标题： 跟踪$f(R)$宇宙学 显示英文标题

标题： Tracking $f(R)$ cosmology

摘要： 度规$f(R)$引力理论在共形变换下等价于物质与暗能量耦合的第五元素模型。 我们在爱因斯坦框架中推导了度规$f(R)$引力理论稳定跟踪解的条件。 我们发现当$-0.361<\omega_{\varphi}<1$存在跟踪解，如果$0<\Gamma<0.217$和$\frac{d}{dt} \ln f'(\tilde{R})>0$，其中$\Gamma=\frac{V_{\varphi\varphi}V}{V_{\varphi}^{2}}$是无量纲函数，$\omega_{\varphi}$是标量场的状态方程参数，$\tilde{R}$指的是 Jordan 框架的曲率标量。此外，我们还表明存在$f(\tilde{R})$引力模型，在 Einstein 框架中具有跟踪行为，因此时空曲率随时间减少，而它们在 Jordan 框架中的解则表现出时空曲率随时间增加。 显示英文摘要

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 $-0.361<\omega_{\varphi}<1$ exist if $0<\Gamma<0.217$ and $\frac{d}{dt} \ln f'(\tilde{R})>0$, where $\Gamma=\frac{V_{\varphi\varphi}V}{V_{\varphi}^{2}}$ is dimensionless function, $\omega_{\varphi}$ 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.