由q-de Sitter驱动的通货膨胀
Inflation driven by q-de Sitter
摘要：
本文提出了一个广义的de Sitter尺度因子，用于描述早期和晚期宇宙的宇宙学，包括称为暴胀子的单个标量场。这种形式的比例因子有一个自由参数$q$，称为非扩展性参数。当为$q=1$时，比例因子为de Sitter。该比例因子是幂律和de Sitter之间的中间形式。我们研究这类家族的宇宙学。我们表明，这两种暗成分，暗能量和暗物质同时描述了这个家庭的解决方案。作为一个有动机的想法，我们调查的$q$ -德西特的框架内的通货膨胀。我们考虑三种通货膨胀的情况。在一个单一的通货膨胀的情况下，我们观察到，通货膨胀结束没有任何特定的结束通货膨胀$ϕ_{end}$，频谱指数和相关的运行的频谱指数是% $ n_\mathrm{s} - 1 \sim -2ε, \quad α_\mathrm{s} \equiv 0 $。为了结束通货膨胀：我们应该有$q=\frac{3}{4}$。我们推导出膨胀结束时的比例因子的演变是$a (t) =e_ {3/4} (t) $。使用此比例因子，无需指定$ϕ_{end}$。作为有终点通货膨胀的替代，我们将在暖通货膨胀的背景下研究q-通货膨胀模型。我们提出了两种形式的阻尼项$Γ$。在第一种情况下，当$Γ=Γ_0$时，我们证明了尺度不变谱（Harrison-Zeldovich谱，即$n_s=1$）可以近似地由（$q=\frac{9}{10},~~N=70$）表示。此外，$R$和$n_s$的值范围与BICEP 2数据兼容，其中$q=\frac{9}{10}$。在情况$Γ=Γ_1V(ϕ)$中，观察到对于小的$q$参数值，确保了许多e折叠的小值。对于$q=\frac{9}{10}$，$R$和$n_s$的值范围与BICEP 2数据兼容。
英文摘要：
We propose a generalised de Sitter scale factor for the cosmology of early and late time universe, including single scalar field is called as inflaton. This form of scale factor has a free parameter $q$ is called as nonextensivity parameter. When $q=1$, the scale factor is de Sitter. This scale factor is an intermediate form between power-law and de Sitter. We study cosmology of such families. We show that both kinds of dark components, dark energy and dark matter simultaneously are described by this family of solutions. As a motivated idea, we investigate inflation in the framework of $q$-de Sitter. We consider three types of scenarios for inflation. In a single inflation scenario, we observe that, inflation ended without any specific ending inflation $ϕ_{end}$, the spectral index and the associated running of the spectral index are %$ n_\mathrm{s} - 1 \sim -2ε, \quad α_\mathrm{s} \equiv 0 $. To end the inflation: we should have $q=\frac{3}{4}$. We deduce that the inflation ends when the evolution of the scale factor is $a (t) =e_ {3/4} (t) $. With this scale factor there is no need to specify $ϕ_{end}$. As an alternative to have inflation with ending point, We will study q-inflation model in the context of warm inflation. We propose two forms of damping term $Γ$. In the first case when $Γ=Γ_0$, we show the scale invariant spectrum, (Harrison-Zeldovich spectrum, i.e. $n_s=1$) may be approximately presented by ($q=\frac{9}{10},~~N=70$). Also there is a range of values of $R$ and $n_s$ which is compatible with the BICEP2 data where $q=\frac{9}{10}$. In case $Γ=Γ_1V(ϕ)$, it is observed that small values of a number of e-folds are assured for small values of $q$ parameter. For $q=\frac{9}{10}$ a range of values of $R$ and $n_s$ is compatible with the BICEP2 data.
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