Horndeski Gravity as an Effective Dark Energy Fluid in Cosmological N-body Simulations

Unraveling the nature of the cosmic expansion, driven by Dark Energy, remains one of the key challenges in modern cosmology. Modified Gravity models provide an alternative to the standard cosmological constant paradigm. The new analysis still awaits peer review, but it already lays out the central claim clearly.

The significance lies in cosmology operates at the edge of what current instruments can measure, where systematic errors and model assumptions are never trivial. Small discrepancies between independent measurements have historically pointed toward missing physics rather than simple calibration errors, and the ongoing tension in the Hubble constant is a live example of how a persistent disagreement between methods can reshape the theoretical landscape. Each new dataset that approaches this territory with independent systematics adds real information to a problem that has resisted easy resolution for more than a decade. Unraveling the nature of the cosmic expansion, driven by Dark Energy (DE), remains one of the key challenges in modern cosmology. Modified Gravity (MG) models provide an alternative to the standard cosmological constant paradigm.

These models predict distinct signatures in the growth of structure, yet analytical predictions are challenging due to the highly non--linear equations involved. To overcome this problem, we study MG as an effective DE fluid.

To this end, we have incorporated linear DE perturbations into the N--body code $\texttt{CO}N\texttt{CEPT}$, which relies on the Einstein--Boltzmann solver $\texttt{CLASS}$. We replaced the $\texttt{CLASS}$ version used by $\texttt{CO}N\texttt{CEPT}$ with $\texttt{mochi\_CLASS}$, a patched version that includes Horndeski family models.

By writing linear DE perturbations ($δρ_{\rm DE}$, $δP_{\rm DE}$, $θ_{\rm DE}$, and $σ_{\rm DE}$) in terms of metric perturbations in the synchronous gauge, the N--body code is. Our current simulations encompass a range of cosmological scenarios ---$w_0w_a$CDM, Hu--Sawicki $f(R)$ and cubic Galileon--- each extended to include massive neutrinos.

The relevance goes beyond one dataset because even small shifts in measured parameters can matter when the field is testing the limits of the standard cosmological model. The Lambda-CDM framework describes the observable universe with remarkable economy, but its success rests on two components, dark matter and dark energy, whose physical nature remains entirely unknown. Any credible measurement that tightens or loosens the constraints on those components moves the entire theoretical enterprise forward, regardless of whether the immediate result looks dramatic on its own terms.

For each of the models, we have found deviations from General Relativity close to what is predicted in the linear regime: a sub-$0. Since our code is the first to implement Horndeski gravity into an N--body code, its validation is a non--trivial computational task.

Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is to see whether the effect survives when independent surveys, different calibration strategies and tighter control of systematic uncertainties enter the picture. Programmes such as Euclid, DESI and the Rubin Observatory will deliver datasets over the next several years that cover the same parameter space with largely independent methods. If the current signal persists through those tests, its theoretical implications will become impossible to set aside. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

Source