The dark energy equation of state, , is directly related to the one used in SN Ia
observations. From Eqs. (4.92
) and (4.93
) it is given by
There are some works that try to reconstruct the forms of f (R) by using some desired form for the
evolution of the scale factor or the observational data of SN Ia [117, 130, 442, 191, 621, 252]. We
need to caution that the procedure of reconstruction does not in general guarantee the stability of
solutions. In scalar-tensor dark energy models, for example, it is known that a singular behavior
sometimes arises at low-redshifts in such a procedure [234, 271
]. In addition to the fact that the
reconstruction method does not uniquely determine the forms of f (R), the observational data of the
background expansion history alone is not yet sufficient to reconstruct f (R) models in high
precision.
Finally we mention a number of works [115, 118, 119, 265
, 319, 515, 542, 90] about the
use of metric f (R) gravity as dark matter instead of dark energy. In most of past works the
power-law f (R) model
has been used to obtain spherically symmetric solutions for
galaxy clustering. In [118] it was shown that the theoretical rotation curves of spiral galaxies
show good agreement with observational data for
, while for broader samples the
best-fit value of the power was found to be
[265]. However, these values are not
compatible with the bound
derived in [62
, 160
] from a number of other
observational constraints. Hence, it is unlikely that f (R) gravity works as the main source for dark
matter.
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