The effective dynamics of loop quantum $R^2$ cosmology

Abstract

The effective dynamics of loop quantum $f(R)$ cosmology in Jordan frame is considered by using the dynamical system method and numerical method. To make the analyze in detail, we focus on $R^2$ model since it is simple and favored from observations. In classical theory, $(\varphi =1,\dot{\varphi }=0)$ is the unique fixed point in both contracting and expanding states, and all solutions are either starting from the fixed point or evolving to the fixed point; while in loop theory, there exists a new fixed point (saddle point) at $(\varphi \simeq 2/3,\dot{\varphi }=0)$ in contracting state. We find the two critical solutions starting from the saddle point control the evolution of the solutions starting from the fixed point $(\varphi =1,\dot{\varphi }=0)$ to bounce at small values of scalar field in $0<\varphi <1$. Other solutions, including the large field inflation solutions, all have the history with $\varphi <0$ which we think of as a problem of the effective theory of loop quantum $f(R)$ theory. Another different thing from loop quantum cosmology with Einstein-Hilbert action is that there exist many solutions do not have bouncing behavior.

arXiv comment8 pages, 7 figures

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• Static Traversable Wormholes in $f(R,T)=R+2\alpha \ln T$ Gravity
• Estimation of Cosmological Parameters, Stability Analysis and Energy Conditions in Viable Modified Gravity
• New rotating AdS/dS black holes in $\mathrm{f}(\mathrm{R})$ gravity
• Cosmological Evolution of Two-Scalar fields Cosmology in the Jordan frame
• Wormhole modeling in $R^2$ gravity with linear trace term
• Multiscalar-torsion Cosmology: Exact and Analytic Solutions from Noether Symmetries
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• Nonclassical cosmological dynamics in the low-energy limit of loop quantum scalar-tensor theory
• Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology