FLRW cosmology in Asymptotically Safe Gravity

Chiang-Mei Chen¹, Akihiro Ishibashi², Rituparna Mandal^1*, Nobuyoshi Ohta^1,2

¹Department of Physics, National Central University, Taoyuan, Taiwan
²Department of Physics, Kindai University, Osaka, Japan

* Presenter:Rituparna Mandal, email:drimit.ritu@gmail.com

We examine FLRW cosmology, incorporating quantum gravitational corrections through the exact renormalization group (RG) flow of the effective action for gravity. We calculate the quantum-corrected scale factor, energy density, and entropy production at late times, using various choices for the RG cut-off scale, k [1]. For this purpose, the cosmological evolution
equations are derived by including the scale dependence of Newton’s constant, G(k), and the cosmological constant, Λ(k), determined using the effective average action formalism for Euclidean quantum gravity in asymptotically safe gravity.

To analyze cosmology, it is essential to link the RG scale k to a physical cut-off scale, which ceases to run in the infrared. Although identifying the RG scale is challenging, existing literature often involves expressing k in terms of scales relevant to the problem, such as particle momenta, field strengths, or the curvature of spacetime [2]. However, there is no precise method in cosmology to directly correlate the RG scale k with the physical scale. In this work, we explore this ambiguity and study cosmology by selecting various cut-off scales: k=$\frac{\xi}{t}$, $k=\zeta H^{\frac{1}{4}}$, $k=\varepsilon H^{\frac{3}{4}}$, and $k = \gamma H$ . Our main observation is that different cut-off choices yield distinct late-time cosmologies. Furthermore, by interpreting physical results, primarily through entropy generation, we find that certain cut-off choices may be more viable than others.

In another ongoing work [3], we generalize these cut-off scales in terms of the Hubble parameter H(t), defining $k(t)=\varsigma G_{0}^{\frac{\beta-1}{2}}H^{\beta}(t)$, as in previous studies [1]. It was found that entropy generation diverges at late times for β = 1/4 and converges to a constant for β = 3/4 and β = 1 [1]. This suggests a critical value of β indicating a significant shift in entropy generation. Here, we show that this critical value is β = 1/2, which changes the scale factor behavior from a power law (β > 1/2) to exponential (β < 1/2), causing the entropy to transition from constant to divergent, respectively.

References:
[1] R. Mandal, S. Gangopadhyay and A. Lahiri , “Cosmology with modified continuity equation in asymptotically safe gravity,” Eur. Phys. J. Plus 137 (2022), 10 [arXiv:2010.09716 [gr-qc]].

[2] A. Bonanno and M. Reuter, “Cosmology of the Planck era from a renormalization group for quantum gravity,” Phys. Rev. D 65 (2002).

[3] C.-M. Chen, A. Ishibashi, R. Mandal and N. Ohta, Work in Progress

Keywords: FLRW cosmology, Asymptotically Safe Gravity, Entropy Generation