Correspondence between n - and m -dimensional inflationary cosmologies
Correspondence between n - and m -dimensional inflationary cosmologies
复制标题
n 维和 m 维暴胀宇宙论之间的对应关系
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
S. Campo
中科院分区：
文献类型：
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作者：
Alberto García;A. Garcia;M. Cataldo;S. Campo
它表明，从任何n维Friedmann-Robertson-步行者（FRW）宇宙学确定的一个单一的标量场最低限度地耦合到重力，可以构建其m维对应，在一个共同的时间坐标和结构不变的比例因子的假设下，为两个时空，通过一个简单的代数对应关系的引力常数和标量场的结构功能。如果所考虑的宇宙学补充了一个完美的流体，拟合一个广泛的状态方程的形式$p+ensuremath{
ho}=ensuremath{gamma}f（ensuremath{
ho}），$则任何n维FRW宇宙学，耦合到一个完美流体和一个标量场，拥有一个m维对应物，反之亦然。特别地，这些断言适用于单标量场暴胀模型。证明了这方面的一个定理。各种家庭的解决方案明确给出，并展示其对应的3+1宇宙时空。
It is shown that, from any n-dimensional Friedmann-Robertson-Walker (FRW) cosmology determined for a single scalar field minimally coupled to gravity, one can construct its m-dimensional counterpart, under the assumption of a common time coordinate and a structurally invariant scale factor for both spacetimes, by means of a simple algebraic correspondence relating gravitational constants and scalar field structural functions. If the considered cosmologies are supplemented with a perfect fluid, fitting a wide class of state equations of the form $p+ensuremath{
ho}=ensuremath{gamma}f(ensuremath{
ho}),$ then any n-dimensional FRW cosmology, coupled to a perfect fluid and a scalar field, possesses an m-dimensional counterpart, and vice versa. In particular, these assertions hold for single scalar field inflation models. A theorem on this respect is demonstrated. Various families of solutions are explicitly given and exhibit their correspondence with 3+1 cosmological spacetimes.