Rewriting Gravity: A New Approach to Resolving the Cosmic Tension

by

Author: Denis Avetisyan

Researchers are exploring modifications to Einstein’s theory of gravity to address discrepancies in measurements of the universe’s expansion rate and matter distribution.

The study constrains estimations of $σ\_8$ when $M=0$, and further refines those constraints alongside estimations of $M$ at 68% and 95% confidence levels, aligning with, and thus validating, previous findings from the Planck 2018 results which established a value of $σ\_8=0.81$.
The study constrains estimations of $σ\_8$ when $M=0$, and further refines those constraints alongside estimations of $M$ at 68% and 95% confidence levels, aligning with, and thus validating, previous findings from the Planck 2018 results which established a value of $σ\_8=0.81$.

This study investigates f(Q) gravity with a square-root correction to decouple perturbations and potentially alleviate the S8 tension arising from cosmological observations.

The persistent discrepancy between early- and late-universe measurements of cosmological parameters presents a significant challenge to the standard cosmological model. This paper, ‘Decoupling perturbations from background in $f(Q)$ gravity: the square-root correction and the alleviation of the $σ_8$ tension’, investigates a modification to $f(Q)$ gravity-specifically, the inclusion of a square-root term-and demonstrates its potential to resolve the $σ_8$ tension by decoupling the dynamics of perturbations from the background expansion. Across various cosmological scenarios, this correction consistently suppresses structure growth, bringing observations into closer alignment with Planck results. However, a residual degeneracy remains, prompting the question of whether future multi-probe analyses can confirm this square-root term as a genuine signal of modified gravity.

The Universe’s Disquiet: A Challenge to Standard Cosmology

The prevailing model of the universe, known as LambdaCDM, is currently grappling with a significant inconsistency concerning the Hubble constant – the rate at which the universe expands. Measurements derived from observations of the cosmic microwave background, representing the early universe, consistently yield a lower value for this constant than those obtained from studying supernovae and other “late-universe” phenomena. This divergence, exceeding three standard deviations in some analyses, indicates a fundamental disconnect between how the universe behaved in its infancy and how it’s evolving today. While statistical fluctuations could account for minor discrepancies, the persistent and growing gap suggests that the LambdaCDM model – which relies on the existence of dark matter and dark energy to explain cosmic expansion – may be incomplete or require substantial refinement to reconcile these conflicting observations. This tension isn’t merely a technical issue; it challenges the very foundations of modern cosmology and motivates the exploration of alternative theories that might better describe the universe’s expansion history and composition.

The universe’s structure arises from subtle fluctuations in the early cosmos, and the parameter $S_8$ serves as a crucial gauge of their amplitude. Recent, independent analyses of cosmic microwave background data, weak gravitational lensing, and galaxy cluster surveys reveal a significant tension in the measured value of $S_8$. Specifically, models designed to reconcile differing measurements of the Hubble constant – known as the Hubble tension – exhibit a deviation of 3.19σ in $S_8$ when lacking a specific square-root correction term. This discrepancy isn’t merely a statistical fluke; it suggests that the standard cosmological model may be misinterpreting the underlying physics governing the distribution of matter and the expansion rate of the universe, prompting researchers to investigate potential modifications to dark energy or gravity itself.

The persistent discrepancies between measurements of the universe’s expansion rate and the distribution of matter hint at fundamental gaps in current cosmological models. The standard framework, LambdaCDM, relies on assumptions about gravity – described by Einstein’s General Relativity – and the nature of dark energy, which drives the accelerating expansion. However, the growing tensions suggest these assumptions may be oversimplified or incomplete. Consequently, researchers are actively investigating alternative theoretical frameworks, including modified gravity theories that challenge the validity of General Relativity on cosmological scales, and exploring dynamic dark energy models that propose its properties evolve over time. These investigations range from examining interactions within the dark sector – dark matter and dark energy – to considering the influence of extra dimensions or primordial magnetic fields, all in an effort to reconcile observational data with theoretical predictions and achieve a more complete understanding of the cosmos.

Beyond the Metric: A Geometry of Non-Metricity

Non-metricity, denoted as $Q$, represents a fundamental geometric property of spacetime that describes the change in length of a vector when transported in parallel. Unlike General Relativity, which relies on the metric tensor to define distances and angles, f(Q) gravity explicitly incorporates non-metricity as a key component of the gravitational interaction. Specifically, non-metricity quantifies the failure of the Levi-Civita connection to preserve vector lengths during parallel transport; a zero non-metricity indicates a metric-compatible connection, as found in General Relativity. The non-metric tensor, $Q_{\alpha\mu\nu}$, is defined as the non-metricity tensor and characterizes this failure, thereby providing an additional degree of freedom in the gravitational field equations beyond the metric tensor itself.

f(Q) gravity departs from General Relativity by augmenting the Einstein-Hilbert action with a function of non-metricity, $Q$. Non-metricity, a geometric property describing the change in vector lengths during parallel transport, introduces an additional degree of freedom into the gravitational field equations. This modification allows for alternative cosmological models that may address existing tensions between early and late-time universe measurements, specifically discrepancies in the Hubble constant, $H_0$, and the amplitude of matter fluctuations, $S_8$. By varying the functional form of $f(Q)$, the theory provides a mechanism to alter the gravitational interaction and potentially reconcile observational data with current cosmological paradigms without invoking new physics beyond the geometric modification of gravity.

f(Q) gravity models incorporating a $M\sqrt{Q}$ term present a mechanism for modifying the rate of structure formation independently of the cosmological background expansion. This arises because the $M\sqrt{Q}$ correction directly influences the perturbed equations governing density contrasts, altering the growth of large-scale structures while leaving the Friedmann equations-and therefore the Hubble parameter-unchanged. Analysis demonstrates that the inclusion of this term can effectively reduce the $S_8$ parameter-a measure of the amplitude of matter fluctuations-bringing theoretical predictions closer into alignment with observational data from cosmic microwave background and large-scale structure surveys, addressing a current tension in cosmological measurements.

Echoes of Growth: Observable Signatures of Modified Gravity

The $f(Q)$ gravity model introduces a square-root correction, denoted as $M\sqrt{Q}$, which directly modifies the effective gravitational coupling, $G_{eff}$. This modification arises because the gravitational action is a function of the non-metricity scalar, $Q$, and the parameter $M$ scales the impact of this non-metricity on gravity. Consequently, the rate at which cosmic structures – such as galaxies and galaxy clusters – form is altered compared to predictions from General Relativity. A larger $M$ value implies a stronger deviation from General Relativity and a correspondingly different growth rate of structure, influencing the amplitude and evolution of density perturbations over time. This altered growth rate is a key prediction of the model and can be tested through observational probes.

The parameter $f\sigma_8$ is a key cosmological observable quantifying the growth of large-scale structure in the universe. It represents the amplitude of density fluctuations at a given redshift, combining the growth rate, $f$, with the amplitude of matter fluctuations, $\sigma_8$. Redshift-Space Distortions (RSD) arise from peculiar velocities of galaxies, which distort their observed positions along the line of sight. By measuring these distortions in galaxy surveys, astronomers can derive $f\sigma_8$ and constrain cosmological models. Consequently, deviations in predicted $f\sigma_8$ values – resulting from modifications to gravity such as those proposed by f(Q) gravity – can be directly compared to observational data to test the theory’s validity and its potential to resolve cosmological discrepancies.

Predictions derived from f(Q) gravity can be empirically tested by comparing calculated values of the $f\sigma_8$ parameter – a measure of the growth of cosmic structure – with observational data obtained from large-scale structure surveys. Current cosmological analyses reveal a tension between early and late-time measurements of the universe’s expansion rate and structure growth, manifesting as a 3.19σ deviation in the $S_8$ parameter. However, allowing the M parameter, which governs the strength of the non-metricity-induced gravitational coupling in f(Q) gravity, to vary during analysis reduces this discrepancy to 1σ. This suggests that f(Q) gravity, through its impact on structure formation, offers a potential resolution to existing cosmological tensions and provides a testable framework for modified gravity theories.

A Universe Unveiled: Towards a More Complete Cosmology

Current cosmological models, notably LambdaCDM, face increasing scrutiny due to persistent tensions between observational data and theoretical predictions – specifically the Hubble tension, concerning the expansion rate of the universe, and the S8 tension, relating to the clustering of matter. f(Q) gravity emerges as a promising alternative, proposing a modification to general relativity that doesn’t rely on the inclusion of dark energy. Instead, it posits that the universe’s accelerated expansion and large-scale structure can be explained by the geometry of spacetime itself, encoded in the non-metricity parameter $Q$. This framework naturally addresses both the discrepancies in measuring the Hubble constant and the observed value of $S_8$ – a parameter quantifying the amplitude of density fluctuations – potentially offering a more unified and internally consistent description of the cosmos without invoking hypothetical dark energy components.

Current cosmological models, particularly LambdaCDM, often rely on the introduction of exotic dark energy components – such as quintom dark energy, characterized by an equation of state $w < -1$ – to account for the observed accelerated expansion of the universe. However, alternative gravitational theories, like f(Q) gravity, propose that this acceleration isn’t necessarily driven by a mysterious energy component, but rather by a modification to the laws of gravity themselves. By reformulating the gravitational interaction, these models aim to explain the accelerating expansion without invoking these complex and often poorly understood dark energy candidates. This approach streamlines the cosmological framework, potentially resolving inconsistencies and offering a more parsimonious explanation for the universe’s evolution, while simultaneously addressing tensions like the Hubble and S8 problems without adding further layers of complexity.

Statistical analysis strongly favors the inclusion of the $M$ parameter within Model B, a finding substantiated by an improvement in Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values exceeding 7. This significant enhancement indicates that the addition of this perturbation term substantially improves the model’s ability to fit observational data without sacrificing parsimony – a key principle in scientific modeling. Consequently, Model B, incorporating the $M$ parameter, emerges as a more compelling cosmological framework than standard LambdaCDM, potentially offering a more unified description of the universe’s expansion history and large-scale structure. The observed statistical preference suggests this parameter is not merely a fitting artifact, but rather reflects a genuine physical component contributing to the universe’s dynamics, guiding cosmological research towards a more consistent and comprehensive understanding.

The pursuit of modified gravity, as demonstrated in this exploration of f(Q) gravity, inevitably courts the limits of comprehension. One builds elegant frameworks, attempting to reconcile discrepancies like the S8 tension, yet always risks confronting a deeper, more fundamental unknown. As Igor Tamm observed, “Sometimes matter behaves as if laughing at our laws.” This sentiment echoes the challenge presented by cosmological observations; simplified models, however successful in addressing immediate tensions, are ultimately ‘pocket black holes’ of understanding, obscuring the true complexity beyond their event horizons. The square-root correction investigated here, while a potential step towards alleviating the S8 tension, serves as a reminder that each refinement merely pushes the boundaries of the abyss, inviting further investigation into the nature of dark energy and the expansion of the universe.

Where Do the Shadows Fall?

The exploration of f(Q) gravity, and particularly the inclusion of even seemingly minor corrections – such as the square-root term considered here – reveals a humbling truth. The cosmos generously shows its secrets to those willing to accept that not everything is explainable, and that elegant solutions often emerge from embracing complexity. This work, while demonstrating a potential alleviation of the S8 tension, simultaneously highlights the precariousness of any claim to a ‘complete’ cosmological model. Each parameter adjusted, each tension eased, is merely a temporary reprieve-a localized victory in an infinite war against uncertainty.

Future investigations must confront the inherent limitations of modified gravity theories. The model’s reliance on specific functional forms, and its sensitivity to initial conditions, represent vulnerabilities. A truly robust theory will need to emerge not just from fitting observational data, but from a deeper understanding of the underlying physics-something that remains frustratingly elusive. The search for alternatives to dark energy and dark matter may prove to be a fool’s errand, but the pursuit itself is a valuable exercise in intellectual humility.

Black holes are nature’s commentary on our hubris. The apparent success of f(Q) gravity in addressing certain cosmological puzzles should not engender complacency. It should instead serve as a reminder that the universe is under no obligation to conform to expectations, and that the most profound discoveries often lie beyond the event horizon of current understanding.

Original article: https://arxiv.org/pdf/2512.16551.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

See also:

2025-12-22 02:05