Best values of parameters for interacting HDE with GO IR-cutoff in Brans–Dicke cosmology
Abstract
We investigate the interacting holographic dark energy (HDE) with Granda–Oliveros (GO) infrared (IR)-cutoff in the framework of Brans–Dicke (BD) cosmology. We obtain the equation of state (EoS) parameter of HDE, wD, the effective EoS parameter weff, the deceleration parameter q and the squared of sound speed 
in a flat Friedmann–Robertson–Walker (FRW) universe. We show that at late-time the cosmic coincidence problem can be alleviated. Also we show that for noninteracting case, HDE can give a unified dark matter–dark energy (DM–DE) profile in BD cosmology, except that it cannot solve the coincidence problem in the future. By studying the EoS parameter, we see that the phantom divide may be crossed. Using the latest observational data, we calculate the best values of the parameters for interacting HDE in BD framework. Computing the deceleration parameter implies that the transition from deceleration to the acceleration phase occurred for redshift z ≥ 0.5. Finally, we investigate the sound stability of the model, and find that HDE with Granda–Oliveros (GO)-cutoff in the framework of BD cosmology can lead to a stable DE-dominated universe favored by observations, provided we take β = 0.44 and b2 < 0.35. This is in contrast to HDE model in Einstein gravity which does not lead to a stable DE-dominated universe.
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