution follows a fractal dimension ( $D$ ) transitioning to homogeneity at a specific scale ( $L$ ).
- Tilted Cosmologies: Using the 1+3 covariant formalism of General Relativity (GR), the thesis analyzes observers moving with peculiar velocities relative to the background Hubble flow. It derives relations connecting the local deceleration parameter ( $\tilde{q}$ ) measured by these "tilted" observers to the global parameter ( $q$ ) and the volume scalar of the bulk flow ( $\tilde{\theta}$ ).
- Relativistic Evolution: The work extends the covariant treatment to the evolution of peculiar velocity fields, comparing relativistic growth rates against Newtonian and semi-Newtonian approximations to identify missing gravitational sources (e.g., energy flux).
Observational Analysis:
- Fractal Modeling: The author constructs LTB models with sharp and smooth transitions from a fractal matter distribution ( $M(r) \propto r^D$ ) to a homogeneous Einstein-de Sitter (EdS) background. These models are tested against the Pantheon+ SNIA sample using Markov Chain Monte Carlo (MCMC) methods to constrain the fractal dimension $D$ and transition scale $L$ .
- Velocity Field Reconstruction: The thesis utilizes the 2M++ galaxy survey data to reconstruct the local peculiar velocity field. It calculates the volume scalar (divergence) of this field using finite differences, integral approximations, and theoretical relations, accounting for potential biases in density normalization and background cosmology dependence.
- Cosmographic Analysis: A model-independent statistical analysis is performed on the Pantheon+ dataset. The deceleration parameter $q_0$ is extracted using cosmographic Taylor expansions of the luminosity distance. The data is binned by redshift and divided into hemispheres relative to the CMB dipole to test for anisotropies and redshift evolution of cosmological parameters.

Key Contributions and Results

Fractal Matter Distribution: The study demonstrates that a purely fractal matter distribution within an LTB framework, assuming a homogeneous Big Bang, cannot explain cosmic acceleration or fit the full Pantheon+ SNIA data better than standard models. While sharp transition models fit low-redshift data reasonably well, they fail at higher redshifts. Smooth transition models yield better parameter stability but still result in poor fits ( $\chi^2_{red} > 1$ ). The conclusion is that fractal structure alone, without unphysical assumptions like an inhomogeneous Big Bang, is insufficient to replace Dark Energy.
Tilted Cosmologies and Bulk Flows: Theoretical derivations confirm that observers within a contracting bulk flow can measure a negative deceleration parameter ( $\tilde{q} < 0$ ) even if the background universe is decelerating ( $q > 0$ ). Applying this to the 2M++ velocity reconstruction, the author finds that the local peculiar velocity field is, on average, contracting (negative divergence) across scales up to 200 Mpc. This supports the theoretical possibility that local contraction could mimic global acceleration.
Relativistic Effects on Velocity Evolution: The thesis establishes a connection between the enhanced growth rate of peculiar velocities in relativistic physics and the semi-Newtonian approach. It suggests that the discrepancy arises from neglecting additional gravitational sources in Newtonian gravity, such as the flux of energy. This implies that relativistic corrections may significantly impact the evolution of large-scale structures.
Cosmographic Anomalies: Statistical analysis of the Pantheon+ data reveals that the deceleration parameter $q_0$ $q_{0}$ is not consistent across different redshift bins, contradicting the assumption of a homogeneous universe.
- Low-Redshift Tensions: Very nearby supernovae ( $z \le 0.008$ ) yield $q_0$ values inconsistent with background parameters, likely due to contamination by local velocity dispersion. Removing these data points reduces tensions between different redshift bins.
- Redshift Evolution: A linear regression of $q_0(z)$ favors a non-zero slope over a constant value, suggesting cosmological parameters may evolve with redshift.
- Hemispheric Analysis: While no significant tension was found between the hemispheres defined by the CMB dipole, a specific tension of $\sim 3.8\sigma$ was detected between redshift bins within the "UP" hemisphere (aligned with the dipole direction).

Significance and Claims
The thesis argues that the magnitude of Large-Scale Structure (LSS) effects on cosmological parameters may be greater than commonly assumed. It posits that:

Local Effects are Underestimated: The geometry and dynamics of the local peculiar velocity field, particularly its contraction, could significantly influence the measurement of cosmological parameters, potentially mimicking acceleration.
Relativistic Corrections are Crucial: The evolution of peculiar velocities and the back-reaction of inhomogeneities are likely underestimated in standard Newtonian treatments. The covariant formulation of GR offers a framework where these effects are naturally included.
Methodological Shift: The author advocates for "blind" and cosmographic statistical analyses that do not presuppose the Cosmological Principle or a specific background model (like $\Lambda$ CDM). Such approaches reveal anomalies (e.g., redshift-dependent $q_0$ ) that are masked when data is forced into a pre-selected model.
Future Directions: The work highlights the need to elucidate the LLSS dynamics independently of background cosmology and to develop reconstruction methods that incorporate general relativistic effects. It suggests that while Dark Energy may still be real, a deeper understanding of local structure and relativistic effects is essential for constraining physical parameters accurately.

The paper concludes that while the specific fractal models tested did not resolve the acceleration problem, the broader investigation into relaxing the Cosmological Principle reveals that current standard models may be missing critical physical ingredients related to inhomogeneity, anisotropy, and relativistic observer effects.

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