Abstract In Phys. Rev. D 92, 103004 (2015), simple analytical solutions of the Friedman equations were obtained for a universe having a stiff matter component at early times together with dark matter (DM) and dark energy (DE) components. In this analysis, the universe is considered to be made of a dark fluid which behaves as stiff matter in the early phase of the universe (when the internal energy dominates). It is also more logical to consider quantum gravitational effects in the early phase of the cosmological evolution. In this analysis, following Phys. Rev. D 65, 043508 (2002), we consider renormalization group (RG) improved modified Friedmann equations, where Newton’s gravitational constant <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(G\)</EquationSource>  </InlineEquation> and the cosmological constant <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Lambda\)</EquationSource>  </InlineEquation> flow with the momentum scale <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(k\)</EquationSource>  </InlineEquation> of the universe. We obtain the momentum scale in terms of the scale factor of the universe when a stiff-matter era is present in the early time regime (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(t\)</EquationSource>  </InlineEquation> being smaller than the Planck time). It is observed that for a universe undergoing a stiff matter era, radiation era, and matter era, inflation is absent in the early time regime when the flow of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(G\)</EquationSource>  </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\Lambda\)</EquationSource>  </InlineEquation> is under consideration. Considering the total equation of state as a combination of linear and polytropic equations of state, we observe that after the Planck time the universe can undergo an inflationary phase, and we find out that the inflation is enhanced by quantum gravitational effects. Finally, we propose a new energy density that shows a transition between a primordial stiff matter era followed by an inflation era just after the Planck time, and then a transition from inflation to a radiation dominated reheating phase around a second transition point in this RG improved cosmological model.

Renormalization Group Improved Cosmology in the Presence of a Stiff Matter Era

期刊论文
发表日期：

2026年5月21日

查看全文

Gopinath Guin,
Soham Sen,
Sunandan Gangopadhyay

摘要

Abstract

In Phys. Rev. D 92, 103004 (2015), simple analytical solutions of the Friedman equations were obtained for a universe having a stiff matter component at early times together with dark matter (DM) and dark energy (DE) components. In this analysis, the universe is considered to be made of a dark fluid which behaves as stiff matter in the early phase of the universe (when the internal energy dominates). It is also more logical to consider quantum gravitational effects in the early phase of the cosmological evolution. In this analysis, following Phys. Rev. D 65, 043508 (2002), we consider renormalization group (RG) improved modified Friedmann equations, where Newton’s gravitational constant \(G\) and the cosmological constant \(\Lambda\) flow with the momentum scale \(k\) of the universe. We obtain the momentum scale in terms of the scale factor of the universe when a stiff-matter era is present in the early time regime ( \(t\) being smaller than the Planck time). It is observed that for a universe undergoing a stiff matter era, radiation era, and matter era, inflation is absent in the early time regime when the flow of \(G\) and \(\Lambda\) is under consideration. Considering the total equation of state as a combination of linear and polytropic equations of state, we observe that after the Planck time the universe can undergo an inflationary phase, and we find out that the inflation is enhanced by quantum gravitational effects. Finally, we propose a new energy density that shows a transition between a primordial stiff matter era followed by an inflation era just after the Planck time, and then a transition from inflation to a radiation dominated reheating phase around a second transition point in this RG improved cosmological model.