In this work, we have constructed deceleration–acceleration and future evolution of cosmic expansion with curved dynamical dark energy models. Closed and open spatial curvatures are calculated by assuming that dark energy density does not exceed 85% of the closure density and by obtaining lower bounds on the ratio of dark energy to matter density, in terms of equation of state of dark energy. The range of transition epoch zt ≈ (0.55 − 0.8) realized for spatial curvature − 0.1 < Ωk(0) < 0.1 is consistent with model independent estimations coming from galactic ages, strong lensing, Type Ia supernovae and recent constraints coming from H0 measurements in non-flat dynamical dark energy models. Two novel parametrizations of dark energy equation of state namely the logarithmic and oscillatory, which are singularity free at future point z →−1 are used to study the deceleration parameter q(z). Irrespective of spatial curvature, cosmic doomsday has been found inevitable for both the parametrizations. The time evolution of logarithmic parametrization, being reminiscent of a quintom field (canonical+phantom), is converted into dynamics of a canonical quintessence and a phantom field for the redshift range (zt,z ≈ 10) and (zt, z →−1). It is found that irrespective of spatial curvature, the quintessence component becomes sub-dominant in future giving it’s way to the phantom component.

中文翻译：

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弯曲暗能量宇宙学的宇宙膨胀：宇宙末日的必然性

在这项工作中，我们用弯曲的动态暗能量模型构建了宇宙膨胀的减速-加速和未来演化。通过假设暗能量密度不超过闭包密度的 85% 并根据暗能量状态方程获得暗能量与物质密度比的下限来计算闭合和开放空间曲率。过渡时期的范围z吨 ≈ (0.55 - 0.8)实现空间曲率 - 0.1 < Ωķ(0) < 0.1与来自银河年龄、强透镜、Ia 型超新星和最近来自H0非平坦动态暗能量模型中的测量。暗能量状态方程的两个新参数化，即对数和振荡，它们在未来点是无奇点的z →-1用于研究减速参数q(z）。无论空间曲率如何，宇宙末日对于这两种参数化都是不可避免的。对数参数化的时间演化，让人联想到五元场（规范+phantom), 被转换为规范精髓的动力学和红移范围的幻象场 (z吨,z ≈ 10） 和 （z吨,z →-1）。研究发现，无论空间曲率如何，精髓成分在未来都将成为次要成分，让其成为幻像成分。