论文标题
使用新颖的几何形状重新定义标量探测字段理论为标量范围场理论
Reformulating Scalar-Tensor Field Theories as Scalar-Scalar Field Theories Using a Novel Geometry
论文作者
论文摘要
在本文中，我将展示Finsler几何形状的概念如何使用标量字段F上的标量字段构建类似的几何形状。我指的是基于洛伦兹结构作为标量尺度场理论的歧管的田间理论。当选择F时，我们将研究这种野外理论，以使M上的指标具有Friedmann-Lemaitre-Robertson-Walker指标的形式，而Lagrangian具有特别简单的形式。可以表明，由该拉格朗日确定的标量量表理论可以产生自动化的宇宙，可以将其拼凑在一起以形成多个非Hausdorff拓扑，其中全局时间函数在t = 0时多触发。这些多个宇宙中的某些宇宙开始爆炸性，然后安顿下来到一个更安静的加速膨胀时期，随后可以崩溃到其原始的前扩张状态。我以讨论如何将概率分配到多元宇宙的各个宇宙的讨论结束。这是通过使用宇宙的动作来实现的，而宇宙的作用更接近零，比具有较大积极价值的宇宙更有可能的行动。为了确保与我们自己的宇宙类似的宇宙模型可能存在，我发现有必要在M上引入第二个标量字段，并修改原始的Lagrangian。最后，我的理论有三个标量字段，在歧管M上有两个。
In this paper I shall show how the notions of Finsler geometry can be used to construct a similar geometry using a scalar field, f, on the cotangent bundle of a differentiable manifold M. This will enable me to use the second vertical derivatives of f, along with the differential of a scalar field phi on M, to construct a Lorentzian metric on M that depends upon phi. I refer to a field theory based upon a manifold with such a Lorentzian structure as a scalar-scalar field theory. We shall study such a field theory when f is chosen so that the resultant metric on M has the form of a Friedmann-Lemaitre-Robertson-Walker metric, and the Lagrangian has a particularly simple form. It will be shown that the scalar-scalar theory determined by this Lagrangian can generate self-inflating universes, which can be pieced together to form multiverses with non-Hausdorff topologies, in which the global time function multifurcates at t=0. Some of the universes in these multiverses begin explosively, and then settle down to a period of much quieter accelerated expansion, which can be followed by a collapse to its original pre-expansion state. I conclude the paper with a discussion of how probabilities can be assigned to the various universes of a multiverse. This is accomplished by using the action of the universes, with universes having action closer to zero being more likely than universes with large positive values for their action. In order to assure that universe models similar to our own universe are likely to exist I found it necessary to introduce a second scalar field on M, and to modify the original Lagrangian. In the end my theory has three scalar fields, two on the manifold M and one on the cotangent bundle of M.
