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# Global phase space analysis for a class of single scalar field bouncing solutions in general relativity

Dec 2022

We carry out a compact phase space analysis of a non-canonical scalar fieldtheory whose generic form of the Lagrangian is $F(X)-V(\phi)$ within generalrelativity. In particular, we focus on the power law and exponential potentialsof the scalar field. A global dynamical system formulation particularlysuitable for investigating nonsingular bouncing cosmologies is used to carryout the analysis. Global dynamical system techniques help us to extract genericconclusions for a wide range of initial conditions. The main aim of this workis to analyze the generic behavior of nonsingular bouncing solutions usingglobal dynamical system tools. We show that for a noncanonical scalar fieldwith exponential potential, nonsingular bouncing cosmologies are a genericfeature and stable in past and future directions. However, the same cannot beconcluded for power law potential due to the non-existence of global past orfuture attractors. Our analysis is intended to show how global phase spaceformulations can be utilized to address questions about the stability ofbouncing solutions.

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