Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-07-17
Int.J.Theor.Phys.49:2113-2120,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
14 pages, accepted for publication in IJTP
Scientific paper
10.1007/s10773-010-0398-y
A model of Einstein-Hilbert action subject to the scale transformation is studied. By introducing a dilaton field as a means of scale transformation a new action is obtained whose Einstein field equations are consistent with traceless matter with non-vanishing modified terms together with dynamical cosmological and gravitational coupling terms. The obtained modified Einstein equations are neither those in $f(R)$ metric formalism nor the ones in $f({\cal R})$ Palatini formalism, whereas the modified source terms are {\it formally} equivalent to those of $f({\cal R})=\frac{1}{2}{\cal R}^2$ gravity in Palatini formalism. The correspondence between the present model, the modified gravity theory, and Brans-Dicke theory with $\omega=-\frac{3}{2}$ is explicitly shown, provided the dilaton field is condensated to its vacuum state.
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