Theoretical Diagnosis Of Holographic Λ(t)CDM Model In Non-flat Universe

The research on dark energy issues is to understand the accelerated expansion and evolutionary process of the universe.In this process,physicists built a large number of different types of dark energy models based on different theories.So how to distinguish these models becomes a very important issue.The best way to distinguish between models is experiment with the data to exclude some models and leave the correct model.But the current problem is that even if there are a lot of data,there are still a lot of models that can’t be excluded,and they all fit the current observations.Therefore,it is considered to use theoretical diagnosis,and the theoretical diagnosis can provide some reference for the accuracy of future experimental observations.First,physicists think of using the different models of the dimensionless Hubble parameter and the evolution curve of the deceleration parameter to distinguish different dark energy models.However,some problems have been encountered in this process.For some similar models,the evolutionary curves of the dark energy models are degeneracy for current observations,so we need to find a better diagnostic method to break this degeneracy.In this paper,we study the holographic A(t)CDM model in non-flat universe from the statefinder hierarchy viewpoint.First,we deduce expressions of the statefinder hierarchy parameter S3(1)(z),S4(1)(z)which contains the third-order and fourth-order derivatives of scale factor and consider radiation and curvature.Then,in this model,by adjusting the values of the parameters c and Ωk0,we plot the evolution of the third and fourth-order statefinder hierarchy S3(1)and S4(1)and growth rate of structure ε,respectively,as well as several combinations of them to distinguish holographic Λ(t)CDM model and ACDM model.This paper discusses three situations are as follows:First,the parameter c takes different values,and then fixes the values of Ωk0;In the second case,we fixed parameter c,and the Ωk0 takes different values on the order of 10-2;The third case we still fixed parameter c,but the Ωk0 take different values on the order of 10-3.After discussion,it was found that in the first case,in the low redshift region,The evolutionary curves of S3(1)and {S3(1),ε} can clearly break the degeneracy.In the second case,we found that the statefinder hierarchy of S4(1)performs better than the statefinder hierarchy of S3(1),in addition,{S3(1),ε} and {S4(1),ε} also can break the degeneracy very well;In the last case,neither the statefinder hierarchy nor the growth rate of structure can effectively break the degeneracy,but we found the growth rate of the structure ε can distinguish the holographic A(t)CDM and the standard model,the cosmological constant model(ACDM model)effectively.Furthermore,we find that the current values of diagnostic parameters are very useful methods.