统一暴胀与早期和晚期暗能量的多场模型：自发破缺标度不变量TMT
Unifying Inflation with early and late Dark Energy in Multi-Fields: Spontaneously broken scale invariant TMT
摘要：
本文讨论了一个统一的三个平坦区多标量场模型。这三个平坦的区域分别是暴胀、早期和晚期的暗能量时期。势是由非黎曼积分测度（或两测度理论（TMT））产生的标度不变性的自发破缺而得到的，我们通过指数势定义了标量场与不同测度的标度不变性耦合.当对定义度量的字段进行积分时，会发生尺度不变性的自发破坏。当转到爱因斯坦框架时，我们得到：（i）具有三个平坦区域的标量场的有效势，其允许统一描述早期宇宙膨胀（在较高能量密度平坦区域中）以及可以用双相实现的当前暗能量时代，即，在两个平坦的区域。(ii)在慢卷暴胀中，只有一个场组合，即在尺度变换下变换的“介子”，具有非平凡动力学，正交场组合，即尺度不变的保持不变。(iv)在宇宙晚期，我们定义了暗物质与暗子的尺度不变耦合。这些耦合定义了一个物质诱导的势能，并将这个势能极值化，确定了标度不变的标量场，而暗物质的所有奇异的非正则行为以及任何可能的$5^{th}$力都消失了。(v)我们计算了在这些条件下的晚期宇宙的演化与实现两种不同的可能实现的$Λ$ CDM类型的方案取决于在晚期宇宙的平坦区域。这两个阶段可能出现在宇宙历史的不同时期。(vi)从普朗克数据中，我们找到了在暴胀时期对参数的约束，这些值被用来获得与当前时期相关的约束。
英文摘要：
A unified multi scalar field model with three flat regions is discussed. The three flat regions are the inflation, early and late dark energy epochs. The potential is obtained by a spontaneous breaking of scale invariance generated by Non Riemannian Measures of integration (or Two Measures Theories (TMT)).We define the scale invariant couplings of the scalar fields to the different measures through exponential potentials. Spontaneous breaking of scale invariance takes place when integrating the fields that define the measures. When going to the Einstein frame we obtain: (i) An effective potential for the scalar fields with three flat regions which allows for a unified description of both early universe inflation (in the higher energy density flat region) as well as of present dark energy epoch which can be realized with a double phase, i.e., in two flat regions. (ii) In the slow roll inflation, only one field combination the ``dilaton", which transforms under scale transformations, has non trivial dynamics, the orthogonal one, which is scale invariant remains constant. (iv) In the late universe we define scale invariant couplings of Dark Matter to the dilaton. These couplings define a matter induced potential for the dilaton and extremizing this potential determines the scale invariant scalar field, while all exotic non canonical behavior of the Dark Matter as well as any possible $5^{th}$ force disappear. (v) We calculate the evolution of the late universe under these conditions with the realization of two different possible realizations of $Λ$CDM type scenarios depending of the flat region in the late universe. These two phases could appear at different times in the history of the universe.(vi) From the Planck data, we find the constraints on the parameters during the inflationary epoch and these values are used to obtain constraints relevant to the present epoch.
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