Matrix model approach to cosmology
Matrix model approach to cosmology
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DOI：
10.1103/physrevd.93.064074
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发表时间：
2016-03-29
影响因子：
5
通讯作者：
Stern, A.
中科院分区：
文献类型：
--
作者：
Chaney, A.;Lu, Lei;Stern, A.
我们对玩具矩阵模型的旋转不变宇宙学解进行了系统的搜索。这些模型对应于d<10维的Lorentzian Ishibashi，Kawai，Kitazawa和Tsuhiya(IKKT)型矩阵模型的玻色子扇形，具体地说，d=3和d=5。取一个连续的(或可交换的)极限后，它们得到d-1维泊松流形。流形有一个洛伦兹诱导度规，它可以与封闭的、开放的或静态的时空相关联。对于d=3，我们得到了递归关系，由此可以产生旋转不变的矩阵解，从而产生连续统极限中的开放宇宙。还发现了与连续统极限中的闭合和静态的二维时空有关的矩阵解的具体例子。这些解决方案至少在玩具矩阵模型的范围内提供了宇宙学奇点的解决方案。交换极限揭示了其他理想的特征，例如描述了从最初的通货膨胀到非通货膨胀时代的平稳过渡的解。许多d=3解具有更高维度的类似物。尤其是d=5的情况，有可能在连续体极限中产生现实的四维宇宙。当矩阵作用中包含一个完全反对称项时，我们得到了四维De Sitter DS(4)或反De Sitter ADS(4)解。在这些流形上附加了一个非平凡的泊松结构，它代表了非对易的最低阶效应。对于ADS(4)的情形，我们发现了一个特殊的极限，其中最低阶非对易性在边界处消失，但在内部不消失。
We perform a systematic search for rotationally invariant cosmological solutions to toy matrix models. These models correspond to the bosonic sector of Lorentzian Ishibashi, Kawai, Kitazawa and Tsuchiya (IKKT)-type matrix models in dimensions d less than ten, specifically d = 3 and d = 5. After taking a continuum (or commutative) limit they yield d - 1 dimensional Poisson manifolds. The manifolds have a Lorentzian induced metric which can be associated with closed, open, or static space-times. For d = 3, we obtain recursion relations from which it is possible to generate rotationally invariant matrix solutions which yield open universes in the continuum limit. Specific examples of matrix solutions have also been found which are associated with closed and static two-dimensional space-times in the continuum limit. The solutions provide for a resolution of cosmological singularities, at least within the context of the toy matrix models. The commutative limit reveals other desirable features, such as a solution describing a smooth transition from an initial inflation to a noninflationary era. Many of the d = 3 solutions have analogues in higher dimensions. The case of d = 5, in particular, has the potential for yielding realistic four-dimensional cosmologies in the continuum limit. We find four-dimensional de Sitter dS(4) or anti-de Sitter AdS(4) solutions when a totally antisymmetric term is included in the matrix action. A nontrivial Poisson structure is attached to these manifolds which represents the lowest order effect of noncommutativity. For the case of AdS(4), we find one particular limit where the lowest order noncommutativity vanishes at the boundary, but not in the interior.