Using variable gravitational and cosmological constants, the mechanism of particle creation in the universe is studied for Friedmann–Robertson–Walker (FRW) space-times at high dimensions to explain the early deceleration and present accelerating phases. To investigate the dynamics of these phases, we consider two scale factor of the forms \(a(t)=\sqrt{t^\alpha{e^t}}\) and \(a(t)=\sqrt[m]{{\rm{sin}}h(kt)}\), which yield two different time-dependent deceleration parameters. Firstly, we modify the d-dimensional time-dependent field equations, including the general formulation of particle creation and entropy generation mechanisms. Then, we investigate the time dependence of a few quantities such as the particle creation rate ψ, the entropy S, the gravitational constant G, the cosmological constant Λ, the energy density ρ, the deceleration parameter q, etc. We show that all constants and quantities, except the gravitational constant G and the entropy S, characteristically decrease with time for two kinds of scale factors in all dimensions. However, the gravitational constant G and the entropy S increase with time. Additionally, we show that the cosmological constant Λ is unexpectedly independent of the particle creation mechanism, unlike G.

中文翻译：

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弗里德曼–罗伯逊–沃克宇宙中的粒子产生

利用可变的引力和宇宙常数，研究了弗里德曼–罗伯逊–沃克（FRW）高时空中宇宙中粒子产生的机理，以解释早期的减速和当前的加速阶段。为了研究这些阶段的动力学，我们考虑两个比例因子，形式为\（a（t）= \ sqrt {t ^ \ alpha {e ^ t}} \）和\（a（t）= \ sqrt [m ] {{\ rm {sin}} h（kt）} \），产生两个不同的时间相关的减速参数。首先，我们修改了d维时变场方程，包括粒子创建和熵产生机制的一般公式。然后，我们研究几个量的时间依赖性，例如粒子产生率ψ，熵S，引力常数G，宇宙常数Λ，能量密度ρ，减速度参数q等。我们证明，除了引力常数G和熵S之外，所有常数和量都随时间减小在所有维度上都有两种比例因子。然而，重力常数G和熵S随时间增加。此外，我们证明宇宙常数Λ出乎意料地独立于粒子生成机制，与G不同。