追踪$f(R)$宇宙学
Tracking $f(R)$ cosmology
摘要：
度规$f(R)$引力理论在共形上等价于物质与暗能量耦合的精粹模型。在Einstein坐标系下，我们导出了度量$f(R)$引力稳定跟踪解的条件.当$0<Γ<0.217$和$\frac{d}{dt} \ln f'(\tilde{R})>0$满足时，我们发现$-0.361<ω_φ<1$跟踪器解存在，其中$Γ=\frac{V_{φφ}V}{V_φ^{2}}$是无量纲函数，$ω_φ$是标量场的状态方程参数，$\tilde{R}$是Jordan标架的曲率标量.我们还证明了存在$f(\tilde{R})$引力模型，它们在Einstein坐标系下具有跟踪行为，时空曲率随时间减小，而在Jordan坐标系下则导致时空曲率随时间增大.
英文摘要：
Metric $f(R)$ gravity theories are conformally equivalent to models of quintessence in which matter is coupled to dark energy. We derive a condition for stable tracker solution for metric $f(R)$ gravity in the Einstein frame. We find that tracker solutions with $-0.361<ω_φ<1$ exist if $0<Γ<0.217$ and $\frac{d}{dt} \ln f'(\tilde{R})>0$, where $Γ=\frac{V_{φφ}V}{V_φ^{2}}$ is dimensionless function, $ω_φ$ is the equation of state parameter of the scalar field and $\tilde{R}$ refers to Jordan frame's curvature scalar. Also, we show that there exists $f(\tilde{R})$ gravity models which have tracking behavior in the Einstein frame and so the curvature of space time is decreasing with time while they lead to the solutions in the Jordan frame that the curvature of space time can be increasing with time.
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