^{1}

^{*}

^{1}

^{1}

We extend our previous analysis and consider the interacting holographic Ricci dark energy (IRDE) model in non-flat universe. We study astrophysical constraints on this model using the recent observations including the type Ia supernovae (SNIa), the baryon acoustic oscillation (BAO), the cosmic microwave background (CMB) anisotropy, and the Hubble parameter. It is shown that the allowed parameter range for the fractional energy density of the curvature is in the presence of the interactions between dark energy and matter. Without the interaction, the flat universe is observationally disfavored in this model.

The current astrophysical observations of the Type Ia supernovae (SNIa) [

Among various attempts to solve these problems, we focus on the holographic dark energy (HDE) models [

where c is a dimensionless parameter, ^{−}^{1} = H [

In this paper, we extend our previous analysis, and consider the interacting RDE (IRDE) model in non-flat universe. This paper is organized as follows. In Section 2, we describe the generalized IRDE model in non-flat universe, and obtain analytic expressions for cosmic time evolution. In Section 3, we discuss the observational constraints on this model. We summarize our results in Section 4.

We study the interaction Ricci Dark Energy (IRDE) model in non-flat universe. The Friedmann-Robertson- Walker metric non-flat univrerse is given by

where k = 1, 0, −1 for closed, flat, and open geometries. The Friedmann Equation in non-flat univrerse takes the form

where

We generalize the energy density of the Ricci dark energy as

where α, b and

We adopt the interaction rate given by

where

The solution to Equation (8) is given by

where

In the case of

where

To derive the Equation of state parameter

In this section, we discuss cosmological constraints on the IRDE model in the non-flat universe

The luminosity distance in the non-flat universe can be written as

The SNIa observations measure the distance modulus μ of a supernova and its redshift z. The distance modulus is given by

We use the Union data set of 580 SNIa [

The CMB shift parameter R is given by

where

Signatures of the baryon acoustic oscillation (BAO) are provided by the observations of large-scale galaxy clustering. The BAO parameter A is defined by

where

The BAO constraints are obtained by minimizing

The Hubble parameter constraints are given by minimizing

where

In

value

In

We have considered the IRDE model in the non-flat universe. We have derived the analytic solutions for the

Hubble parameter (9), the dark energy density (14) and matter energy density (15). We have also studied astrophysical constraints on this model using the recent observations including SNIa, BAO, CMB anisotropy, and the Hubble parameter. We have shown that the allowed parameter range for the fractional energy density of the curvature is

We would like to thank T. Nihei for his valuable discussion, helpful advice and reading the manuscript.