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arXiv 2302.07799gr-qc
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量子分数宇宙学:K-essence 理论

Quantum fractionary cosmology: K-essence theory

J. Socorro, J. Juan Rosales

AI总结:

本文在量子 K-essence 标量场框架下,从 FLRW 模型的 Wheeler-DeWitt 方程中自然导出分数阶微分方程,并依据正压参数给出阶数区间及相应量子解。

摘要:

利用一种特定形式的量子 K-essence 标量场,我们证明在量子形式体系中,对于 Friedmann-Lemaître-Robertson-Walker(FLRW)模型中的某些时期(例如辐射时期和类暴胀时期),标量场变量中会自然出现一个分数阶微分方程。在经典分析中,标量场的动能可以证伪标准物质,其意义在于:通过使用哈密顿形式体系,我们在宇宙的所有情景中都得到了标度因子的时间行为,这些结果与在含标准物质的爱因斯坦场方程中通过代数程序得到的结果类似。在标量场 $ϕ$ 的量子 Wheeler-DeWitt(WDW)方程情形下,得到了一个阶数为 $β=\frac{2α}{2α-1}$ 的分数阶微分方程。该分数阶方程属于不同的区间,具体取决于正压参数的值;也就是说,当 $ ω_X \in [0,1]$ 时,阶数属于区间 $1\leq β\leq 2$,而当 $ ω_X \in [-1,0)$ 时,阶数属于区间 $0< β\leq 1$。文中还给出了相应的量子解。

英文摘要:

Using a particular form of the quantum K-essence scalar field, we show that in the quantum formalism, a fractional differential equation in the scalar field variable, for some epochs in the Friedmann-Lemaître-Robertson-Walker (FLRW) model (radiation and inflation-like epochs, for example), appears naturally. In the classical analysis, the kinetic energy of scalar fields can falsify the standard matter in the sense that we obtain the time behavior for the scale factor in all scenarios of our Universe by using the Hamiltonian formalism, where the results are analogous to those obtained by an algebraic procedure in the Einstein field equations with standard matter. In the case of the quantum Wheeler-DeWitt (WDW) equation for the scalar field $ϕ$, a fractional differential equation of order $β=\frac{2α}{2α-1}$ is obtained. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; that is to say, when $ ω_X \in [0,1]$, the order belongs to the interval $1\leq β\leq 2$, and when $ ω_X \in [-1,0)$, the order belongs to the interval $0< β\leq 1$. The corresponding quantum solutions are also given.

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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