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Exploring the Sharma–Mittal HDE models with different diagnostic tools

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Abstract

In this paper, we have examined the Sharma–Mittal holographic dark energy model (SMHDE) in the framework of an isotropic and spatially homogeneous flat Friedmann–Robertson–Walker Universe by considering different values of parameter \(\delta \) and R, where the infrared cut-off is taken care by the Hubble horizon. We examined the SMHDE model through the analysis of statefinder hierarchy and the growth rate of perturbation. The evolutionary trajectories of the statefinder hierarchy \(S_3^1\), \(S_3^2\)\(S_4^1\), \(S_4^2\) versus redshift z, show satisfactory behaviour throughout the Universe evaluation. One promising tool for investigating the dark energy models is the CND \(\{ S_3^1 - \epsilon \}\) and \(\{ S_4^1 - \epsilon \}\), where the evolutionary trajectories of the \(S_3^1 - \epsilon \) and \(S_4^1 - \epsilon \) pair present different properties and the departure from \(\Lambda \hbox {CDM}\) could be well evaluated. Additionally, we investigated the dynamical analysis of the model by \(\omega _{D}-\omega '_{D}\) pair analysis.

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Acknowledgements

The authors are thankful for valuable suggestions given by Dr. Prateek Pandey, GLA University, Mathura, India, in this research work. The authors are also thankful to the anonymous referee for his/her constructive comments which helped to improve the quality of paper in the present form.

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  1. Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University, Mathura, Uttar Pradesh, 281406, India

    Umesh Kumar Sharma & Vipin Chandra Dubey

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Sharma, U.K., Dubey, V.C. Exploring the Sharma–Mittal HDE models with different diagnostic tools. Eur. Phys. J. Plus 135, 391 (2020). https://doi.org/10.1140/epjp/s13360-020-00411-x

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