Genetic algorithms test the Hu–Sawicki f(R) gravity model against DESI and Pantheon+ data ✛ ✎ ✦
Context
Recent data from supernovae and baryon acoustic oscillations from the DESI collaboration hint at a possible evolution of dark energy, casting doubt on the standard ΛCDM model. Testing alternative theories of gravity, such as f(R) models, becomes critically important. These theories generalize Einstein's general relativity, and their cosmological solutions are considered in the Friedmann–Lemaître metric. In them, the accelerated expansion of the Universe is explained not by a cosmological constant but by a modification of spacetime geometry, which effectively describes dynamic dark energy. However, many such models face stability problems and fail local gravity tests.
Methods
To find viable F(R) functions, the study used machine learning—genetic algorithms that, through symbolic regression, reconstruct analytic perturbations around the Hu–Sawicki model. The survival of functions was assessed by their ability to satisfy theoretical stability conditions (including absence of tachyonic instabilities and the chameleon screening mechanism) while also fitting supernova data from Pantheon+ and BAO from DESI DR2 at various redshifts. For each candidate, a system of modified Friedmann equations, derived from the Einstein equations for the f(R) metric, was solved numerically, and the cosmological evolution was found via numerical simulation.
Results
The best reconstructed F(R) function shows only negligible deviations from ΛCDM: the amplitude of variation in the effective equation of state of dark energy $w_{eff}$ is on the order of 10⁻⁷, and the Om(z) diagnostic deviates from a constant by no more than 0.1% at low redshifts. The model confidently recovers the standard gravity limit at high energies, and chameleon screening suppresses the fifth force in dense environments. A slight decrease in χ² compared to ΛCDM does not allow statistically significant superiority of modified gravity to be claimed.
Implications
The results mean that current observations of the expansion of the Universe impose tight constraints on modifications of gravity: the allowed class of f(R) models must practically coincide with ΛCDM at all redshifts except the very smallest. This aligns with the chameleon mechanism, which effectively hides deviations from general relativity in laboratory and astrophysical systems. Thus, if dynamic dark energy exists, its manifestation in background data is minimal.
Future development
Future studies should include perturbation analyses (growth rate of structures, weak lensing) where gravity modifications manifest more prominently. Expanding the machine search to more general functional forms of f(R), as well as using data from upcoming surveys (Euclid, Roman), will either detect deviations or push the model even closer to ΛCDM.
Impact
The work impacts cosmology and gravity theories, encouraging a shift from phenomenological parameterizations of dark energy to physically motivated models, and demonstrates the power of machine learning in solving inverse problems of fundamental physics.
Next steps
Direct comparison of reconstructed f(R) functions with the CPL parameterization under a unified statistical analysis, and inclusion of cosmic microwave background data for tighter constraints.
Key open problems
The paper addresses one of the key problems in physics—the nature of dark energy and the cosmological constant problem—proposing a method to search for microscopic deviations from ΛCDM within viable modifications of gravity.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors applied genetic algorithms for symbolic regression of perturbations around the Hu–Sawicki model in f(R) gravity, testing them against stability conditions and data from DESI DR2 and Pantheon+. The best reconstructed function F(R) showed deviations from ΛCDM only at the level of 10⁻⁷ in the effective equation of state, and the diagnostic parameter Om(z) — no more than 0.1% at low z.
Where its strength is
The method automatically finds viable forms of f(R) compatible with data, without manual searching, and rigorously incorporates theoretical constraints such as chameleon screening and the absence of tachyonic instabilities.
Where it could go next
- It might be interesting to see how the found f(R) models manifest in the dynamics of large-scale structure, especially in the context of recent hints of dark energy evolution. Nearby in the archive there is an analysis of how the dark energy constant ceases to be constant, providing context for testing models beyond background evolution.based on: Dark Energy: When the Constant Stops Being Constant arXiv:2607.01226v1
- Since the allowed deviations turned out to be extremely small, it is useful to compare them with constraints imposed by primordial nucleosynthesis. In our archive there is a quick review of a paper on how the newborn cosmos cooked helium, which could provide additional tests for f(R) models in the early Universe.based on: How the newborn cosmos brewed helium arXiv:2607.17252
Worth trying
- Test how small deviations of f(R) from ΛCDM affect predictions for primordial nucleosynthesis, using the approach from the paper on helium cooking.
- Apply the found f(R) functions to calculate the gravitational-wave signal from neutron star mergers and compare with constraints from gravitational sirens described in a related paper.
Why this may matter
Even minuscule deviations from ΛCDM, if confirmed at other stages of evolution, could point to the need for modified gravity. Combining background constraints with tests from the early Universe and gravitational-wave observations could close the loop on testing the viability of f(R) models.
Nearby works in our archive
- Cosmic Mirages Test the Law of Gravitysimilarity 0.72
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The archive is crowded around this work: 4 reviews nearby, closest at 0.72. This ground is well walked — and there is plenty to compare against.
Genetic algorithms work like biological evolution: random mutations and crossovers generate generations of functions, and only those best adapted to the data and physical constraints survive. In this study, the surviving functions turned out to be almost indistinguishable from the cosmological constant.
Key numbers
- Hubble constant H0: 68.70 km/s/Mpc
- Matter density parameter Ω_m: 0.306
- Deviation scale of f_R from unity: <10⁻⁷
- Om(z) variation at low z: ~0.1%
- χ² of the best f(R) model: 1418.9