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Cosmology · analytical and computational manuscript · September 2026

RCD and KGB: what does the alternative-gravity test actually show?

New gravitational models can be mathematically interesting. What matters is whether their dynamics are well defined, their limits stable, and their quantitative predictions consistent with cosmological observations.

Abstract and scientific scope

RCD/KGB research includes mathematical constructions of gravitational models and statistical comparisons with cosmological data. The branches have different assumptions and limitations; one calculation's results therefore do not automatically validate the entire family of hypotheses.

From a physical variable to a theory

Relational Capacity Dynamics (RCD) starts from a positive relational-capacity field C(τ, x). For the classical scalar sector, the supplied manuscript describes an action, variational equations, a Hamiltonian, Noether currents, finite-response transport and linear-stability analysis. This provides mathematical foundations, but does not automatically establish a unique gravitational interpretation. Moving from RCD to a particular gravitational realisation requires separate assumptions.

Multiple branches, multiple tests

The programme distinguishes the original covariant metric–khronon completion, the separate low-energy RFG-R EFT branch, and luminal Kinetic Gravity Braiding (KGB). Local gravitational limits, stability conditions and degrees of freedom enter differently in each branch. For example, recovery of general relativity in a constant local domain cannot be extended to the entire interpolation region without additional analysis.

How the KGB branch was tested

According to the public research record, direct H-EFTCAMB evolution included photons, baryons, cold dark matter and neutrinos. Subsequent evaluation used Planck 2018 CMB and lensing, Pantheon+, DESI DR2 BAO and cosmic chronometers. This computational pipeline is intended to test the model against multiple observations simultaneously, rather than merely reconstruct a suitable expansion curve.

The Bayesian comparison

The author's nested-sampling analysis reports log Z(KGB) = −1250.3771730 ± 0.4241604 and log Z(ΛCDM) = −1250.9013480 ± 0.4135692. The difference, Δ log Z = +0.5241750 ± 0.5924116, corresponds to a Bayes factor of approximately 1.6891. The central value slightly favours KGB, but the difference is smaller than the reported numerical uncertainty. It therefore establishes neither decisive empirical preference nor a replacement for ΛCDM.

Open problems

Further development requires particular attention to degrees of freedom and stability in the interpolation region, complete local gravitational tests, checks of likelihood settings, and reproduction of numerical calculations. The reported RSD audit remains a numerical audit, rather than a full survey-likelihood analysis. Nor do the programme's branches automatically form one consistent model.

Why such a result is useful

An inconclusive test has scientific value: it clarifies which model variants can be computed, which assumptions require refinement and how strong new evidence would need to be. The goal is to construct a testable alternative transparently, rather than prematurely declare victory over established cosmology.

Papers and public research records

Related public records and identifiers are listed below. A DOI does not, by itself, establish the correctness of findings or guarantee peer review.

Read also

Testing an alternative cosmology →

The opening graphic is a conceptual thematic illustration, not an experimental record.