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A new interacting two fluid model and its consequences

German S. Sharov, Subhra Bhattacharya, Supriya Pan, Rafael C. Nunes, Subenoy Chakraborty

TL;DR

This work analyzes a flat FLRW universe with two interacting fluids—pressureless dark matter and dark energy—via a nongravitational coupling $Q = \alpha H (\rho_m^\prime + \rho_d^\prime)$, allowing the dark energy EoS to be constant or time-dependent. For a constant DE EoS, the authors obtain analytic solutions and perform an asymptotic analysis, revealing possible phantom crossing and a sign-changing interaction; they then constrain the model with SN Ia, H(z), and BAO data. For a variable DE EoS, they adopt a CPL-like parametrization within a unified $\omega_d(z)$ framework and solve the resulting dynamics numerically, finding that CPL best fits the data among dynamical forms, though model selection via AIC prefers the interacting $\Lambda$ case. Overall, all interacting models remain remarkably close to $\Lambda$CDM, with the data favoring a very small coupling and, in some cases, phantom-like behavior of DE.

Abstract

In the background of a homogeneous and isotropic spacetime with zero spatial curvature, we consider interacting scenarios between two barotropic fluids, one is the pressureless dark matter (DM) and the other one is dark energy (DE), in which the equation of state (EoS) in DE is either constant or time dependent. In particular, for constant EoS in DE, we show that the evolution equations for both fluids can be analytically solved. For all these scenarios, the model parameters have been constrained using the current astronomical observations from Type Ia Supernovae, Hubble parameter measurements, and baryon acoustic oscillations distance measurements. Our analysis shows that both for constant and variable EoS in DE, a very small but nonzero interaction in the dark sector is favored while the EoS in DE can predict a slight phantom nature, i.e. the EoS in DE can cross the phantom divide line `$-1$'. On the other hand, although the models with variable EoS describe the observations better, but the Akaike Information Criterion supports models with minimal number of parameters. However, it is found that all the models are very close to the $Λ$CDM cosmology.

A new interacting two fluid model and its consequences

TL;DR

This work analyzes a flat FLRW universe with two interacting fluids—pressureless dark matter and dark energy—via a nongravitational coupling , allowing the dark energy EoS to be constant or time-dependent. For a constant DE EoS, the authors obtain analytic solutions and perform an asymptotic analysis, revealing possible phantom crossing and a sign-changing interaction; they then constrain the model with SN Ia, H(z), and BAO data. For a variable DE EoS, they adopt a CPL-like parametrization within a unified framework and solve the resulting dynamics numerically, finding that CPL best fits the data among dynamical forms, though model selection via AIC prefers the interacting case. Overall, all interacting models remain remarkably close to CDM, with the data favoring a very small coupling and, in some cases, phantom-like behavior of DE.

Abstract

In the background of a homogeneous and isotropic spacetime with zero spatial curvature, we consider interacting scenarios between two barotropic fluids, one is the pressureless dark matter (DM) and the other one is dark energy (DE), in which the equation of state (EoS) in DE is either constant or time dependent. In particular, for constant EoS in DE, we show that the evolution equations for both fluids can be analytically solved. For all these scenarios, the model parameters have been constrained using the current astronomical observations from Type Ia Supernovae, Hubble parameter measurements, and baryon acoustic oscillations distance measurements. Our analysis shows that both for constant and variable EoS in DE, a very small but nonzero interaction in the dark sector is favored while the EoS in DE can predict a slight phantom nature, i.e. the EoS in DE can cross the phantom divide line `'. On the other hand, although the models with variable EoS describe the observations better, but the Akaike Information Criterion supports models with minimal number of parameters. However, it is found that all the models are very close to the CDM cosmology.

Paper Structure

This paper contains 14 sections, 51 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Interacting Dynamics in flat FLRW
  3. Constant EoS in DE
  4. Asymptotic behavior of the energy densities and the sign of the interaction
  5. Interacting dynamics for variable equation of state in DE
  6. Observational Constraints on the model parameters
  7. Supernovae Type Ia data
  8. Hubble data
  9. Baryon Acoustic Oscillation data
  10. Results of the joint analysis
  11. Constant equation of state in DE
  12. Variable equation of state in DE
  13. Model selection
  14. Summary and Discussions

Figures (3)

  • Figure 1: The figure shows the 1$\sigma$, 2$\sigma$, 3$\sigma$ confidence-level contour plots of the model parameters with their best fit values for the interacting DE model with constant EoS, $\omega_d \neq -1$ (Eq. (\ref{['solution-constant-EoS']})), using different combinations of the observational data sets as SN$+$ OHD$+$BAO (blue filled contours), SN$+$ BAO (red contours), SNe$+$ OHD (green contours). We note that the contour lines for SN$+$ H($z$) do not appear properly in all the plots.
  • Figure 2: The figure shows the 1$\sigma$, 2$\sigma$, 3$\sigma$ confidence-level contour plots of the model parameters with their best fit values for the interacting cosmological constant (Eq. (\ref{['CC-total']})), using different combinations of the observational data sets as SN$+$ OHD$+$BAO (blue filled contours), SN$+$ BAO (red contours), SNe$+$ OHD (green contours).
  • Figure 3: In the top-left panel we show the dependence of min $\chi^2_{tot}$ on the free parameter '$\beta$' of the general EoS given in (\ref{['eos-variable']}) using the observational data SN$+$OHD$+$BAO. It shows that $\beta= 1$, i.e. the interacting model with CPL parametrization (eqn. (\ref{['cpl']})) is the viable interacting model with variable EoS in DE in compared to the others. The other panels represent the contour plots at 1$\sigma$, 2$\sigma$ confidence levels for various quatities of the interacting DE model with CPL parametrization (eqn. (\ref{['cpl']}), i.e. $\beta=1$) using the same observational data SN$+$OHD$+$BAO.