Cosmological Dynamics of Hyperbolic Evolution Models in $f(Q,L_m)$ Gravity

TL;DR

This paper investigates cosmological dynamics in the modified symmetric teleparallel gravity $f(Q,\mathcal{L}_m)$ using two hyperbolic evolution models for the scale factor. By adopting a linear-coupled form $f(Q,\mathcal{L}_m)= -Q/2 + \alpha Q^{\mu}\mathcal{L}_m + \beta$, the authors derive the modified Friedmann equations and an effective EoS parameter that governs dark energy behavior. Both models yield a quintessence-like EoS that asymptotically approaches $-1$, with current values around $\omega_0\approx -0.8$ to $-0.9$, and exhibit a transition from early deceleration to late-time acceleration, consistent with observations. Energy conditions show NEC and DEC holding while SEC is violated during acceleration, reinforcing the physical viability of these models. The results demonstrate that $f(Q,\mathcal{L}_m)$ gravity with hyperbolic evolution can reproduce key features of $\Lambda$CDM at late times while providing a geometric mechanism for cosmic acceleration.

Abstract

This paper highlights cosmologically viable sine and cosine hyperbolic evolution functions in the framework of $f(Q,\mathcal{L}_m)$ gravity. The models have been tested to check the behavior of the equation of state (EoS) parameter under the variation of parametric values. The EoS parameter experiences a quintessence phase, and is approaching to $-1$ at late time. The models are showing inclined behaviour with the $Λ$CDM model at the late time. The viability of both the models is retested using the widely accepted energy conditions in both cases. The violation of the strong energy condition admits the accelerating behaviour of the models. The same has been explained through the analysis of the profile of deceleration parameter, which concretely supports the evidence that the models explain early deceleration to late time acceleration phenomena.

Figures (7)

• Figure 1: Evolution of deceleration parameter as functions of redshift $z$ for $\gamma=0.18$.
• Figure 2: Evolution of energy density as functions of redshift $z$ for $\alpha=0.18, \mu=1.3, \beta=0.5, \gamma=0.18$.
• Figure 3: Evolution of the EoS parameter with respect to redshift $z$ for the parametric values mentioned in the caption of Fig. \ref{['fig:energy-density:m1']}.
• Figure 4: Evolution of deceleration parameter as functions of redshift $z$ for $\eta=-2.5$.
• Figure 5: Evolution of energy density as functions of redshift $z$ for $\alpha=0.18, \mu=-0.3, \beta=0.5$, $n=1.1$, $\eta=-2.5$.