Tracking $f(R)$ cosmology

Details Tracking $f(R)$ cosmology Tracking $f(R)$ cosmology

2009-05-03

arxiv.org/abs/0905.0247v1

Phys.Rev.D79:103510,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

2 figures. To appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.79.103510

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.

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