Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tracking $f(R)$ cosmology   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.

16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph