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arXiv 1202.4807gr-qcastro-ph.COhep-th
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Born-Infeld类修正引力

Born - Infeld-like modified gravity

S. I. Kruglov

备注：
RevTex, 5 pages, one figure, minor corrections, references added, journal version, accepted in IJTP
发表信息：
Int. J. Theor. Physics (52) 2477-2484 (2013)
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摘要：

本文提出并分析了一个用函数$F(R) = (1-\sqrt{1-2λR})/λ$表示的修正引力理论。当引入的参数$λ$很小时，作用量转化为Einstein $-$ Hilbert作用量.该理论是一致的，局部测试给出了一个约束的参数$λ\leq 2\times 10^{-6}$ cm $^2$的值。我们考虑了得到标量场势的约当标架和爱因斯坦标架。得到了该模型的静态Schwarzschild $-$ de Sitter解，并进行了分析.证明了de Sitter空间是不稳定的，而Ricci标量为零的解是稳定的。结果表明，该模型不存在物质不稳定性.

英文摘要：

A modified theory of gravity with the function $F(R) = (1-\sqrt{1-2λR})/λ$ is suggested and analyzed. At small value of the parameter $λ$ introduced the action is converted into Einstein$-$Hilbert action. The theory is consistent with local tests which gives a bound on the value of the parameter $λ\leq 2\times 10^{-6}$ cm$^2$. I have considered the Jordan frame as well as the Einstein frame in which the potential of the scalar field was obtained. The static Schwarzschild$-$de Sitter solutions of the model are obtained and analyzed. It was demonstrated that the de Sitter space is unstable but a solution with zero Ricci scalar is stable. It is shown that there is no matter instability in the proposed model.

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