In this paper, we update constraints on the Holographic Dark Energy (HDE) model and the Interacting Holographic Dark Energy (IHDE) models in a non-flat universe, building upon our previous work in which the flat HDE and IHDE models were tested using same datasets, including DESI DR2 BAO, the five-year supernovae sample from DES, CMB distance priors, observational Hubble parameter data, and the local measurement of Hubble constant. Our results indicate that in the HDE model, an open universe is supported at $$6\sigma $$ , whereas in the IHDE models a closed universe is favored at over $$3\sigma $$ . The model parameter $\textit{c}$ is anti-correlated with $$H_0$$ in all these models, implying that a resolution to $$H_0$$ tension by reducing the parameter $\textit{c}$ comes at the expense of a Big Rip fate. Furthermore, using AIC, BIC, DIC, and Bayes evidence, we find that within the non-flat framework, the $$\Lambda $$ CDM model remains the most strongly supported by the data, while the HDE model is the most disfavored. Compared with the HDE model, the IHDE models demonstrate markedly improved agreement with the data, and the most strongly supported IHDE model is the one with the interaction term $$Q=3\beta H_{\textrm{0}}\frac{\rho _{\textrm{dm}}\rho _{\textrm{de}}}{\rho _{\textrm{dm}}+\rho _{\textrm{de}}}$$ .

China

Xiaofang Shen

Bing Xu

Kaituo Zhang

Xiangyun Fu

Qihong Huang

Liangliang Ren

Zelin Zhang

Updated observational constraints on interacting holographic dark energy models in a non-flat universe

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 ( $$\rho _{\textrm{de} }$$ ) and dark matter ( $$\rho _{\textrm{dm} }$$ ). 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 $$\Lambda $$ 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 $$Q=3\beta H_{\textrm{0} }\rho _{\textrm{de} }$$ and $$Q=3\beta H_{\textrm{0} }\sqrt{\rho _{\textrm{dm} }\rho _{\textrm{de} } }$$ , are the most strongly supported by the observational data, where $$\beta $$ 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.

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

Based on the entropy of anti-de Sitter black hole, a new holographic dark energy model has been proposed. When the Hubble horizon and particle horizon are chosen as the IR cutoff, the late-time accelerated expansion of universe is realized. In this paper, we consider the Hubble horizon as the IR cutoff to investigate holographic inflation and slow-roll inflation in this model. We find that slow-roll inflation with the chaotic potential $$V_{0}\phi ^{n}$$ is favored by Planck results for some special cases, such as $$n=1/3$$ and $$n=1/2$$ , while holographic inflation is not supported by Planck results. Then, we analyze the reheating temperature and the number of reheating e-folds in this model, and we find that the results favor the cases $$n=1/3$$ and $$n=1/2$$ . Finally, we use the dynamical analysis method, statefinder diagnostic pairs, and the Hubble diagram to analyze this model. Our results indicate that when $$b^{2}$$ takes a small value, this model cannot be distinguished from the standard $$\Lambda $$ CDM model and can serve as an alternative to it.

He Huang

Holographic inflation and holographic dark energy from entropy of the anti-de Sitter black hole

In this work, we propose to utilize the observed ratio of spherically-averaged distance to the sound horizon scale from Baryon Acoustic Oscillation (BAO) data to test the cosmic distance duality relation (CDDR) by comparing the luminosity distances (LDs) obtained from Type Ia supernovae (SNIa) observations with angular diameter distances (ADDs) derived from these ratio measurements, using a cosmological-model-independent method. To match the LDs with the ADDs at the identical redshifts, we employ two methods: a compressed form of the Pantheon sample and a hybrid approach that combines the binning method with an artificial neural network (ANN). The Hubble parameter ( ) at any redshift is reconstructed from the observed Hubble parameter data with the ANN to derive the ADD. To avoid potential biases resulted from the specific prior values of the absolute magnitude $$M_{\textrm{B}}$$ of SNIa and the sound horizon scale $$r_{\textrm{d}}$$ from BAO measurements, we introduce the fiducial parameter $$\kappa \equiv 10^{M_{\textrm{B}} \over 5}\, r_{\textrm{d}}^{3 \over 2} $$ and marginalize their impacts by treating them as nuisance parameters with flat prior distributions in our statistical analysis. Subsequently, we update the measurements of ratio of the transverse comoving distance to the sound horizon scale from the latest BAO data released by the Dark Energy Spectroscopic Instrument (DESI) collaboration for CDDR testing. Our results indicate that BAO observation provides a powerful tool for testing the CDDR, independent of both the absolute magnitude $$M_{\textrm{B}}$$ and sound horizon scale $$r_{\textrm{d}}$$ , as well as any cosmological model.

Fan Yang

Yang Huang

Ying Yang

Testing the cosmic distance duality relation using Type Ia supernovae and BAO observations

In this work, we test the cosmic distance duality relation (CDDR) by comparing the angular diameter distance (ADD) derived from the transverse Baryon Acoustic Oscillations (BAO) data with the luminosity distance (LD) from the Pantheon type Ia supernova (SNIa) sample. The binning method and Gaussian process are employed to match ADD data with LD data at the same redshift. First, we use nonparametric and parametric methods to investigate the impact of the specific prior values of the absolute magnitude  $$M_\textrm{B}$$  <math> <msub> <mi>M</mi> <mtext>B</mtext> </msub> </math>   from SNIa observations and the sound horizon scale  $$r_\textrm{s}$$  <math> <msub> <mi>r</mi> <mtext>s</mtext> </msub> </math>   from transverse BAO measurements on the CDDR tests. The results obtained from the parametric and non-parametric methods indicate that specific prior values of  $$M_\textrm{B}$$  <math> <msub> <mi>M</mi> <mtext>B</mtext> </msub> </math>   and  $$r_\textrm{s}$$  <math> <msub> <mi>r</mi> <mtext>s</mtext> </msub> </math>   lead to significant biases on the CDDR test. Then, to avoid these biases, we propose a method independent of  $$M_\textrm{B}$$  <math> <msub> <mi>M</mi> <mtext>B</mtext> </msub> </math>   and  $$r_\textrm{s}$$  <math> <msub> <mi>r</mi> <mtext>s</mtext> </msub> </math>   to test CDDR by considering the fiducial value of  $$\kappa \equiv 10^{M_\textrm{B} \over 5}r_\textrm{s}$$  <math> <mrow> <mi>κ</mi> <mo>≡</mo> <msup> <mn>10</mn> <mfrac> <msub> <mi>M</mi> <mtext>B</mtext> </msub> <mn>5</mn> </mfrac> </msup> <msub> <mi>r</mi> <mtext>s</mtext> </msub> </mrow> </math>   as a nuisance parameter and then marginalizing its influence with a flat prior in the analysis. No violation of the CDDR is found, and the transverse BAO measurement can be used as a powerful tool to verify the validity of CDDR in the cosmological-model-independent method.

Min Wang

Zhenyan Lu

Testing the cosmic distance duality relation with Type Ia supernova and transverse BAO measurements

Based on the holographic principle and the Barrow entropy, Barrow holographic dark energy had been proposed. In order to analyze the stability and the evolution of Barrow holographic dark energy, we, in this paper, apply the dynamical analysis and statefinder methods to Barrow holographic dark energy with different IR cutoff and interacting terms. In the case of using Hubble horizon as IR cutoff with the interacting term  $$Q=\frac{\lambda }{H}\rho _{m}\rho _{D}$$  <math> <mrow> <mi>Q</mi> <mo>=</mo> <mfrac> <mi>λ</mi> <mi>H</mi> </mfrac> <msub> <mi>ρ</mi> <mi>m</mi> </msub> <msub> <mi>ρ</mi> <mi>D</mi> </msub> </mrow> </math>  , we find this model is stable and can be used to describe the whole evolution of the universe when the energy transfers from the pressureless matter to the Barrow holographic dark energy. When the dynamical analysis method is applied to this stable model, an attractor corresponding to an accelerated expansion epoch exists and this attractor can behave as the cosmological constant. Furthermore, the coincidence problem can be solved in this case. Then, after using the statefinder analysis method to this model, we find this model can be discriminated from the standard  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model. Finally, we have discussed the turning point of Hubble diagram in Barrow holographic dark energy and find the turning point does not exist in this model.

Feiquan Tu

Jun Chen

Dynamical analysis and statefinder of Barrow holographic dark energy

The existence of light sterile neutrinos is a long-standing question in particle physics. Several experimental “anomalies” might be explained by introducing eV mass scaled light sterile neutrinos. Many experiments are actively searching for such light sterile neutrinos through neutrino oscillation. For long baseline experiments, the matter effect should be treated carefully for precise calculation of the neutrino oscillation probabilities. However, this is usually time-consuming or analytically complex. In this manuscript, we adopt a Jacobi-like method to diagonalize the Hermitian Hamiltonian matrix and derive analytically simplified neutrino oscillation probabilities for 3 (active) + 1 (sterile)-neutrino mixing for a constant matter density. These approximations can reach a considerably high numerical accuracy while retaining their analytical simplicity and fast computing speed. This would be useful for current and future long baseline neutrino oscillation experiments.

Bao-Biao Yue

Wei Li

Jia-Jie Ling

Fan-Rong Xu

A compact analytical approximation for a light sterile neutrino oscillation in matter Jiajie Ling acknowledges the support from National Key R&D program of China (2018YFA0404103) and National Natural Science Foundation of China (11775315). F. Xu is supported partially by NSFC (11605076), as well as the FRFCU (Fundamental Research Funds for the Central Universities in China) (21616309)

In this paper, we probe the cosmic opacity with the newest Pantheon type Ia supernovae (SNIa) and the observational Hubble parameter  $$\left( H(z)\right) $$  <math> <mfenced> <mi>H</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mfenced> </math>   data based on the  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM and wCDM models with or without spatial curvature. In the analysis, we marginalize the likelihood function of SNIa data over the pertinent nuisance parameter  $${\mathcal {M}}$$  <math> <mi>M</mi> </math>  , a combination of the absolute magnitude of SNIa  $$M_{\mathrm{B}}$$  <math> <msub> <mi>M</mi> <mi>B</mi> </msub> </math>   and the Hubble constant  $$H_0$$  <math> <msub> <mi>H</mi> <mn>0</mn> </msub> </math>  , with a flat prior. Two parameterizations of the optical depth  $$\tau (z)$$  <math> <mrow> <mi>τ</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </math>   associated to the cosmic absorption, namely  $$\tau (z)=2\varepsilon z$$  <math> <mrow> <mi>τ</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> <mo>=</mo> <mn>2</mn> <mi>ε</mi> <mi>z</mi> </mrow> </math>   and  $$\tau (z)= (1+z)^{2\varepsilon }-1$$  <math> <mrow> <mi>τ</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mi>ε</mi> </mrow> </msup> <mo>-</mo> <mn>1</mn> </mrow> </math>  , are adopted. We find that the results are not sensitive to the fiducial cosmological models, the spatial curvature and parameterizations of  $$\tau (z)$$  <math> <mrow> <mi>τ</mi> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> </math>  . Moreover, the results from the Pantheon data alone are consistent with a transparent universe ( $$\varepsilon =0$$  <math> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0</mn> </mrow> </math>  ). And once the H(z) data is combined,  $$\varepsilon =0$$  <math> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0</mn> </mrow> </math>   falls within the 68% confidence level (CL) of the best fit when a flat  $$H_0$$  <math> <msub> <mi>H</mi> <mn>0</mn> </msub> </math>   prior or the distance priors are used, while it falls within the 95% CL when a Gaussian distribution prior of  $$H_0=74.03\pm 1.42$$  <math> <mrow> <msub> <mi>H</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>74.03</mn> <mo>±</mo> <mn>1.42</mn> </mrow> </math>   km  $$\mathrm {s}^{-1}\, \mathrm {Mpc}^{-1}$$  <math> <mrow> <msup> <mrow> <mi>s</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mspace width="0.166667em"></mspace> <msup> <mrow> <mi>Mpc</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math>   is used.