| Summary: | The cosmic expansion phenomenon is being studied through the interaction of newly proposed dark energy models (Tsallis, Rényi and Sharma-Mittal holographic dark energy (HDE) models) with cold dark matter in the framework of loop quantum cosmology. We investigate different cosmic implications such as equation of state parameter, squared sound speed and cosmological plane (<inline-formula><math display="inline"><semantics><msub><mi>ω</mi> <mi>d</mi> </msub> </semantics> </math> </inline-formula>-<inline-formula> <math display="inline"> <semantics> <msubsup> <mi>ω</mi> <mrow> <mi>d</mi> </mrow> <mo>′</mo> </msubsup> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <msub> <mi>ω</mi> <mi>d</mi> </msub> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msubsup> <mi>ω</mi> <mi>d</mi> <mo>′</mo> </msubsup> </semantics> </math> </inline-formula> represent the equation of state (EoS) parameter and its evolution, respectively). It is found that EoS parameter exhibits quintom like behavior of the universe for all three models of HDE. The squared speed of sound represents the stable behavior of Rényi HDE and Sharma-Mittal HDE at the latter epoch while unstable behavior for Tsallis HDE. Moreover, <inline-formula> <math display="inline"> <semantics> <msub> <mi>ω</mi> <mi>d</mi> </msub> </semantics> </math> </inline-formula>-<inline-formula> <math display="inline"> <semantics> <msubsup> <mi>ω</mi> <mrow> <mi>d</mi> </mrow> <mo>′</mo> </msubsup> </semantics> </math> </inline-formula> plane lies in the thawing region for all three HDE models.
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