论文标题
谎言对称性的新通货膨胀精确解决方案
New inflationary exact solution from Lie symmetries
论文作者
论文摘要
对于Adflaton场，我们通过使用Lie对称分析来确定一种新的精确解决方案。具体而言，我们通过假设密度扰动的频谱索引$ n_ {s} $和标量与张量比$ r $与$ n_ {s} -1 = h \ left（r \ right）$相关。函数$ h \ left（r \ right）$是根据主方程的接收谎言对称的分类。可能接收的谎言对称形式$ a_ {2} $，$ a_ {3,2} $，$ a_ {3,3} $和$ sl \ left（3，r \ right）$ lie代数。 $ a_ {3,3} $代数的谎言对称性回收了新的通货膨胀解决方案。标量场电位明确得出，而我们将所得光谱指数与观测值进行比较。
For the inflaton field we determine a new exact solution by using the Lie symmetry analysis. Specifically, we construct a second-order differential master equation for arbitrary scalar field potential by assuming that the spectral index for the density perturbations $n_{s}$ and the scalar to tensor ratio $r$ are related as $n_{s}-1=h\left( r\right) $. Function $h\left( r\right) $ is classified according to the admitted Lie symmetries for the master equation. The possible admitted Lie symmetries form the $A_{2}$, $A_{3,2}$, $A_{3,3}$ and $sl\left( 3,R\right) $ Lie algebras. The new inflationary solution is recovered by the Lie symmetries of the $A_{3,3}$ algebra. Scalar field potential is derived explicitly, while we compare the resulting spectral indices with the observations.
