We investigate the quantum modified cosmological dynamical equations in a Friedmann–Lemaître–Robertson–Walker universe filled with a barotropic fluid and a general non-canonical scalar field characterized by a Lagrangian similar to k-essence model but with a potential term. Quantum corrections are incorporated by considering the running of the gravitational and potential couplings, employing the functional renormalization group approach. Covariant conservation of the non-canonical scalar field and the background barotropic fluid is considered separately, imposing a constraint resulting from the Bianchi identity. This constraint determines the evolution of the cut-off scale with the scale factor and also reveals the cosmic fixed points, depending on whether the flow ceases or continues to evolve. We explore how the general non-canonical scalar field parameter affects the different types of cosmic fixed points and how it differs from the canonical case. Furthermore, we establish a bound on the ratio of the renormalization group parameters involving the non-canonical parameter for which the universe may exhibit accelerated expansion for mixed fixed points. This bound indicates the non-canonical scalar field includes larger sets of asymptotically safe renormalization group fixed point which may give rise to an accelerated universe.

中文翻译：

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非正则标量场渐近安全宇宙学


我们研究了充满正压流体和一般非正则标量场的 Friedmann-Lemaître-Robertson-Walker 宇宙中的量子修正宇宙动力学方程，其特征在于类似于 k 本质模型的拉格朗日模型，但具有势项。通过考虑引力和势耦合的运行，采用函数重正化群方法，纳入量子校正。单独考虑非正则标量场和背景正压流体的协变守恒，施加由比安奇恒等式产生的约束。该约束决定了截止尺度随比例因子的演化，并且还揭示了宇宙不动点，具体取决于流动是停止还是继续演化。我们探讨一般非规范标量场参数如何影响不同类型的宇宙不动点以及它与规范情况有何不同。此外，我们对涉及非规范参数的重整化群参数的比率建立了界限，对于该非规范参数，宇宙可能表现出混合固定点的加速膨胀。这个界限表明非正则标量场包括更大的渐近安全重整化群不动点集，这可能会导致加速宇宙。