We consider the cosmologies that arise in a subclass of f ( R ) gravity with f ( R ) = R + \mu ^ { 2 n + 2 } / ( - R ) ^ { n } and n \in ( -1 , 0 ) in the metric ( as opposed to the Palatini ) variational approach to deriving the gravitational field equations .
The calculations of the isotropic and homogeneous cosmological models are undertaken in the Jordan frame and at both the background and the perturbation levels .
For the former , we also discuss the connection to the Einstein frame in which the extra degree of freedom in the theory is associated with a scalar field sharing some of the properties of a ’ chameleon ’ field .
For the latter , we derive the cosmological perturbation equations in general theories of f ( R ) gravity in covariant form and implement them numerically to calculate the cosmic-microwave-background temperature and matter-power spectra of the cosmological model .
The CMB power is shown to reduce at low l ’ s , and the matter power spectrum is almost scale-independent at small scales , thus having a similar shape to that in standard general relativity .
These are in stark contrast with what was found in the Palatini f ( R ) gravity , where the CMB power is largely amplified at low l ’ s and the matter spectrum is strongly scale-dependent at small scales .
These features make the present model more adaptable than that arising from the Palatini f ( R ) field equations , and none of the data on background evolution , CMB power spectrum , or matter power spectrum currently rule it out .