Non-minimal Derivative Coupling Scalar Field and Bulk Viscous Dark Energy
Behrang Mostaghel, Hossein Moshafi, S. M. S. Movahed
TL;DR
This work proposes a bulk-viscous dark energy model in a spatially flat two-component Universe and establishes a correspondence with a non-minimal derivative coupling (NMDC) scalar field of zero potential. The viscosity parameter $\gamma$ controls the DE dynamics, while the NMDC coupling $\kappa$ is tied to $\gamma$ and $\Omega_{\rm DE}^0$, with a ghost-free constraint $\kappa=\varepsilon\big/\big(9H_0^2(1-\Omega_{\rm DE}^0)\big)\exp\left(-\tfrac{2\sqrt{\Omega_{\rm DE}^0}}{3\gamma}\right)$. Observational analyses using JLA SNIa, GRBs, BAO, HST, and Planck data yield best-fit late-time values around $\Omega_{\rm DE}^0\approx0.696$–$0.701$ and $\gamma\approx0.14$, with $H_0\approx68$ km s$^{-1}$ Mpc$^{-1}$, while Planck TT data allow larger $\gamma$ (≈0.32) and help alleviate the Hubble tension. The model supports Phantom crossing without a Big Rip, predicts a Little-Rip fate, and can reconcile cosmological age observations, making it a viable dynamical dark-energy candidate compatible with current data. It also provides diagnostic tools (Om, cosmographic parameters, and distance ratios) to distinguish it from $\Lambda$CDM, particularly at late times.
Abstract
Inspired by thermodynamical dissipative phenomena, we consider bulk viscosity for dark fluid in a spatially flat two-component Universe. Our viscous dark energy model represents Phantom crossing avoiding Big-Rip singularity. We propose a non-minimal derivative coupling scalar field with zero potential leading to accelerated expansion of Universe in the framework of bulk viscous dark energy model. In this approach, coupling constant ($κ$) is related to viscosity coefficient ($γ$) and energy density of dark energy at the present time ($Ω_{\rm DE}^0$). This coupling is bounded as $κ\in [-1/9H_0^2(1-Ω_{\rm DE}^0), 0]$ and for $γ=0$ leads to $κ=0$. To perform robust analysis, we implement recent observational data sets including Joint Light-curve Analysis (JLA) for SNIa, Gamma Ray Bursts (GRBs) for most luminous astrophysical objects at high redshifts, Baryon Acoustic Oscillations (BAO) from different surveys, Hubble parameter from HST project, {\it Planck} data for CMB power spectrum and CMB Lensing. Joint analysis of JLA$+$GRBs$+$BAO$+$HST shows that $Ω_{\rm DE}^0=0.696\pm 0.010$, $γ=0.1404\pm0.0014$ and $H_0=68.1\pm1.3$ at $1σ$ confidence interval. {\it Planck} TT observation provides $γ=0.32^{+0.31}_{-0.26}$ at $68\%$ confidence limit for viscosity coefficient. Tension in Hubble parameter is alleviated in this model. Cosmographic distance ratio indicates that current observed data prefer to increase bulk viscosity. Finally, the competition between Phantom and Quintessence behavior of viscous dark energy model can accommodate cosmological old objects reported as a sign of age crisis in $Λ$CDM model.