https://doi.org/10.1140/epjc/s10052-023-12377-y
Regular Article – Theoretical Physics
Global phase space analysis for a class of single scalar field bouncing solutions in general relativity
1
Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, 500078, Hyderabad, India
2
The Institute for Fundamental Study “The Tah Poe Academia Institute”, Naresuan University, 65000, Phitsanulok, Thailand
3
Center for Space Research, North-West University, 2745, Mahikeng, South Africa
4
Mathematics Division, Department of Basic Sciences and Social Sciences, North Eastern Hill University, 793022, Shillong, Meghalaya, India
5
Inter University Centre for Astronomy and Astrophysics, 411 007, Pune, India
6
Department of Mathematics, St. Anthony’s College, 793001, Shillong, Meghalaya, India
c
bivu@hyderabad.bits-pilani.ac.in
Received:
21
August
2023
Accepted:
22
December
2023
Published online:
19
January
2024
We carry out a compact phase space analysis of a non-canonical scalar field theory whose Lagrangian is of the form 
within general relativity. In particular, we focus on a kinetic term of the form 
(
) with power-law potential 
and exponential potential 
of the scalar field. The Cuscuton case 
where the scalar field is non-dynamical is left out of consideration. The main aim of this work is to investigate the genericity of nonsingular bounce in these models and to investigate the cosmic future of the bouncing cosmologies when they are generic. A global dynamical system formulation that is particularly suitable for investigating nonsingular bouncing cosmologies is used to carry out the analysis. We show that when (
), nonsingular bounce is generic for a power law potential 
only within the parameter range 
and for an exponential potential 
only within the parameter range 
. Except in these cases, nonsingular bounce in these models is not generic due to the non-existence of global past or future attractors. Our analysis serves to show the importance of a global phase space analysis to address important questions about nonsingular bouncing solutions, an idea that may and must be adopted for such solutions even in other theories.
© The Author(s) 2024
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