AI 中文总结
该研究在圈量子宇宙学中分析暴胀子质量对原初功率谱的影响，用三种方法计算功率谱，所得结果与观测数据吻合，为早期宇宙动力学提供了新的唯象约束。
AI 中文摘要
将质量参数作为自由唯象参数，我们研究了圈量子宇宙学（LQC）中由正则标量场驱动、不同势函数下的暴胀。我们发现，对于二次势，较小的质量值更容易获得足够的e折叠数；而对于Starobinsky势，较大的质量值会获得更多的e折叠数。通过估计慢滚暴胀的概率，我们发现所有考虑的情形下该概率始终非常接近1。针对反弹时动能主导的情况，我们采用三种方法计算原初功率谱：修饰度规法、混合法和替代质量函数法。两种势函数及不同质量值对应的功率谱，在三种方法中均呈现相同的定性模式：小k处被抑制、中间范围被放大且振荡、大k处近似标度不变。三种方法的主要差异在于功率谱收敛至该区域的速度，混合法收敛最快，其次是替代质量函数法和修饰度规法。我们发现 pivot 标度 $k_\star$ 对暴胀子质量高度敏感，质量仅变化百分之几，$k_\star$ 就会变化一个数量级以上。利用 $k_\star$ 处的张量功率谱，我们计算了标量谱指数 $n_s$ 和张量标量比 $r$，发现其与当前数据吻合良好。最后，将标量功率谱输入 CAMB 代码以获得角功率谱，并与Planck 2018数据及最佳拟合的ΛCDM模型进行比较。三种方法在多极矩较高时均与数据一致，而在多极矩较低时，混合法吻合度最高，修饰度规法偏差最大。
英文摘要
Considering the mass parameters as free phenomenological parameters, we investigate inflation driven by a canonical scalar field with different potentials in LQC. We find that a smaller mass value makes it easier to obtain a sufficient number of e-folds for the quadratic potential, while for the Starobinsky potential, more e-folds are obtained for larger mass values. By estimating the probability of slow-roll inflation, we find that it remains very close to unity for all considered cases. We compute the primordial power spectrum using three approaches: the dressed metric, the hybrid, and the alternative mass function approaches for the case that the kinetic energy dominated at bounce. The resulting power spectrum for both potentials and different mass values shows the same qualitative pattern in all three approaches. It is suppressed at small $k$, amplified and oscillating over an intermediate range, and nearly scale-invariant at large $k$. The approaches mainly differ in how fast the power spectrum converges to this regime, with the hybrid approach converging the fastest, followed by the alternative mass function and dressed metric approaches. We find that the pivot scale $k_\star$ is highly sensitive to the inflaton mass, changing by more than an order of magnitude for a mass variation of only a few percent. Using the tensor power spectrum at $k_\star$, we calculate the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$, finding good agreement with current data. Finally, the scalar power spectra are fed into the CAMB code to obtain the angular power spectrum and compare with the Planck 2018 data and the best-fit $Λ$CDM model. All three approaches are consistent with data at high multipoles, while at low multipoles the hybrid approach gives the closest agreement and the dressed metric approach shows the largest deviation.
Comments23 pages, 4 figures, 5 tables
