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arXiv 0907.3027gr-qc
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标度变换、修正引力和Brans-Dicke理论

Scale transformation, modified gravity, and Brans-Dicke theory

F. Darabi

备注：
14 pages, accepted for publication in IJTP
发表信息：
Int.J.Theor.Phys.49:2113-2120,2010
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摘要：

研究了尺度变换下的Einstein-Hilbert作用量模型。通过引入介子场作为尺度变换的手段，得到了一个新的作用量，其爱因斯坦场方程与无痕物质相一致，具有非零的修正项以及动力学的宇宙学和引力耦合项。得到的修正Einstein方程既不是$f(R)$度规形式的方程，也不是$f({\cal R})$ Palatini形式的方程，而修正的源项{ \it形式}等价于Palatini形式的$f({\cal R})=\frac{1}{2}{\cal R}^2$引力源项.给出了本模型、修正的引力理论和带有$ω=-\frac{3}{2}$的Brans-Dicke理论之间的对应关系，只要介子场被压缩到真空态。

英文摘要：

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 $ω=-\frac{3}{2}$ is explicitly shown, provided the dilaton field is condensated to its vacuum state.

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