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arXiv 0911.2297gr-qc
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标量场宇宙中的加速宇宙膨胀

Accelerated cosmic expansion in a scalar-field universe

Swastik Bhattacharya, Pankaj S. Joshi, Ken-ichi Nakao

摘要:

我们在这里考虑一个球对称但不均匀的宇宙充满了一个无质量的标量场。该模型服从两个约束。第一个是标量场的梯度处处类时。第二个约束是径向坐标基矢量是共动坐标系中的单位矢量场。我们发现,由此产生的动力学解决方案组成一个单参数家庭的自相似模型,这是众所周知的罗伯茨解决方案。解决方案分为三类。第一类是在同步同动图中只有一个类空奇点的解。第二类由两个奇点分别为零和类空的解决方案。第三类由具有两个类空奇点的解组成,分别对应于大爆炸和大挤压。我们看到,在第一种情况下,同动体积像暴胀时期一样呈指数膨胀;流体元素从对称中心向外加速,即使满足强能量条件。这种行为与在均匀和各向同性的宇宙中观察到的行为非常不同,在均匀和各向同性的宇宙中,如果满足强能量条件,流体元素将减速向外移动。因此,我们能够实现宇宙的加速膨胀的模型考虑在这里,而不需要违反能量条件。模型的宇宙学特征进行了详细的研究。

英文摘要:

We consider here a spherically symmetric but inhomogeneous universe filled with a massless scalar field. The model obeys two constraints. The first one is that the gradient of the scalar field is timelike everywhere. The second constraint is that the radial coordinate basis vector is a unit vector field in the comoving coordinate system. We find that the resultant dynamical solutions compose a one-parameter family of self-similar models which is known as the Roberts solution. The solutions are divided into three classes. The first class consists of solutions with only one spacelike singularity in the synchronous-comoving chart. The second class consists of solutions with two singularities which are null and spacelike, respectively. The third class consists of solutions with two spacelike singularities which correspond to the big bang and big crunch, respectively. We see that, in the first case, a comoving volume exponentially expands as in an inflationary period; the fluid elements are accelerated outwards form the symmetry center, even though the strong energy condition is satisfied. This behavior is very different from that observed in the homogeneous and isotropic universe in which the fluid elements would move outwards with deceleration, if the strong energy conditions are satisfied. We are thus able to achieve the accelerated expansion of the universe for the models considered here, without a need to violate the energy conditions. The cosmological features of the models are examined in some detail.

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