Summary in Seconds: The accelerating expansion of the Universe, discovered in 1998, remains one of modern cosmology’s greatest mysteries. While the standard ΛCDM model attributes this acceleration to a cosmological constant, alternative explanations—including dynamic dark energy and possible modifications to Einstein’s general relativity—are being actively explored. Using data from large-scale surveys such as the Dark Energy Survey, researchers test gravity on cosmic scales through theoretical extensions like Horndeski models and phenomenological parameters (μ and η) that capture potential deviations from Einstein’s equations. Recent analyses suggest a mild (3-sigma) tension between observations and general relativity, particularly in how large-scale structures have evolved over the past several billion years. Although not yet conclusive, upcoming high-precision data from the Euclid mission may determine whether cosmic acceleration is driven by dark energy, modified gravity, or entirely new physics.
The accelerating expansion of the Universe, first identified in 1998, remains one of the most profound puzzles in modern physics. Despite decades of progress in cosmology, scientists still debate the fundamental cause of this acceleration. Some attribute it to a cosmological constant [1]—a constant energy density permeating space itself. Others propose a dynamic form of dark energy that evolves over time. A more radical possibility suggests that the phenomenon signals a breakdown of Einstein’s theory of general relativity on cosmic scales.
To evaluate these competing ideas, researchers rely on large-scale cosmological surveys that map the distribution of galaxies and matter across vast stretches of space and time. These surveys provide the empirical foundation for testing whether gravity behaves as Einstein predicted—or whether new physics is required.
Beyond the ΛCDM Model
The standard cosmological framework, known as the ΛCDM (Lambda Cold Dark Matter) model [2], has long served as the backbone of modern cosmology. It successfully explains a wide range of observations, from the cosmic microwave background to the large-scale structure of the Universe. However, increasingly precise data have begun to expose tensions that may lie beyond the model’s explanatory reach.
To probe these discrepancies, researchers are exploring two complementary strategies.
The first approach investigates broad theoretical frameworks that extend general relativity. Among these are Horndeski theories [3], which represent the most general class of scalar–tensor models with second-order equations of motion. These theories attempt to bridge observational data and fundamental physics by introducing additional gravitational degrees of freedom. However, their complexity presents a challenge: multiple parameters can produce overlapping observational effects, making it difficult to extract unambiguous conclusions from current datasets.
The second approach adopts a more phenomenological strategy [4]. Rather than committing to a specific theory, it modifies Einstein’s equations using two effective parameters—μ and η—that capture potential deviations from general relativity.
- μ quantifies modifications to Poisson’s equation [5], thereby describing how gravitational potentials respond to matter.
- η measures the ratio between spatial and temporal distortions in space-time, offering insight into how gravity influences cosmic structure formation.
These parameters can be constrained using observational data from major surveys such as the Dark Energy Survey [6], as well as galaxy clustering measurements [7] from BOSS and eBOSS. By refining these techniques, scientists aim to determine whether the accelerating expansion arises from dark energy, modified gravity, or an as-yet-unknown mechanism.
Observational Challenges
Despite its promise, the μ–η framework faces notable challenges. Constraints on these parameters vary with redshift [8], meaning they evolve with cosmic time. Interpreting the data therefore requires either adopting a predefined functional form or employing advanced reconstruction techniques.
Moreover, the analysis typically assumes that Euler’s equation [9] governing dark matter remains valid. If this assumption fails under modified gravity scenarios, it could complicate the interpretation of observational results. These theoretical subtleties underscore the difficulty of testing gravity on the largest scales imaginable.
Putting General Relativity to the Test
Since its formulation in 1915, Einstein’s general relativity has revolutionized our understanding of gravity. Its predictions have been confirmed repeatedly, beginning with the 1919 solar eclipse [10] expedition that measured the bending of starlight—an effect now known as gravitational lensing. By studying how massive objects warp space-time and deflect light, scientists can probe both the geometry and the evolution of the Universe.
Yet an open question remains: does general relativity remain valid across billions of light-years?
Researchers from the University of Geneva (UNIGE) and Toulouse III – Paul Sabatier have sought to address this question using data from the Dark Energy Survey. Rather than merely mapping matter distribution, their study directly measured distortions in space and time [11], enabling a direct comparison with Einstein’s predictions.
Camille Bonvin, associate professor at UNIGE, emphasized the novelty of the approach: instead of using survey data solely to trace matter, the team analyzed it to measure the structure of space-time itself.
A Universe Slightly Out of Sync
The Dark Energy Survey cataloged approximately 100 million galaxies spanning four distinct cosmic epochs—roughly [12] 3.5, 5, 6, and 7 billion years ago. These observations allowed researchers to track the evolution of gravitational wells [13], regions where matter density warps space-time.
Lead author Isaac Tutusaus reported a striking pattern: at earlier epochs (6–7 billion years ago), the depth of these gravitational wells aligns closely with Einstein’s predictions. At more recent epochs (3.5–5 billion years ago), however, the wells appear shallower than expected.
Intriguingly, this deviation coincides with the period when cosmic expansion began accelerating. The findings suggest a possible connection between the slower growth of large-scale structures and the onset of accelerated expansion—raising the possibility that both phenomena share a common underlying cause.
The 3-Sigma Tension
Statistically, the discrepancy corresponds to a 3-sigma deviation [14] from Einstein’s predictions. In scientific terms, this level of significance is suggestive but not definitive. As co-author Nastassia Grimm noted, the result is compelling yet insufficient to overturn general relativity.
Further investigation is essential.
To that end, researchers are now turning to the Euclid space telescope [15], launched by the European Space Agency. Over its six-year mission, Euclid will survey approximately 1.5 billion galaxies, delivering unprecedented precision in gravitational lensing measurements. Its data will provide a far more stringent test of Einstein’s equations and the nature of cosmic acceleration.
On the Edge of a New Understanding
The effort to test general relativity on cosmological scales represents one of the most ambitious endeavors in contemporary physics. Whether the accelerating expansion arises from dark energy, modified gravity, or entirely new physics remains uncertain.
What is clear, however, is that the boundaries of our current understanding are being pushed to their limits. With next-generation data from Euclid and other observatories, the coming years may redefine our conception of gravity and the large-scale structure of the Universe.
The mystery that began with the discovery of cosmic acceleration in 1998 may yet lead to a deeper and more unified theory of the cosmos—one that reshapes our understanding of space, time, and the fundamental laws governing reality.
Notes
1. Cosmological constant
The cosmological constant is a term Einstein added to his field equations representing a constant energy density that fills space uniformly. Today, it is commonly interpreted as the simplest explanation for dark energy, driving the accelerating expansion of the Universe.
2. ΛCDM (Lambda Cold Dark Matter) model
The ΛCDM model is the standard model of cosmology, combining the cosmological constant (Λ) with cold dark matter (CDM). It successfully explains large-scale cosmic observations, including the cosmic microwave background and galaxy distribution, though some recent data reveal tensions with its predictions.
3. Horndeski
Horndeski theories are the most general class of scalar–tensor gravity theories with second-order equations of motion, avoiding mathematical instabilities. They extend general relativity by introducing an additional scalar field that can modify gravity on cosmic scales.
4. Phenomenological strategy
A phenomenological strategy focuses on describing observable effects without committing to a specific underlying theory. In cosmology, this approach modifies gravitational equations using effective parameters to test deviations from general relativity directly against data.
5. Poisson’s equation
Poisson’s equation in gravity relates the gravitational potential to the distribution of matter producing it. Modifications to this equation can indicate changes in how gravity operates on large cosmic scales.
6. Dark Energy Survey
The Dark Energy Survey is an international astronomical project that mapped hundreds of millions of galaxies to study cosmic acceleration. By analyzing gravitational lensing and large-scale structure, it provides crucial data for testing dark energy and modified gravity models.
7. Galaxy clustering measurements
Galaxy clustering measurements analyze how galaxies group together across different scales. These patterns reveal how matter evolves under gravity and serve as sensitive probes of cosmological models.
8. Redshift
Redshift refers to the stretching of light toward longer wavelengths as the Universe expands. In cosmology, it serves as a measure of distance and cosmic time, allowing scientists to observe how structures evolved billions of years ago.
9. Euler’s equation
In cosmology, Euler’s equation describes the motion of matter under gravitational forces in an expanding Universe. It is a fundamental assumption in structure formation models, and altering it could signal new gravitational physics.
10. 1919 solar eclipse
The 1919 solar eclipse provided the first experimental confirmation of Einstein’s general relativity. Observations led by Arthur Eddington showed that starlight was bent by the Sun’s gravity exactly as Einstein had predicted.
11. Distortions in space and time
Distortions in space and time refer to the curvature of space-time caused by mass and energy, as described by general relativity. These distortions determine how matter moves and how light travels through the Universe.
12. Epochs—roughly
In cosmology, epochs are distinct periods in the history of the Universe characterized by specific physical conditions. When described as “roughly,” the term indicates approximate time ranges measured in billions of years.
13. Gravitational wells
Gravitational wells are regions where matter concentration creates a deep gravitational potential. The deeper the well, the stronger the gravitational pull, influencing galaxy formation and cosmic structure growth.
14. 3-sigma deviation
A 3-sigma deviation indicates that an observed result differs from a prediction at a level of three standard deviations from the mean. Statistically, this corresponds to about a 99.7% confidence level, suggesting a meaningful but not definitive discrepancy.
15. Euclid space telescope
The Euclid space telescope is a European Space Agency mission designed to map the geometry of the dark Universe. By observing billions of galaxies and measuring weak gravitational lensing, it aims to test dark energy models and probe possible deviations from general relativity.
Source
Shavit, Joshua. “Breakthrough Research Questions Einstein’s Theory of General Relativity.” Brighter Side of News, 22 January 2025.
Was Einstein wrong? Controversial theory claims the speed of light is not a constant
Beall, Abigail. “Was Einstein wrong? Controversial theory claims the speed of light is not a constant.” Wired-UK, 13 December 2016.