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 investigated the effect of an isospin chemical potential ( $ \mu_{I} $ ) within the quark-meson model, which approximates quantum chromodynamics (QCD) by modeling low-energy phenomena such as chiral symmetry breaking and phase structure under varying conditions of temperature and chemical potential. Using the functional renormalization group (FRG) flow equations, we calculated the phase diagram in the chiral limit within the two-flavor quark-meson model in a finite $ \mu_{I} $ with $\textit{ρ}$ vector meson interactions. Fluctuation effects significantly decrease the critical chemical potential from the mean-field (MF) value $\mu_{I,{\rm MF}} \gt m_\rho$ to a lower value at which the $\textit{ρ}$ vector meson condensates alongside the chiral condensate once the isospin chemical potential exceeds the critical value $ \mu_{I}^{{\rm{crit}}} $ . This $\textit{ρ}$ condensation was investigated numerically for different meson coupling strengths. The $\textit{ρ}$ meson dominated region is delineated from other phases by a second-order phase transition at lower $ \mu_{I} $ and a first-order transition at slightly higher $ \mu_{I} $ .

Mohammed Osman

Defu Hou

Wentao Wang

United States

Hui Zhang

Functional renormalization group study of $\textit{ρ}$ meson condensate at a finite isospin chemical potential in the quark meson model * Supported in part by the National Key Research and Development Program of China (2022YFA1604900). This work is also partly supported by the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Hui Zhang acknowledges the financial support from the Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008) and the National Natural Science Foundation of China (12047523, 12105107)

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 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.

Probing cosmic opacity with the type Ia supernovae and Hubble parameter

We present a systematic short time expansion for the generating function of the one point height probability distribution for the KPZ equation with droplet initial condition, which goes much beyond previous studies. The expansion is checked against a numerical evaluation of the known exact Fredholm determinant expression. We also obtain the next order term for the Brownian initial condition. Although initially devised for short time, a resummation of the series allows to obtain also the long time large deviation function, found to agree with previous works using completely different techniques. Unexpected similarities with stationary large deviations of TASEP with periodic and open boundaries are discussed. Two additional applications are given. (i) Our method is generalized to study the linear statistics of the Airy point process, i.e. of the GUE edge eigenvalues. We obtain the generating function of the cumulants of the empirical measure to a high order. The second cumulant is found to match the result in the bulk obtained from the Gaussian free field by Borodin and Ferrari [1,2], but we obtain systematic corrections to the Gaussian free field (higher cumulants, expansion towards the edge). This also extends a result of Basor and Widom [3] to a much higher order. We obtain large deviation functions for the Airy point process for a variety of linear statistics test functions. (ii) We obtain results for the counting statistics of trapped fermions at the edge of the Fermi gas in both the high and the low temperature limits.

France

Alexandre Krajenbrink

Pierre Le Doussal

Sylvain Prolhac

Systematic time expansion for the Kardar–Parisi–Zhang equation, linear statistics of the GUE at the edge and trapped fermions

We improve the Monte-Carlo based QCD sum rules by introducing the rigorous Hölder-inequality-determined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function. In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum. Therefore, an unbiased prediction can be obtained for the phenomenological parameters (the hadronic mass and width etc.). We test the new approach in the ρ meson channel with re-examination and inclusion of αs corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels.

Qi-Nan Wang

Canada

Zhu-Feng Zhang

T.G. Steele

Hong-Ying Jin

Zhuo-Ran Huang

A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rulesSupported by NSFC (11175153, 11205093, 11347020), Open Foundation of the Most Important Subjects of Zhejiang Province, and K. C. Wong Magna Fund in Ningbo University, TGS is Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), Z. F. Zhang and Z. R. Huang are Grateful to the University of Saskatchewan for its Warm Hospitality

We investigate the running cosmological constant model with dark energy linearly proportional to the Hubble parameter, Λ=σH+Λ0 , in which the ΛCDM limit is recovered by taking σ=0 . We derive the linear perturbation equations of gravity under the Friedmann–Lemaïtre–Robertson–Walker cosmology, and show the power spectra of the CMB temperature and matter density distribution. By using the Markov chain Monte Carlo method, we fit the model to the current observational data and find that σH0/Λ0≲2.63×10−2 and 6.74×10−2 for Λ(t) coupled to matter and radiation-matter, respectively, along with constraints on other cosmological parameters.

Taiwan

Chao-Qiang Geng

Chung-Chi Lee

Running cosmological constant with observational tests

With the assumption that a perfect fluid with a constant equation of state is the only energy component on the brane, we study the stability of Einstein static state solution under homogeneous and inhomogeneous scalar perturbations in both spatially flat Randall–Sundrum (RS) and Shtanov–Sahni (SS) braneworlds. We find that if the perfect fluid has a phantom-like property and the “Weyl fluid” originating from the projection of the bulk Weyl tensor onto the brane behaves like a radiation with positive energy density, the Einstein static state solution is stable in the SS braneworld, but unstable in the RS one. Furthermore, we demonstrate that the static state solution is also stable in the bulk with a timelike extra dimension. Thus, in the model where the extra dimension is timelike, our universe can stay at the Einstein static state past-eternally, which means that the big bang singularity might be resolved successfully by an emergent scenario.

Puxun Wu

Hongwei Yu

Ling-Wei Luo

Stability of Einstein static state universe in the spatially flat branemodels