暗能量引起的宇宙加速膨脹之非均向性

Dark Energy Induced Anisotropy in Cosmic Expansion

陳建廷(Chien-Ting Chen)

指導教授 ： 陳丕燊

國立臺灣大學/理學院/物理學研究所/博士(2019年)

https://doi.org/10.6342/NTU201903140

摘要

為瞭解宇宙晚期加速膨脹的本質，根據實驗測定暗能量是否為宇宙常數或具有動態性質是非常重要的。合理的假設暗能量若在宇宙暴脹時期已經存在，可以預期一個動態的暗能量會在宇宙晚期加速膨脹的非均向性上留下痕跡。為證明上述想法的可行性，我們引入第五元素(quintessence)為觀測上所允許最簡易的動態暗能量模型，藉以研究第五元素在暴脹時期產生的量子擾動(為暗能量擾動本身的物理性起源)效應，此量子擾動與初始曲率擾動為完全正相關，並估計在宇宙加速膨脹所引起的非均向性。我們證明第五元素的量子擾動初始振福與張量純量比r有關，並計算一階微擾的光度距離及其功率譜，可藉以測定宇宙晚期加速膨脹的非均向性。計算結果發現第五元素模型相比於宇宙常數模型，在宇宙晚期大尺度的重力位有較少的衰減，以致第五元素模型的光度距離功率譜在較低的紅移(redshift)與多極(multipole)上，比宇宙常數模型的功率譜相對更小。此結論與文獻上第五元素量子擾動對宇宙微波背景輻射溫度非均向性影響的研究結果一致。

關鍵字

暗能量 ； 第五元素 ； 量子擾動 ； 光度距離微擾 ； 光度距離功率譜

並列摘要

In order to understand the nature of the accelerating expansion of the late-time universe, it is important to experimentally determine whether dark energy is a cosmological constant or dynamical in nature. If dark energy already exists prior to inflation, which is a reasonable assumption, then one expects that a dynamical dark energy would leave some footprint in the anisotropy of the late-time accelerated expansion. To demonstrate the viability of this notion, we invoke the quintessence field with the exponential potential as one of the simplest dynamical dark energy models allowed by observations. We investigate the effects of its quantum fluctuations (the physical origin of the perturbation being isocurvature) generated during inflation and having fully positive correlation with the primordial curvature perturbations, and estimate the anisotropy of the cosmic expansion so induced. We show that the primordial amplitude of quantum fluctuations of quintessence field can be related to the tensor-to-scalar ratio r, and we calculate the perturbed luminosity distance to first order and the associated luminosity distance power spectrum, which is an estimator of anisotropicity of late-time accelerated expansion. We find that the gravitational potential at large scales and late times is less decayed in QCDM compared to that in $ Lambda $CDM so that the smaller the redshift and multipole, the more relative deficit of power in QCDM. Our results of luminosity distance power spectrum also show the similar conclusions of suppression as that of the previous investigation regarding the effect of quantum fluctuations of quintessence field on the CMB temperature anisotropies.

並列關鍵字

Dark energy ； Quintessence ； Quantum fluctuation ； Perturbed luminosity distance ； Luminosity distance power spectrum

參考文獻

[1] N. Suzuki et al. The Hubble Space Telescope Cluster Supernova Survey: V. Improving the Dark Energy Constraints Above z > 1 and Building an Early-Type-Hosted Supernova Sample. Astrophys. J., 746:85, 2012.

[2] S. Perlmutter et al. Measurements of the cosmological parameters Omega and Lambda from the first 7 supernovae at z ≥ 0.35. Astrophys. J., 483:565, 1997.

[3] S. Perlmutter et al. Discovery of a supernova explosion at half the age of the Universe and its cosmological implications. Nature, 391:51–54, 1998.

[4] S. Perlmutter et al. Measurements of Omega and Lambda from 42 high redshift supernovae. Astrophys. J., 517:565–586, 1999.

[5] Adam G. Riess et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J., 116:1009–1038, 1998.