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arXiv 1901.04640gr-qc
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辐射耦合的Hoenava-Lifshitz模型的量子宇宙学

Quantum cosmology of a Hořava-Lifshitz model coupled to radiation

G. Oliveira-Neto, L. G. Martins, G. A. Monerat, E. V. Corrêa Silva

备注：
33 pages and 15 figures. Few modifications in the text and new references added. Submitted to IJMPD
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摘要：

本文正则地刻划了一个均匀各向同性的具有常正空间截面的耦合辐射的Hoenava-Lifshitz宇宙学模型。我们考虑没有细致平衡条件的引力理论的可投射版本。我们使用ADM形式来写模型的引力哈密顿量，使用Schutz变分形式来写理想流体哈密顿量。我们发现惠勒-德威特方程的模型，这取决于几个参数。我们研究的情况下，参数值的选择，使惠勒-德威特方程的解决方案是有界的。最初，我们使用{ \it Many Worlds}解释来解决它。利用Wheeler-DeWitt方程解计算的波包，得到标量因子期望值$\left<a\right>$。我们表明，这个数量之间振荡有限的最大值和最小值，永远不会消失。这样的结果表明，该模型是免费的奇异性，在量子水平。我们通过从期望值$\left<a\right>$中减去一个标准差单位来加强这一指示，后者仍然是正的。然后，我们使用{ \it DeBroglie-Bohm}解释。最初，我们计算玻姆的轨迹的比例因子，并表明，他们永远不会消失。然后，我们表明，每个轨迹符合相应的$\left<a\right>$。最后，我们计算量子势，这有助于理解为什么标度因子永远不会消失。

英文摘要：

In the present paper, we canonically quantize an homogeneous and isotropic Hořava-Lifshitz cosmological model, with constant positive spatial sections and coupled to radiation. We consider the projectable version of that gravitational theory without the detailed balance condition. We use the ADM formalism to write the gravitational Hamiltonian of the model and the Schutz variational formalism to write the perfect fluid Hamiltonian. We find the Wheeler-DeWitt equation for the model, which depends on several parameters. We study the case in which parameter values are chosen so that the solutions to the Wheeler-DeWitt equation are bounded. Initially, we solve it using the {\it Many Worlds} interpretation. Using wavepackets computed with the solutions to the Wheeler-DeWitt equation, we obtain the scalar factor expected value $\left<a\right>$. We show that this quantity oscillates between finite maximum and minimum values and never vanishes. Such result indicates that the model is free from singularities, at the quantum level. We reinforce this indication by showing that by subtracting one standard deviation unit from the expected value $\left<a\right>$, the latter remains positive. Then, we use the {\it DeBroglie-Bohm} interpretation. Initially, we compute the Bohm's trajectories for the scale factor and show that they never vanish. Then, we show that each trajectory agrees with the corresponding $\left<a\right>$. Finally, we compute the quantum potential, which helps understanding why the scale factor never vanishes.

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