Preinflationary and inflationary fast-roll eras and their signatures in the low CMB multipoles
Preinflationary and inflationary fast-roll eras and their signatures in the low CMB multipoles
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通货膨胀前和通货膨胀的快速滚动时代及其在低 CMB 多极点中的特征
DOI：
10.1103/physrevd.81.063520
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发表时间：
2009
影响因子：
5
通讯作者：
N. Sanchez
中科院分区：
文献类型：
--
作者：
C. Destri;H. Vega;H. Vega;N. Sanchez
我们研究了一般初始条件下暴胀子的尺度因子和尺度因子的耦合演化。一般的早期宇宙演化有三个阶段：减速的快速滚动，然后是暴胀的快速滚动，然后是暴胀的缓慢滚动（一个吸引子总是达到一般的初始条件）。这种演化对所有规则暴胀子势都是有效的。此外，我们发现一个特殊的（极端）慢滚解决方案开始于t1/4/1，其中快速滚动阶段缺席。在某个时间t/4 t�，从t0开始的时间向后演化一般达到一个数学奇点，在那里ainteger消失，哈勃参数变得奇异。我们确定了奇点附近的一般行为。在t ≥ 10 t普朗克的情况下，经典的齐次暴胀子描述在暴胀开始之前是有效的，量子环效应在那里可以忽略不计。在经典处理的有效区域中，奇点永远不会达到，因此它在这里不是真实的物理现象。快滚和慢滚制度进行了详细分析，包括状态演化方程，解析和数值。快速滚动时代的特征时间尺度变成t1/4普朗克= m普朗克= 1/2 3 M 4 p 10 4 tPlanck，其中V是双阱暴胀子势，m是暴胀子质量，M是暴胀的能量尺度。计算了波动沿着减速和暴胀的快卷和慢卷时代的整个演化。Bunch-Davies的初始条件推广到目前的情况下，感受到的波动的潜力永远不能忽略。涨落在t1/4 t奇点附近感受到一个奇异的吸引势（就像一个粒子在中心奇异势中的情况一样），这个吸引势正好具有允许落向中心的临界强度（1/4 =4）。准确地说，波动表现出对数行为，描述了下降到t1/4 t3的过程。通过初始条件的传递函数D_（？）k_（？），在有限时间内，快速滚动时代的影响和Bunch-Davies初始条件的选择对功率谱进行了动态修改。功率谱在k1/4 0处消失：Dk 1/2在k2 = k 0时出现第一个峰值（k 0是共形初始时间），然后随着振幅的减小而振荡，并在k1/4时渐近消失！1 .传递函数Dwk影响低宇宙微波背景多极子C '：对于1 π“π 5，变化C'= C'被计算为波动开始时刻t0的函数。宇宙微波背景四极矩观测表明，大的supplies，这是很好地再现的范围t0 � t� *
We study the entire coupled evolution of the inflaton � ðtÞ and the scale factor aðtÞ for general initial conditions � ðt0Þ and d� ðt0Þ=dt at a given initial time t0. The generic early Universe evolution has three stages: decelerated fast roll followed by inflationary fast roll and then inflationary slow roll (an attractor always reached for generic initial conditions). This evolution is valid for all regular inflaton potentials vð� Þ. In addition, we find a special (extreme) slow-roll solution starting at t ¼� 1 in which the fast-roll stages are absent. At some time t ¼ t� , the evolution backwards in time from t0 reaches generically a mathematical singularity where aðtÞ vanishes and the Hubble parameter becomes singular. We determine the general behavior near the singularity. The classical homogeneous inflaton description turns to be valid for tt� > 10tPlanck well before the beginning of inflation, quantum loop effects are negligible there. The singularity is never reached in the validity region of the classical treatment and therefore it is not a real physical phenomenon here. Fast-roll and slow-roll regimes are analyzed in detail including the equation of state evolution, both analytically and numerically. The characteristic time scale of the fast-roll era turns to be t1 ¼ð 1=mÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Vð0Þ=½3M 4 � p � 10 4 tPlanck, where V is the double-well inflaton potential, m is the inflaton mass, and M the energy scale of inflation. The whole evolution of the fluctuations along the decelerated and inflationary fast-roll and slow-roll eras is computed. The Bunch-Davies initial conditions are generalized for the present case in which the potential felt by the fluctuations can never be neglected. The fluctuations feel a singular attractive potential near the t ¼ tsingularity (as in the case of a particle in a central singular potential) with exactly the critical strength ( � 1=4) allowing the fall to the center. Precisely, the fluctuations exhibit logarithmic behavior describing the fall to t ¼ t� . The power spectrum gets dynamically modified by the effect of the fast-roll eras and the choice of Bunch-Davies initial conditions at a finite time through the transfer function DðkÞ of initial conditions. The power spectrum vanishes at k ¼ 0:DðkÞ presents a first peak for k � 2=� 0 (� 0 being the conformal initial time), then oscillates with decreasing amplitude and vanishes asymptotically for k !1 . The transfer function DðkÞ affects the low cosmic microwave background multipoles C': the changeC'=C' for 1 � ' � 5 is computed as a function of the starting instant of the fluctuations t0. Cosmic microwave background quadrupole observations indicate large suppressions, which are well reproduced for the range t0 � t� *