Dynamical Dark Energy from a Massive Vector Field in Generalized Proca Theory

TL;DR

This work probes dynamical dark energy through a massive vector field $B^{\mu}$ non-minimally coupled in Generalised Proca theory, motivated by DESI DR2 hints of deviation from $\Lambda$CDM. The authors embed the model in a ghost-free GP framework, derive the FRW dynamics with a de Sitter attractor, and obtain an analytic expression for the EoS $w(\tilde H)$ that depends on the couplings $\lambda$, $\gamma$, and $m$. Using GW speed and real-root constraints, plus DESI+CMB+Pantheon+ data, they constrain $\lambda<2.98\times10^{-11}$, $-0.405\le\log_{10}\tilde\gamma\le-0.38$, and $3.14\times10^{-66}\text{g}\le m\le3.36\times10^{-66}\text{g}$, yielding present-day $w_0$ with $0.107\le\delta\le0.217$ and reproducing the DESI-inferred deviation. The model approaches $\Lambda$CDM at late times ($t\gtrsim28$ Gyr) via a single de Sitter attractor, linking the parameters to dynamical dark energy and DESI observations.

Abstract

In this paper, we emphasise the recent observational findings from the Dark Energy Spectroscopic Instrument Data Release 2 (DESI DR2), which provide compelling evidence for a possible deviation from the standard $Λ$CDM (Cold Dark Matter) cosmology, suggesting the presence of a dynamically evolving effective dark energy component. Motivated by this, we construct a theoretical framework in which a massive cosmological vector field, $B^μ$, couples non-minimally to the background curvature through marginal interactions, offering a controlled mechanism to realise the deviation from the $Λ$CDM model. A detailed analysis of the effective Equation of State (EoS) parameter $w(\tilde H)$ reveals a narrow region of parameter space consistent with current cosmological observations presented by DESI. The analysis yields a stringent upper bound for the coupling constant $λ$ to be $λ<2.98\times10^{-11}$, a very strong bound on mass $3.1356\times10^{-66}~\text{g} \leq m \leq 3.3627\times10^{-66}~\text{g},$ and the admissible range $-0.405 \leq \log_{10}\tildeγ\leq -0.38$ for which present-day value $w_0 = w(\tilde H = 1)$ corresponding to a deviation $δ= w_0 + 1$ that lies within the region $0.107 \leq δ\leq 0.217$. This interval reproduces the deviation inferred from the combined DESI, Cosmic Microwave Background (CMB), and Pantheon+ data, reflecting a controlled departure from the $Λ$CDM behaviour. In summary, the results suggest that the proposed framework of a massive vector field can account for the departure from $Λ$CDM behaviour highlighted by DESI in the current cosmic acceleration. Furthermore, the framework approaches the $Λ$CDM behaviour in late-time $t\gtrsim28$ Gyr, establishing a direct phenomenological link between the underlying parameters and the observed dynamical nature of dark energy.

Figures (4)

• Figure 1: Deviation ($\delta$) of the equation-of-state parameter $w(\tilde{H})$ for the allowed range of model parameters.
• Figure 2: Zoomed-in projection highlighting the viable range of $\tilde{\gamma}$ consistent with the observational deviation $\delta$ from DESI+CMB+Pantheon+ data.
• Figure 3: Variation of $\delta$ with respect to $r$ showing the unphysical region ($\delta=1$ corresponds to $w_0=0$).
• Figure 4: EoS Vs Rescaled Hubble parameter for different values of $\tilde{\gamma}$.