In this paper, we investigate a recent proposed model -so called the Tsallis holographic dark energy (THDE) model with consideration of the Hubble and the event future horizon as IR cutoffs. In this case, we consider the non-gravitational and phenomenological interaction between dark sectors. We fit the free parameters of the model using Pantheon Supernovae Type Ia data, Baryon Acoustic Oscillations, Cosmic Microwave Background, Gamma-Ray burst and the the local value of the Hubble constant. We examine the THDE model to check its compatibility with observational data using objective Information Criterion (IC). We find that the THDE models cannot be supported by observational data once the CDM is considered as the referring model. Therefore we re-examine the analysis with the standard holographic dark energy model (HDE) as another reference. Changing the CDM to main standard dark energy model (HDE), we observe the compatibility of the THDE models. Using the Alcock-Paczynski (AP) test we check the deviation of the model compared to CDM and HDE. Surveying the evolution of squared of sound speed v 2 s as an another test we check the stability of the interacting and non-interacting THDE models and we find that while the THDE model with the Hubble horizon as IR cutoff is unstable against the background perturbation, the future event horizon as IR cutoff show stability at the late time. In addition, using the modified version of the CAMB package, we observe the suppressing the CMB spectrum at small K-modes and large scale.Eur. Phys. J. C

Purpose To evaluate the prevalence of Demodex blepharitis by its pathognomonic sign, collarettes, in patients presenting for any reason to eye care clinics in the United States. Patients and Methods In this retrospective study by 7 investigators at 6 eye care clinics, case records of consecutive patients who underwent a slit-lamp examination, regardless of chief complaint, were reviewed for Demodex blepharitis, as identified by the presence of collarettes. Patient characteristics, including age, gender, race, relevant ocular and systemic diagnoses, ocular medications, lid hygiene practices and contact lens wear, were also recorded. Results Of 1032 patients (mean age: 60.2 ± 17.8 years), 57.7% had Demodex blepharitis. While the prevalence of Demodex blepharitis in patients with dry eye disease (DED) (58.9%) and cataract (55.7%) was similar to the overall prevalence of Demodex blepharitis, it was higher in patients with blepharitis (69.1%) and glaucoma (64.8%). Among patients with collarettes, 44.0% had never been diagnosed with blepharitis. Among those on anti-inflammatory DED treatment, 60.0% had Demodex blepharitis. Demodex blepharitis prevalence was significantly higher among those using topical tea tree oil versus those who were not (74.5% versus 56.7% p = 0.014); prevalence was comparable among those using/not using lid wipes (56.9% versus 55.5%). Conclusion Demodex blepharitis, based on the pathognomonic finding of collarettes, is common and likely underdiagnosed among patients seeking eye care. These collarettes are still found in patients using over-the-counter treatments for blepharitis. The present study highlights the importance of screening patients for collarettes and Demodex blepharitis as part of every slit-lamp examination.

In this paper, we study an interacting holographic dark energy model in the framework of fractal cosmology. The features of fractal cosmology could pass ultraviolet divergencies and also make a better understanding of the universe in different dimensions. We discuss a fractal FRW universe filled with the dark energy and cold dark matter interacting with each other. It is observed that the Hubble parameter embraces the recent observational range while the deceleration parameter demonstrates an accelerating universe and a behavior similar to ΛCDM. Plotting the equation of state shows that it lies in phantom region for interaction mode. We use Om-diagnostic tool and it shows a phantom behavior of dark energy which is a condition of avoiding the formation of black holes. Finally we execute the StateFinder diagnostic pair and all the trajectories for interacting and non-interacting state of the model meet the fixed point ΛCDM at the start of the evolution. A behavior similar to Chaplygin gas also can be observed in statefinder plane. We find that new holographic dark energy model (NHDE) in fractal cosmology expressed the consistent behavior with recent observational data and can be considered as a model to avoid the formation of black holes in comparison with the main model of NHDE in the simple FRW universe. It has also been observed that for the interaction term varying with matter density, the model generates asymptotic de-Sitter solution. However, if the interaction term varies with energy density, then the model shows Big-Rip singularity. Using our modified CAMB code, we observed that the interacting model suppresses the CMB spectrum at low multipoles l < 50 and enhances the acoustic peaks. Based on the observational data sets used in this paper and using Metropolis-Hastings method of MCMC numerical calculation, it seems that the best value with 1σ and 2σ confidence interval are Ω m0 = 0.278 +0.008 +0.010 −0.007 −0.009 , H 0 = 69.9 +0.95 +1.57 −0.95 −1.57 , r c = 0.08 +0.02 +0.027 −0.002 −0.0027 , β = 0.496 +0.005 +0.009 −0.005 −0.009 , c = 0.691 +0.024 +0.039 −0.025 −0.037 and b 2 = 0.035 according to which we find that the proposed model in the presence of interaction is compatible with the recent observational data.

We study the cosmological consequences of interacting Tsallis holographic dark energy model in the framework of the fractal universe, in which, the Hubble radius is considered as the IR cut-off. We drive the equation of state (EoS) parameter, deceleration parameter and the evolution equation for the Tsallis holographic dark energy density parameter. Our study shows that this model can describe the current accelerating Universe in both noninteracting and interacting scenarios, and also a transition occurs from the deceleration phase to the accelerated phase, at the late time. Finally, we check the compatibility of free parameters of the model with the latest observational results by using the Pantheon supernovae data, eBOSS, 6df, BOSS DR12, CMB Planck 2015, Gamma-Ray Burst.

In this paper, we study the interacting DGP braneworld Holographic Dark Energy model in a spatially flat FRW universe. Mainly, in this study we concentrate our attention on both interacting and non-interacting form of the model. The study shows that the equation of state and the deceleration parameter depict an accelerated universe for all variety of interactions. On the other hand, the StateFinder analysis shows that of the interacting and non-interacting behave similar to both quintessence and phantom dark energy and for the present value obey the behavior of quintessence. Moreover, the result of Om-diagnostic is an emphasis on the result of the equation of state showing that the current model is in the quintessence are with Phantom-like behavior in the late time. By the use of the squared sound speed v 2 s we find that the present mode has a good stability. In order to obtain the best fit values of the parameters in this work we used the latest observational data (Pantheon, Boss DR12 and Planck 2015) implementing MCMC method by the use of EMCEE python package. We also employ Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) model selection tools and compare the model with ΛCDM as the reference model.