Dynamical analysis of interacting non-canonical scalar field model Goutam Mandal, 1, ∗ Soumya Chakraborty, 2, † Sudip Mishra, 2, ‡ and Sujay Kr. Biswas 1, § 1 Department of Mathematics, Ramakrishna Mission Vivekananda Centenary College, Rahara, Kolkata-700 118, West Bengal, India 2 Department of Mathematics, Jadavpur University, Kolkata-700 032, West Bengal, India In this work, considering the background dynamics of flat Friedmann-Lemaitre-Robertson- Walker(FLRW) model of the universe, we investigate a non-canonical scalar field model as dark energy candidate which interacting with the pressureless dust as dark matter in view of dynamical systems analysis. Two interactions from phenomenological point of view are chosen: one is depend- ing on Hubble parameter H, another is local, independent of Hubble parameter. In Interaction model 1, an inverse square form of potential as well as coupling function associated with scalar field is chosen and a two dimensional autonomous system is obtained. From the 2D autonomous system, we obtain scalar field dominated solutions representing late time accelerated evolution of the universe. Late time scaling solutions are also realized by the accelerated evolution of the uni- verse attracted in quintessence era. Center Manifold Theory can provide the sufficient conditions on model parameters such that the de Sitter like solutions can be stable attractor at late time in this model. In the Interaction model 2, potential as well as coupling function are considered to be evolved exponentially on scalar field and as a result of which a four dimensional autonomous system is achieved. From the analysis of 4D system, we obtain non-hyperbolic sets of critical points which are analyzed by the Center Manifold Theory. In this model, de Sitter like solutions represent the transient evolution of the universe. PACS numbers: 95.36.+x, 95.35.+d, 98.80.-k, 98.80.Cq. Keywords: Non-canonical scalar field, Interaction, Dynamical system, Center Manifold Theory, Phase space, Stability 1. INTRODUCTION Theoretical cosmology does not agree with the recent observational evidences [1, 2] which predict that currently the Universe is enduring an accelerated expansion. So, cosmologists have been trying to explain these observational predictions for more than one decade separated in two groups. One group of cosmologists has been trying to explain the observational facts by introducing an exotic quantity commonly known as dark energy (DE) with large negative pressure, while the other group is focused to explain the observational evidences theoretically by modifying the Einstein Gravity theory. In the literature, there are various choices of DE but cosmological constant is observationally more preferable as well as the simplest one. But this choice also consists of two severe conceptual problems, (1) cosmological constant problem and (2) coincidence problem. On the other hand, there is no well-accepted modification of gravity theory as an alternative choice to the cosmologists. Cosmological constant problem can be overcome by introducing new type of time varying DE model in which the canonical scalar field model: Quintessence is the popular one where equation of state parameter ω φ for Quintessence takes any value in the range −1 <ω φ < − 1 3 . After that various DE models based on scalar field such as K-essence, phantom, quintom etc. have been studied in the literature. The scalar field model, where energy density and pressure having a non-canonical form of kinetic term, i.e., kinetic term appears with a coupling function (non-canonical term) depending on scalar field φ, is the non-canonical scalar field model [3–7] which has also been studied extensively to solve several cosmological issues [8]. On the other hand, coincidence problem can be alleviated by introducing an interaction term in between the dark energy and the dark matter. Since at present the evolution of the universe is assumed to be dominated by the dark energy and the dark matter, the possibility of having interaction between them cannot be ignored. Also, an appropriate form of interaction can provide a possible mechanism to alleviate the coincidence problem. However, due to unknown nature of DE, one can choose the interaction term phenomenologically which can be a function of energy density of either DE or DM * Electronic address: goutam.math@rkmvccrahara.org † Electronic address: soumyachakraborty150@gmail.com ‡ Electronic address: sudipcmiiitmath@gmail.com § Electronic address: sujaymathju@gmail.com arXiv:2101.04496v1 [gr-qc] 9 Jan 2021