Chern-Simons引力中的加速FRW解
Accelerated FRW Solutions in Chern-Simons Gravity
摘要：
我们考虑一个五维Einstein-Chern-Simons作用量，它由一个引力扇区和一个物质扇区组成，其中引力扇区由Chern-Simons引力作用量而不是Einstein-Hilbert作用量给出，物质扇区由所谓的理想流体给出.结果表明：（i）Einstein-Chern-Simons（EChS）场方程在适当的条件下可以写成与Einstein-Maxwell场方程类似的形式;（ii）当理论参数$α$大于零时，EChS场方程的解描述了宇宙的三种可能的宇宙学模型，即球形膨胀、平坦膨胀和双曲膨胀.这一结果使我们能够推测，这些解与暗能量时代是相容的，并且场$h^{a}$（来自陈-西蒙斯引力作用量的玻色子规范场）的能量-动量张量对应于正的宇宙学常数的形式。它还表明，EChS场方程的解决方案兼容的时代的物质：（i）在一个开放的宇宙的情况下，解决方案对应于一个加速膨胀（$α>0$）与一个最小的标度因子在初始时间，当时间走向无穷大，标度因子的行为作为一个双曲正弦函数。(ii)在平坦宇宙的情况下，描述加速膨胀的解，其标度因子随着时间的增长表现为指数函数。\item在封闭宇宙的情况下，膨胀的宇宙只有一个解，当时间增长时，它表现为双曲余弦函数。
英文摘要：
We consider a five-dimensional Einstein-Chern-Simons action which is composed of a gravitational sector and a sector of matter, where the gravitational sector is given by a Chern-Simons gravity action instead of the Einstein-Hilbert action and where the matter sector is given by the so called perfect fluid. It is shown that (i) the Einstein-Chern-Simons (EChS) field equations subject to suitable conditions can be written in a similar way to the Einstein-Maxwell field equations; (ii) these equations have solutions that describe accelerated expansion for the three possible cosmological models of the universe, namely, spherical expansion, flat expansion and hyperbolic expansion when $α$, a parameter of theory, is greater than zero. This result allow us to conjeture that this solutions are compatible with the era of Dark Energy and that the energy-momentum tensor for the field $h^{a}$, a bosonic gauge field from the Chern-Simons gravity action, corresponds to a form of positive cosmological constant. It is also shown that the EChS field equations have solutions compatible with the era of matter: (i) In the case of an open universe, the solutions correspond to an accelerated expansion ($α>0$) with a minimum scale factor at initial time that, when the time goes to infinity, the scale factor behaves as a hyperbolic sine function. (ii) In the case of a flat universe, the solutions describing an accelerated expansion whose scale factor behaves as a exponencial function when time grows. \item In the case of a closed universe it is found only one solution for a universe in expansion, which behaves as a hyperbolic cosine function when time grows.
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