Causal Field Theory as a Dynamical Dark Energy Model: Cosmological Background Evolution and Constraints from Pantheon+ Supernovae

Abstract

The nature of dark energy remains one of the most pressing questions in modern cosmology. The standard $\Lambda$CDM model invokes a cosmological constant $\Lambda$, but its observed value is $\sim120$ orders of magnitude smaller than theoretical expectations, and the persistent Hubble tension challenges the model's completeness. In this work we apply the recently proposed Causal Field Theory (CFT) --- a minimal extension of General Relativity rooted in the Principle of Causal Optimality --- to the homogeneous and isotropic cosmological background. CFT introduces a dimensionless scalar field $\phi$ with an exponential potential $V(\phi)=\beta(e^{2\phi}-1-2\phi)$ and a non‑minimal coupling to the trace of the matter stress‑energy tensor, characterised by the dimensionless constant $\lambda$. From the modified Friedmann equations and the scalar field equation we evolve the background cosmology and calibrate the two free parameters to the present‑day Hubble constant $H_0$ and the dark‑energy density parameter $\Omega_\phi=0.7$. The best‑fit values are $\beta=1.0216$ and $\lambda=2.5150$ (in units $8\pi G=c=H_0=1$). The resulting expansion history is in excellent agreement with the Pantheon+ compilation of 277 Hubble‑flow type Ia supernovae, giving $\chi^2=138.4$ for 276 degrees of freedom ($\chi^2/\mathrm{dof}=0.50$). A rigorous model comparison using the Akaike and Bayesian information criteria shows that $\Lambda$CDM with a free matter density parameter is statistically preferred over CFT in this particular test ($\Delta\mathrm{AIC}=20.5$, $\Delta\mathrm{BIC}=24.2$). Nevertheless, CFT provides an equally good fit to the data and, crucially, offers a unified physical origin for dark energy derived from a single foundational principle, without invoking a cosmological constant. These results establish CFT as a viable dynamical dark energy candidate and motivate its further testing on galactic and cosmological scales.