Revisiting the constraints on interacting holographic dark energy models with current observational data

Abstract We update the observational constraints on the interacting holographic dark energy (IHDE) models by considering ten representative interaction forms, each defined in terms of the energy densities of dark energy ( $$\rho _{\textrm{de} }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mtext>de</mml:mtext> </mml:msub> </mml:math> ) and dark matter ( $$\rho _{\textrm{dm} }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mtext>dm</mml:mtext> </mml:msub> </mml:math> ). This analysis utilizes the latest observational datasets, including baryon acoustic oscillation (BAO) measurements from the second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI), type Ia supernova (SNIa) data from the full five-year observations of the Dark Energy Survey (DES), cosmic microwave background (CMB) observations from Planck 2018, observational Hubble parameter data (OHD), and the local measurement of Hubble constant. Using AIC, BIC and Bayes factor, we find that the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model remains the most strongly favored by the data, while the holographic dark energy (HDE) model is ruled out. Relative to the HDE model, the IHDE models provide a significantly better fit to the data, and the interaction can help alleviating the Big Rip problem. Among the ten IHDE models considered, the two with interaction terms $$Q=3\beta H_{\textrm{0} }\rho _{\textrm{de} }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mi>β</mml:mi> <mml:msub> <mml:mi>H</mml:mi> <mml:mtext>0</mml:mtext> </mml:msub> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mtext>de</mml:mtext> </mml:msub> </mml:mrow> </mml:math> and $$Q=3\beta H_{\textrm{0} }\sqrt{\rho _{\textrm{dm} }\rho _{\textrm{de} } }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mi>β</mml:mi> <mml:msub> <mml:mi>H</mml:mi> <mml:mtext>0</mml:mtext> </mml:msub> <mml:msqrt> <mml:mrow> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mtext>dm</mml:mtext> </mml:msub> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mtext>de</mml:mtext> </mml:msub> </mml:mrow> </mml:msqrt> </mml:mrow> </mml:math> , are the most strongly supported by the observational data, where $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> is the coupling parameter. Additionally, the AIC, BIC, and Bayes factor values for the majority of IHDE models are nearly identical, indicating minimal differences in their fitting performance with the current data. This implies that more precise future observations will be necessary to better distinguish between these interaction forms.