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arXiv 2008.09186gr-qchep-th
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嵌入宇宙学和引力

Embedding Cosmology and Gravity

Abhishek Goswami

摘要:

我从一个场景开始,宇宙是一个具有$d$维度的抽象空间$\mathcal{M}$。嵌入是一个二维曲面到$\mathcal{M}$的映射,该映射具有西格玛模型描述的场论。我把$\mathcal{M}$的$d$方向作为嵌入的拉格朗日量的对称群SU(n)的生成元。这意味着嵌入有n种口味。然后在理论中引入了自发对称性破缺,并定义了对称性破缺发生的方向为时间。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膨胀的关系。然后构造了一个以嵌入为暴胀子的暴胀情景,并讨论了它与Starobinsky $R^{2}$模型的联系。最后讨论了暴胀对时空非对易性的影响。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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