论文标题
嵌入宇宙学和重力
Embedding Cosmology and Gravity
论文作者
论文摘要
我从一个场景开始，其中宇宙是具有$ d $ dimensions的抽象空间$ \ MATHCAL {M} $。其中有二维表面。嵌入是从嵌入式表面到$ \ MATHCAL {M} $的地图，其具有Sigma模型描述的字段理论。我将$ \ Mathcal {M} $的$ D $方向作为嵌入Lagrangian的对称组SU（N）的发电机。这意味着嵌入具有N口味。 然后，我在理论中引入了自发的对称性破裂，并定义了对称性破裂作为时间的方向。接下来，我写下修改后的爱因斯坦方程，包括嵌入。 然后，我讨论嵌入与宇宙扩展的关系。之后，我构建了一种充气式嵌入的通货膨胀方案，并讨论了与Starobinsky $ r^{2} $模型的联系。最后，我讨论了通货膨胀对时空非交通性的影响。
I start with a scenario where the universe is an abstract space $\mathcal{M}$ having $d$ dimensions. There is a two dimensional surface embedded in it. Embedding is a map from the embedded surface to $\mathcal{M}$ that has a field theory described by Sigma model. I take $d$ directions of $\mathcal{M}$ to be the generators of a symmetry group SU(n) of the Lagrangian of the embedding. This means embedding has n flavors. Then I introduce spontaneous symmetry breaking in the theory and define the direction along which the symmetry breaking occurs as time. Next I write down the modified Einstein's equation including the embedding. Then I discuss embedding's relation to the expansion of the universe. After that I construct an inflationary scenario with embedding as inflaton and discuss its connection to Starobinsky $R^{2}$ model. Finally, I discuss the effect of inflation on the non-commutativity of the spacetime.
