Tracking $f(R)$ cosmology

Abstract

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

2 figures. To appear in Phys. Rev. D

References in corpus (8)

• Disappearing cosmological constant in f(R) gravity
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Conditions for the cosmological viability of f(R) dark energy models
• Are f(R) dark energy models cosmologically viable ?
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Matter instability in modified gravity
• Power-laws f(R) theories are cosmologically unacceptable
• Tracking quintessence and k-essence in a general cosmological background

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