论文标题
新的非局部重力模型的一些宇宙学解决方案
Some Cosmological Solutions of a New Nonlocal Gravity Model
论文作者
论文摘要
在本文中，我们调查了对一般相对性（GR）的非局部修改，并使用动作$ s = \ frac {1} {16πg} \ int [r-2λ+（r-4λ）\，\ Mathcal {f} {f} {f}（\ box）\，（\ box） d^4x，$ whene $ \ nathcal {f}（\ box）= \ sum_ {n = 1}^{+\ infty} f_n \ box^n $是d'Alembertian $ \ box $的分析函数。我们发现了相应运动方程的一些精确宇宙学解。有两种解决方案仅在$λ\ neq 0，\，k = 0，$中有效，并且它们没有像宇宙常数$λ$的einsten重力中的类似物。这两个解决方案中的一种是$ a（t）= a \，\ sqrt {t} \，e^{\fracλ{4} t^2}，$，$模拟了类似于辐射和暗能之间的干扰。另一个解决方案是非弹跳1 -$ a（t）= a \，e^{λt^2} $。对于这两种解决方案，讨论了一些宇宙学方面。我们还找到了非本地运算符$ \ MATHCAL {F}（\ box）$的明确形式，该形式满足了必要的条件。
In this paper, we investigate a nonlocal modification of general relativity (GR) with action $S = \frac{1}{16πG} \int [ R- 2Λ+ (R-4Λ) \, \mathcal{F}(\Box) \, (R-4Λ) ] \, \sqrt{-g}\; d^4x ,$ where $\mathcal{F} (\Box) = \sum_{n=1}^{+\infty} f_n \Box^n$ is an analytic function of the d'Alembertian $\Box$. We found a few exact cosmological solutions of the corresponding equations of motion. There are two solutions which are valid only if $Λ\neq 0, \, k = 0,$ and they have not analogs in Einsten's gravity with cosmological constant $Λ$. One of these two solutions is $ a (t) = A \, \sqrt{t} \, e^{\fracΛ{4} t^2} ,$ that mimics properties similar to an interference between the radiation and the dark energy. Another solution is a nonsingular bounce one -- $ a (t) = A \, e^{Λt^2}$. For these two solutions, some cosmological aspects are discussed. We also found explicit form of the nonlocal operator $\mathcal{F}(\Box)$, which satisfies obtained necessary conditions.
