EFC vs LCDM bullet cluster comparison
For decades, the Bullet Cluster has stood as one of the most striking pieces of evidence for dark matter. Two galaxy clusters have collided, their hot gas clouds have slammed into each other and slowed down, and yet the gravitational lensing signal appears to trace the galaxies rather than the gas. In the standard ΛCDM picture, this is explained by invisible, collisionless dark matter halos that pass through the collision along with the galaxies. The visible gas, being collisional, lags behind.
But there is another way to look at the same phenomenon.
Instead of adding an unseen mass component, one can ask whether gravity itself might respond differently to different kinds of structure in matter — not just to how much mass is present, but to how that matter is organized and how far from thermodynamic equilibrium it is. This is the starting point of Energy-Flow Cosmology (EFC), a framework in which gravitational effects emerge from spatial variations in energy flow and entropy gradients. In this picture, gravity is not purely local. Its response can be spread out over space through a kernel with a characteristic length scale, usually denoted λ.
In recent modeling work, we tested whether such a non-local, component-sensitive gravitational response can reproduce the lensing morphology of a Bullet-like cluster merger — without introducing dark matter as an extra mass component.
The key ingredients are straightforward. First, we map the distribution of galaxies, which behave approximately collisionlessly during the merger. Second, we construct a field related to the thermodynamic structure of the gas, using entropy proxies derived from X-ray data. These two components are then fed into a forward model where the gravitational convergence field κ is not computed from a simple Poisson equation, but from a spatial convolution: the sources are filtered through a Yukawa-type kernel with a characteristic length λ. This kernel spreads the gravitational response over a finite range, making the theory explicitly non-local.
We then compare the resulting κ maps to observed lensing reconstructions using a standard likelihood framework and Markov Chain Monte Carlo sampling. Importantly, we also perform a nested model test to see whether including the gas component actually improves the fit.
The outcome is striking but needs to be interpreted carefully. For the Bullet-type system, the best fits are obtained when the gravitational response is dominated by the galaxy distribution, with the gas contribution statistically irrelevant. In other words, the model naturally produces a situation where the lensing signal follows the collisionless component rather than the hot gas. This is exactly the qualitative behavior that, in ΛCDM, is attributed to dark matter halos.
In addition, the modeling yields a well-defined non-local length scale λ. When realistic galaxy distributions are used instead of smooth approximations, λ settles to a value on the order of a few arcminutes, corresponding to a few hundred kiloparsecs at the cluster’s distance. This scale is not arbitrarily tuned for each feature; it emerges as the characteristic range over which the gravitational response is smoothed.
Does this mean dark matter has been replaced? No — not yet, and not in this paper. What it does mean is that at least some of the phenomenology usually attributed to dark matter in cluster mergers can be reproduced by modifying the structure of the gravitational response itself, rather than by adding an unseen mass component. In ΛCDM, the spatial extent of the gravitational field comes from the geometry and history of dark matter halos. In EFC, it comes from a built-in response length in how gravity couples to structured, out-of-equilibrium matter. Both approaches can generate extended lensing signals; they simply place the underlying “length scale” in different parts of the physics.
This work should therefore be seen as a proof of viability, not a final verdict. The lensing maps used are based on approximate reconstructions rather than full shear catalog inversions. Only a small number of cluster systems have been explored so far. And no claims are made yet about consistency with cosmic microwave background data or large-scale structure statistics, where ΛCDM is tightly constrained.
Nevertheless, something important has emerged. A non-local gravitational response with a physically interpretable length scale can reproduce the key qualitative feature of the Bullet Cluster — the separation between gas and the dominant lensing signal — without invoking an additional invisible mass field. That alone makes it a serious candidate for further testing.
The next steps are clear. The same model must be confronted with full weak-lensing shear data, applied to multiple independent merging clusters, and tested in very different regimes such as galaxy rotation curves and statistical lensing surveys. If a consistent length scale and coupling form continue to appear without retuning, then we would be looking at evidence for a new structural element in gravity itself. If not, the model will fail, and that is equally informative.
For now, the result stands as an invitation: perhaps the gravitational field in complex, non-equilibrium systems carries more information about structure than we usually assume. Whether that path leads beyond dark matter or simply deepens our understanding of it is a question that only broader data can answer.
DOI: https://doi.org/10.6084/m9.figshare.31190233
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