| There are two periods of accelerated expansion in the expansion history of the universe occurring in the very early universe and the current late universe.In order to explain these two special periods within the framework of the standard cosmology model,the inflationary theory is proposed for supplementary,and the extra component of dark energy is introduced to drive the accelerated expansion today.In this paper,we research the generalized natural inflationary model and the Tsallis holographic dark energy model in detail,respectively.Moreover,we discuss the black hole shadows with quintessence dark energy and different dark matter density profiles.Firstly,based on the dynamics of single scalar field slow-roll inflation and the theory of reheating,we investigate the generalized natural inflationary(GNI)model.The GNI model adds the parameter m on the basis of the natural in-flationary model and the research result shows that the model parameter m has the significant effect on the model behaviors.Concretely,we give constraints on the scalar spectral index ns and tensor-to-scalar ratio r for ACDM+r model ac-cording to the latest data from Plack 2018 TT,TE,EE+lowE+lensing(P18)and BICEP2/Keck 2015 season(BK15),i.e.,ns=0.9659±0.0044 at 68%confidence level(CL)and r<0.0623 at 95%CL.We find that the GNI model is favored by P18 plus BK15 in the ranges of log10(f/Mp)=0.62(?)and m=0.35(?)at 68%CL.In addition,the corresponding predictions of the general and two-phase reheating are respectively discussed,the temperature and the e-folding numbers at the end of the general reheating and the minimum of the coupling constant to realize the two-phase reheating have been obtained.Secondly,we consider the interacting Tsallis holographic dark energy(THDE)model in the respective case of dark energy and dark matter with viscosity,and the Hubble horizon is taken as the IR cutoff.Concretely,by studying the cosmo-logical evolution and dynamical stability as well as reconstruction of the inter-acting THDE model with viscosity,we find that the viscosity does not influence background equations except for the equation of state of dark energy in the case of only dark energy with viscosity.Hence,the reconstructed potential energy and kinetic energy based on the equation of state are influenced.However,in the case of only dark matter with viscosity,the viscosity could result in different cosmological evolutions.Moreover,we find there are the dynamical attractors,i.e.,stable points,which would be influenced by the interaction and viscosity.It means that the stable points in the dark energy-dominated phase would give constraints on the interaction strength and the viscous parameter.In addition,as we know,the geometrical diagnostic methods can break the degeneracy for dark energy models.Thus,we apply the geometrical diagnostic methods to the THDE model with three different cutoffs.The results show that the low order statefinder hierarchy diagnostic S3(1)performs well for this kind of models.Finally,we investigate the black hole shadows in quintessence dark energy and dark matter halos with different dark matter density profiles.The spherically symmetric static metric and the rotating metric have been deduced.Based on the obtained black hole metric,we discuss the black shadows and find that they are influenced by the dark sectors.The results show that the deformations of the shadows increase with the increasing rotation parameter and the increasing inclination angle.Moreover,the sizes of the shadows increase with the increas-ing quintessential energy strength and the decreasing equation of state.While,the distortion parameter increases with the increasing equation of state and the decreasing energy strength.Besides,the increasing central densities of the NFW and Hernquist density profiles make the sizes increase,while,the constant and Moore density profiles make the sizes decrease.The deformation is largest cor-responding to the constant profile,and it is smallest corresponding to the NFW profile. |
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