Interactions in Scalar Field Cosmology

TL;DR

This work analyzes flat FRW cosmologies with a scalar field having an exponential potential $V=\Lambda e^{k\phi}$ and a barotropic fluid, incorporating energy transfer between the scalar and matter via interaction terms motivated by scalar-tensor and string theories. By recasting the equations into an expansion-normalized dynamical system with variables $x$ and $y$, the authors map the phase space and identify how different couplings modify late-time outcomes, including novel attractors where the scalar energy density remains a fixed fraction of the matter energy density and inflation persists. A key finding is that certain couplings produce an attracting focus, causing the scalar field to oscillate while inflation continues, which may provide a mechanism for exit and reheating in these models. The results connect to long-standing questions about quintessence, early-universe inflation with dissipation, and the role of scalar-tensor dynamics in cosmology, highlighting the potential observational relevance for late-time acceleration and scalar-field-driven cosmologies. $V=\Lambda e^{k\phi}$, and late-time behavior characterized by a fixed ratio $\ \Omega_{\phi}/\Omega$ with $\gamma_{\phi}<\gamma$ are central to the analysis.

Abstract

We investigate spatially flat isotropic cosmological models which contain a scalar field with an exponential potential and a perfect fluid with a linear equation of state. We include an interaction term, through which the energy of the scalar field is transferred to the matter fields, consistent with a term that arises from scalar--tensor theory under a conformal transformation and field redefinition. The governing ordinary differential equations reduce to a dynamical system when appropriate normalized variables are defined. We analyse the dynamical system and find that the interaction term can significantly affect the qualitative behaviour of the models. The late-time behaviour of these models may be of cosmological interest. In particular, for a specific range of values for the model parameters there are late-time attracting solutions, corresponding to a novel attracting equilib rium point, which are inflationary and in which the scalar field's energy-density remains a fixed fraction of the matter field's energy density. These scalar field models may be of interest as late-time cosmologies, part icularly in view of the recent observations of the current accelerated cosmic expansion. For appropriate values of the interaction coupling parameter, this equilibrium point is an attracting focus, and hence as inflating solutions approach this late-time attractor the scalar field oscillates. Hence these models may also be of importance in the study of inflation in the early universe.

Figures (3)

• Figure 1: Phase diagram of the system (\ref{['i_xy_1']}) when $\delta=-a\dot\phi\mu$ for the choice of parameters $k=1$, $\gamma=4/3$ and $a=8$. In this figure, the black dot represents the source (i.e., the point ${\cal K}^-$), the large grey dot represents the sink (i.e., the point $N$) and small black dots represent saddle points. The region above the grey dashed line represents the inflationary portion of the phase space. Arrows on the trajectory indicate the direction of time.
• Figure 2: A magnification of the attracting region of the phase space depicted in figure 1. See also caption to figure 1.
• Figure 3: Phase diagram of the system (\ref{['i_xy_1']}) when $\delta=-a\dot\phi\mu$ for the choice of parameters $\gamma=2$ and $k>\sqrt6$. Note that the past attractor is a heteroclinic cycle. See also caption to figure2.