论文标题
F（g）Noether宇宙学
f(G) Noether cosmology
论文作者
论文摘要
我们开发了$ f（\ Mathcal {g}）$重力的$ n $二维宇宙学，其中$ \ Mathcal {g} $是\ emph {gauss-bonnet}拓扑不变。具体来说，通过所谓的Noether对称方法，我们选择$ f（\ Mathcal {g}）\ simeq \ Mathcal {g}^k $ powerlaw模型，其中$ k $是一个真实的数字。特别是，$ k = 1/2 $ for $ n = 4 $结果等于一般相对论，这表明我们不需要强加行动$ r+f（\ mathcal {g}）$重现爱因斯坦理论。作为进一步的结果，在$ f（\ mathcal {g}）$无限制地耦合到标量字段的情况下，将恢复DE Sitter Solutions。这意味着在此框架中可以解决通货膨胀和黑暗能源之类的问题。最后，我们为相关的迷你uperspace开发了哈密顿的形式主义，并讨论了该模型的量子宇宙学。
We develop the $n$-dimensional cosmology for $f(\mathcal{G})$ gravity, where $\mathcal{G}$ is the \emph{Gauss-Bonnet} topological invariant. Specifically, by the so-called Noether Symmetry Approach, we select $f(\mathcal{G})\simeq \mathcal{G}^k$ power-law models where $k$ is a real number. In particular, the case $k = 1/2$ for $n=4$ results equivalent to General Relativity showing that we do not need to impose the action $R+f(\mathcal{G})$ to reproduce the Einstein theory. As a further result, de Sitter solutions are recovered in the case where $f(\mathcal{G})$ is non-minimally coupled to a scalar field. This means that issues like inflation and dark energy can be addressed in this framework. Finally, we develop the Hamiltonian formalism for the related minisuperspace and discuss the quantum cosmology for this model.
