Abstract
The current accelerating expansion of the Universe is explained either by dark energy or by modified gravity theories. Both of them can explain exactly the same background evolution of the Universe, however this degeneracy may be broken when the observation of large scale structure formation is taken into account. Two observables are parameterized by the so-called dark energy equation of state, ω and the growth index parameter, γ. From these observed parameters, one may reconstruct the model parameters of the so-called scalar-tensor gravity theory, one of the modified gravity theories. Especially, the scalar-tensor gravity theory is described both in Jordan frame and in Einstein frame. If cosmological observations are interpreted in one frame, then all of the observables should also be interpreted in that frame. This explicitly shows conformal inequality of cosmological observables.
Highlights
Cosmological observations support the current Universe in the phase of accelerating expansion
We shall deal with one of the simplest but long-standing modified gravity theories (MG), the so-called scalar-tensor gravity (STG) which is natural in the viewpoint of string theory
Comparison to the observable quantities determines these two theoretically introduced functions which are reconstructed in terms of the dark energy (DE) equation of state (EOS), ! [1, 2] and the growth index parameter (GIP), γ [3]
Summary
Cosmological observations support the current Universe in the phase of accelerating expansion. The other is to invoke modified gravity theories (MG) and tries to replace the DE with the modifications of the Friedmann equations as an ejective dark energy. We explicitly show that some cosmological observables are frame-dependent and if one obtains model parameters in one frame, one should interpret all the other observables in that frame. For this purpose, we express two functions of STG in both the JF and the EF in terms of frame-independent observable parameters, the redshift z . We show explicitly that one should keep using the only one frame for probing cosmological observables
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