Testing Non-Coincident $f(Q)$-gravity with DESI DR2 BAO and GRBs

TL;DR

This work examines non-coincident $f(Q)$-gravity in a flat FLRW universe, revealing a two-field (canonical and phantom) quintom-like description arising from a non-trivial connection. For a power-law model $f(Q)\simeq Q^{\hat{n}}$, the authors derive an analytic expression for the geometric dark-energy equation of state $w_{f(Q)}(a)$ via a Lambert $W$-function solution and provide the corresponding Hubble evolution. They constrain the model with DESI DR2 BAO, Pantheon+ SN, GRBs, and cosmic chronometers, finding a best-fit $n$ near $0.33$ and a range of $H_0$ and $\Omega_{m0}$ depending on the data combination; the model sometimes improves the fit under AIC, though BIC often prefers $\Lambda$CDM. The results indicate that the non-coincidence connection can influence dark-energy phenomenology and motivate further tests of non-Riemannian formulations in cosmology.

Abstract

We consider the $f\left( Q\right) $-theory for the description of dark energy with a non-trivial connection defined in the non-coincident gauge. The resulting field equations form a two-scalar-field, quintom-like gravitational model. For the power-law model $f\left( Q\right) \simeq Q^{\frac{n}{n-1}}$, we construct an analytic expression for the dynamical evolution of dark energy, which depends on the parameter $n$. We constrain this dark energy model using the the baryon acoustic oscillations from DESI DR2, and gamma-ray bursts. The cosmological data provides $n\simeq0.33$. The $f\left( Q\right) $-model challenges the $Λ$CDM by providing a smaller value for $χ_{\min}^{2}$. Although the Akaike Information Criterion indicates that the two cosmological models fit the data from the Pantheon+, the cosmic chronometers and the baryonic acoustic oscillators in a similar way, when the gamma-ray bursts are introduced there is weak evidence in favor of the $f\left( Q\right) $-theory.

Figures (4)

• Figure 1: Qualitative evolution of the equation of state parameter$~w_{f\left( Q\right) }\left( z\right)$ given by expression (\ref{['ll.05']}) for different values of the free parameters $n$ and $I_{0}$.
• Figure 2: Contour plots on the parametric space $\left( n,I_{0}\right)$ for the equation of state parameter$~w_{f\left( Q\right) }\left( z\right)$ given by expression (\ref{['ll.05']}) for different for specific redshifts $z$.
• Figure 3: Confidence space for the best-fit parameters for the power-law $f\left( Q\right)$-gravity, for the datasets SN+OHD+BAO and SN+OHD+BAO+GRB.
• Figure 4: Confidence space for the best-fit parameters for the power-law $f\left( Q\right)$-gravity, for the datasets SN$_{0}$+OHD+BAO and SN$_{0}$+OHD+BAO+GRB with the Cepheid calibration for the supernova.