arXiv 1003.55002010-03hep-thgr-qc

低能Kaluza-Klein双膜世界宇宙学

Kaluza-Klein two-brane-worlds cosmology at low energy

S. Feranie, Arianto, Freddy P. Zen

备注：: 11 pages, minor typos corrected, published version
发表信息：: Phys.Rev.D81:084058,2010
DOI：: 10.1103/PhysRevD.81.084058

摘要：

我们研究了嵌入在$(5+n)$维时空中的两个$(4+n)$维膜。利用梯度展开近似，我们发现有效理论是由具有特定耦合函数的$(4+n)$维标量张量引力描述的。基于这一理论，我们研究了低能的卡鲁扎-克莱因双膜世界宇宙学，包括静态和非静态的内部维度。在静态内维数情况下，导出的Friedmann方程中的有效引力常量依赖于膜物质的状态方程，暗辐射项自然出现。在非静态的情况下，我们采用$b(t)=a^γ(t)$形式的外部和内部尺度因子之间的关系，其中膜世界以两个尺度因子演化。在这种情况下，在膜上导出的Friedmann方程在有效引力常量和与$a^{-4β}$成比例的项上进行了修正。对于暗辐射，我们发现$γ=-2/(1+n)$。最后，我们讨论的问题，自然产生的标量张量理论的共形框架。我们发现，在约旦框架中的静态内部尺寸可能成为非静态的爱因斯坦框架。

英文摘要：

We study two $(4+n)$-dimensional branes embedded in $(5+n)$-dimensional spacetime. Using the gradient expansion approximation, we find that the effective theory is described by $(4+n)$-dimensional scalar-tensor gravity with a specific coupling function. Based on this theory we investigate the Kaluza-Klein two-brane-worlds cosmology at low energy, in both the static and the nonstatic internal dimensions. In the case of the static internal dimensions, the effective gravitational constant in the induced Friedmann equation depends on the equations of state of the brane matter, and the dark radiation term naturally appears. In the nonstatic case we take a relation between the external and internal scale factors of the form $b(t)=a^γ(t)$ in which the brane world evolves with two scale factors. In this case, the induced Friedmann equation on the brane is modified in the effective gravitational constant and the term proportional to $a^{-4β}$. For dark radiation, we find $γ=-2/(1+n)$. Finally, we discuss the issue of conformal frames which naturally arises with scalar-tensor theories. We find that the static internal dimensions in the Jordan frame may become nonstatic in the Einstein frame.

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