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Using gamma-ray bursts as standard candles for cosmological parameter constraints rely on their empirical luminosity relations and low-redshift calibration. In this paper, we examine the Amati relation and its potential corrections based on the A118 sample of higher-quality gamma-ray bursts, using both Hubble data set and Pantheon+ samples as calibration samples in the redshift range of z < 1.965. In calibrating gamma-ray bursts using these two datasets, we employ Gaussian processes to obtain corresponding Hubble diagrams to avoid the dependence on cosmological models in the calibration process. We first divided the low-redshift sample of GRBs into two bins and examined the Amati relation and its potential modifications. We found that under both calibrations, the Amati relation did not show evidence of redshift evolution (68% confidence level). For the other two Amati relations that include redshift evolution terms, the central values of the redshift evolution coefficients deviated from 0, but due to the limitations of the sample size and the increase in the number of parameters, most of the redshift evolution coefficients were not able to be excluded from 0 at the 1 sigma level. Therefore, to assess their situation across the entire redshift range, we employed MCMC to globally fit three types of Amati relations. By computing AIC and BIC, we found that for the GRB A118 sample, the standard Amati relation remains the most fitting empirical luminosity formula, and no potential redshift evolution trend was observed for two different low-redshift calibrating sources.

The basic premise of using HII starburst galaxies (HIIGs) as cosmic "standard candels" is that there is a significant correlation between the H$\beta$ luminosity ($L$) and the velocity dispersion ($\sigma$) of the ionized gas from HIIGs measurements, which can be called as the empirical $L$ - $\sigma$ relation. However, the scaling $L$ - $\sigma$ relation well-calibrated with the lower-redshift HIIGs is unfitted for the higher-redshift HIIGs. To solve this problem, we explore new relational expression for the $L$ - $\sigma$ relation which should be suitable for both lower-redshift and higher-redshift HIIGs. After reconstructing the Hubble diagram with the Gaussian process (GP) method from the Pantheon+ supernovae Ia sample, we examine and compare six different revised formulas of $L$ - $\sigma$ relation. Furthermore, we use the Bayesian evidence to compare the revised $L$ - $\sigma$ relations with the analysis of a joint sample of 36 giant extragalactic HII regions (GEHRs) and 145 HIIGs. It turns out that the redshift-dependent bilinear correction and the quadratic $\sigma$ based correction are significantly better than the others. Moreover, a quadratic $\sigma$ based correction is the most supported one. It suggests that the appropriate corrections to the $L$ - $\sigma$ relation should be considered when the HIIGs are used as a kind of cosmological probes., Comment: 12 pages, 4 figures

In this paper, we introduce two coupling models of early dark energy (EDE) and cold dark matter aimed at alleviating cosmological tensions. We utilize the EDE component in the coupling models to relieve the Hubble tension, while leveraging the interaction between dark matter and dark energy to alleviate the large-scale structure tension. The interaction is implemented in the form of pure momentum coupling and Yukawa coupling. We employed various cosmological datasets, including cosmic microwave background radiation, baryon acoustic oscillations, Type Ia supernovae, the local distance-ladder data (SH0ES), and the Dark Energy Survey Year-3 data, to analyze our models. We first exclude SH0ES data from the entire dataset to constrain the parameters of novel models. We observe that the constraints on $H_0$ from two coupling models are slightly higher than that from the $\Lambda$CDM model, but they exhibit a significant inconsistency with the SH0ES data, consistent with prior research findings in the EDE model. Subsequently, we incorporate SH0ES data to re-constrain the parameters of various models, our findings reveal that both coupling models yield best-fit values for $H_0$ approximately around $72.23$ km/s/Mpc, effectively mitigating the Hubble tension. Similar to the EDE model, the coupling models yield the $S_8$ values that still surpasses the result of the $\Lambda$CDM model. Nevertheless, the best-fit values for $S_8$ obtained with the two new models are 0.8192 and 0.8177, respectively, which are lower than the 0.8316 achieved by the EDE model. Consequently, although our coupling models fail to fully resolve the large-scale structure tension, they partially mitigate the adverse effect of the original EDE model., Comment: 14 pages, 9 figures. In this replacement, we have amalgamated the original content of this manuscript with that of a previous paper [arXiv:2310.09798]. arXiv admin note: substantial text overlap with arXiv:2310.09798

In this paper, we investigate the momentum coupling between early dark energy (EDE) and cold dark matter to alleviate cosmological tensions. EDE has exhibited promising efficacy in addressing the Hubble tension, but it exacerbates the large-scale structure tension. We consider the interaction between EDE and cold dark matter, introducing a pure momentum exchange between them to alleviate the large-scale structure tension introduced by the EDE model. We find that this coupling model is consistent with the EDE model, yielding a higher value for $H_0$, which can resolve the Hubble tension. Additionally, the new model exhibits a suppressive effect on structure growth, contributing to the alleviation of the large-scale structure tension. By utilizing the Markov Chain Monte Carlo method and incorporating various cosmological data, the coupling model constrains the best-fit values for $H_0$ to be $72.23$ km/s/Mpc and for $S_8$ to be 0.8192. Compared to the $\Lambda$CDM model, the new models have not fully resolved the large-scale structure tension. However, in contrast to the best-fit value of 0.8316 for $S_8$ obtained from the EDE model, the new model alleviates the negative impact of the EDE model., Comment: This paper has been merged into the latest version of another paper, [arXiv:2312.01410]

In this paper, we investigate the process in which axion dark matter undergoes thermal friction, resulting in energy injection into dark radiation, with the aim of mitigating the Hubble tension and large-scale structure tension. In the early universe, this scenario led to a rapid increase in the energy density of dark radiation; in the late universe, the evolution of axion dark matter is similar to that of cold dark matter, with this scenario resembling decaying dark matter and serving to ease the large-scale structure tension. We employ cosmological observational data, including cosmic microwave background (CMB), baryon acoustic oscillation (BAO), supernova data (SNIa), $H_0$ measurement from SH0ES, and $S_8$ from the Dark Energy Survey Year-3 (DES), to study and analyze this model. Our results indicate that the thermal friction model offers partial alleviation of the large-scale structure tension, while its contribution on alleviating Hubble tension can be ignored. The new model yields the value of $S_8$ is $0.795\pm 0.011$ at a 68% confidence level, while the $\Lambda$CDM model yields a result of $0.8023\pm 0.0085$. In addition, the new model exhibits a lower $\chi^2_\mathrm{tot}$ value, with a difference of -2.60 compared to the $\Lambda$CDM model. Additionally, we incorporate Lyman-$\alpha$ data to re-constrain the new model and find a slight improvement in the results, with the values of $H_0$ and $S_8$ being $68.76^{+0.39}_{-0.35}$ km/s/Mpc and $0.791\pm 0.011$ at a 68% confidence level, respectively., Comment: 12 pages, 8 figures

In this paper, we investigate the kinetically coupled early dark energy (EDE) and scalar field dark matter to address cosmological tensions. The EDE model presents an intriguing theoretical approach to resolving the Hubble tension, but it exacerbates the large-scale structure tension. We consider the interaction between dark matter and EDE, such that the drag of dark energy on dark matter suppresses structure growth, which can alleviate large-scale structure tension. We replace cold dark matter with scalar field dark matter, which has the property of suppressing structure growth on small scales. We employed the Markov Chain Monte Carlo method to constrain the model parameters, our new model reveals a non-zero coupling constant of $0.030 \pm 0.026$ at a 68% confidence level. The coupled model yields the Hubble constant value of $72.38^{+0.71}_{-0.82}$ km/s/Mpc, which resolves the Hubble tension. However, similar to the EDE model, it also obtains a larger $S_8$ value compared to the $\Lambda$CDM model, further exacerbating the large-scale structure tension. The EDE model and the new model yield the best-fit values of $0.8316$ and $0.8146$ for $S_8$, respectively, indicating that the new model partially alleviates the negative effect of the EDE model. However, this signature disappears when comparing marginalised posterior probabilities, and both models produce similar results. The values obtained from the EDE model and the new model are $0.822^{+0.011}_{-0.0093}$ and $0.819^{+0.013}_{-0.0092}$, respectively, at a 68% confidence level., Comment: 11 pages, 8 figures

The Hubble constant ${H}_0$ is a crucial parameter in cosmology. However, different cosmic observations have resulted in varying posterior results for ${H}_0$, leading to what is known as the ${H}_0$ tension. In order to address this issue, it is beneficial to use other dataset to constrain ${H}_0$. In this paper, via the cosmographic approach based on the Friedman-Lemaitre-Robertson-Walker (FLRW) metric to the dispersion measure of the intergalactic medium ${\rm{DM}}_{\rm{IGM}}(z)$ of Fast Radio Bursts (FRBs), we obtain the Taylor expansion of $\langle{\rm{DM}}_{\rm{IGM}}(z)\rangle$ in terms redshift $z$. The result for Hubble constant $H_0=65.5^{+6.4}_{-5.4}$ ${\rm{km~s^{-1}~Mpc^{-1}}}$ $(68$$\%$ ${\rm{C.L.}}) $, cosmological deceleration parameter $q_0=-0.50\pm 0.20 $ and the jerk parameter $j_0=-0.1^{+2.0}_{-2.5}$ using uncalibrated Supernova Ia (SNe Ia) Pantheon dataset combined with 18 localized FRBs are obtained. To demonstrate the impact of parameter degeneracies on our analysis methods, we compare the results using three different forms of $f_{\rm{IGM}}(z)$ and two different prior distributions for $\Omega_{\rm{b,0}}$. Then we find that the uncertainty in $H_0$ is not significantly affected by the prior range of $f_{\rm{IGM}}(z)$ and $\Omega_{\rm{b,0}}$, but the mean value is influenced by the priors for $f_{\rm{IGM}}(z)$ and $\Omega_{\rm{b,0}}$ due to parameter degeneracies with $H_0$. Employing $f_{\rm{IGM}}(z)$ that evolves with redshift, we obtain the constraints for $H_0=69.0^{+6.7}_{-5.7}$ ${\rm{km~s^{-1}~Mpc^{-1}}}$. Furthermore, the mock analyses give a posterior estimation of $H_0$ with an accuracy of 4.6\% and higher precision for $q_0$ and $j_0$ in the near future.

In this paper, we investigate the interaction between early dark energy (EDE) and scalar field dark matter, proposing a coupled scalar fields model to address the Hubble tension and $S_8$ tension. While the EDE model successfully alleviates the Hubble tension, it exacerbates the $S_8$ tension. To mitigate the negative impact of EDE, we introduce the interaction between EDE and dark matter. Specifically, we replace cold dark matter with scalar field dark matter, given its capability to suppress structure growth on small scales. We constrained the new model using cosmological observations including the temperature and polarization anisotropy power spectra data of cosmic microwave background radiation (CMB) from \textit{Planck} 2018 results, baryon acoustic oscillations (BAO) measurements extracted from 6dFGS, SDSS and BOSS, the Pantheon sample of type Ia supernovae (SNIa), the local distance-ladder data (SH0ES), and the Dark Energy Survey Year-3 data. Employing Markov Chain Monte Carlo method, we find that this novel model yields best-fit values of $H_0$ and $S_8$ equal to $71.13$ km/s/Mpc and $0.8256$, respectively. Compared to the $\Lambda$CDM model, the new model alleviates the Hubble tension but still fails to resolve the $S_8$ tension. However, we obtain a smaller value of $S_8$ compared to the result of $0.8316$ obtained for EDE model, which mitigates to some extent the shortcoming of the EDE model., Comment: 11 pages, 7 figures

In this paper, a modified factor $\mu$, which characterizes modified gravity in the linear matter density perturbation theory, is reconstructed in a data-driven and almost model-independent way via Gaussian process by using currently available cosmic observations. Utilizing the Pantheon+ SNe Ia samples, the observed Hubble parameter $H(z)$ and the redshift space distortion $f\sigma_8(z)$ data points, one finds out a time varying $\mu$ at low redshifts. The reconstructed $\mu$ implies that more complicated modified gravity beyond the simplest general relativity and the Dvali-Gabadadze-Porrati braneworld model is required., Comment: 14 pages, 3 figures

In this paper, we firstly calibrate the Amati relation (the $E_{\rm p}-E_{\rm iso}$ correlation) of gamma ray bursts (GRBs) at low redshifts ($z<0.8$) via Gaussian process by using the type Ia supernovae samples from Pantheon+ under the philosophy that objects at the same redshift should have the same luminosity distance in any cosmology. As a result, this calibration derives the distance moduli of GRBs at high redshifts ($z>0.8$). For an application of these derived distance modulus of GRBs to cosmology, via Gaussian process again, a series of cosmography parameters, which describe kinematics of our Universe, up to the fifth oder and the redshift $z\sim 5$, i.e. the Hubble parameter $H(z)$, the deceleration parameter $q(z)$, the jerk parameter $j(z)$, the snap parameter $s(z)$ and the lerk parameter $l(z)$, are reconstructed from the cosmic observations. The reconstructed cosmography parameters show a transition singularity at $z\sim 6$, it may resort to two possible explanations: one is that the GRBs data points at high redshift $z>5$ are still reliable, it means that new physics beyond the $\Lambda$CDM model happens; another one is that the quality and quantity of GRBs data points at high redshift $z>5$ are not good enough to give any viable prediction of the kinematics of our Universe. To pin down this problem, more high redshifts $z>5$ cosmic observational are still needed., Comment: 22 pages, 6 figures and 1 table. to appear in JCAP

The Hubble horizon at matter-radiation equality ($k^{-1}_{\rm{eq}}$) and the sound horizon at the last scattering surface ($r_s(z_*)$) provides interesting consistency check for the $\Lambda$CDM model and its extensions. It is well known that the reduction of $r_s$ can be compensated by the increase of $H_0$, while the same is true for the standard rulers $k_{\rm{eq}}$. Adding extra radiational component to the early universe can reduce $k_{\rm{eq}}$. The addition of early dark energy (EDE), however, tends to increase $k_{\rm{eq}}$. We perform $k_{\rm{eq}}$- and $r_s$-based analyses in both the EDE model and the Wess-Zumino Dark Radiation (WZDR) model. In the latter case we find $\Delta H_0 = 0.4$ between the $r_s$- and $k_{\rm{eq}}$-based datasets, while in the former case we find $\Delta H_0 = 1.2$. This result suggests that the dark radiation scenario is more consistent in the fit of the two standard rulers ($k_{\rm{eq}}$ and $r_s$). As a forecast analyses, we fit the two models with a mock $k_{\rm{eq}}$ prior derived from \emph{Planck} best-fit $\Lambda$CDM model. Compared with the best-fit $H_0$ in baseline $\Lambda$CDM model, we find $\Delta H_0 = 1.1$ for WZDR model and $\Delta H_0 = - 2.4$ for EDE model., Comment: 12 pages, 7 figures

In this work, we explore the phenomenology of generalized dark matter (GDM) which interacts with photons ($\gamma$). We assume that DM establishes elastic scattering with $\gamma$ when it has already become nonrelativistic, otherwise the abundance of DM today is disfavored by current observations. Within this scenario, the equation of state (EoS) of DM is determined by its mass ($m_\chi$) and the DM-$\gamma$ scattering cross-section. The distinctive imprints of a nonzero EoS of DM on CMB angular power spectrum allow us to set a lower limit on $m_\chi$ with Planck 2018 data alone, i.e., $m_{\chi} > 8.7$ keV at $95\%$ C.L. In the study of cosmic concordance problems, we find that the GDM scenario preserves the sound horizon ($r_s(z_*)$) predicted in the fiducial $\Lambda$CDM model, and thus does not solve the $H_0$ tension. When performing the joint analysis of Planck+LSS datasets, the best-fit $S_8= 0.785\pm 0.017$ closely matches the given $S_8$ prior. This suggests that the GDM scenario can be counted as a viable candidate to restore the $S_8$ ($\sigma_{8}$) tension., Comment: 14 pages, 9 figures

We investigate the general properties of a class of scalar-field dark energy models (i.e., $\phi$CDM models) which behave like cosmological trackers at early times. Particularly, we choose three $\phi$CDM models with typical potentials, i.e., $V(\phi)\propto \phi^{-\alpha}$ (inverse power-law (IPL) model), $V(\phi)\propto \coth^{\alpha}{\phi}$ (L-model) and $V(\phi)\propto \cosh(\alpha\phi)$ (Oscillatory tracker model), where the latter two models are based on the $\alpha$-attractors originated from the study of inflation. These models, which reduce to the $\Lambda$CDM model with $\alpha \to 0$, are studied and compared with the recent observations, including the Pantheon sample of type Ia supernovae (SNe Ia), baryon acoustic oscillations (BAO) measurements extracted from 6dFGS, BOSS and eBOSS, as well as the temperature and polarization anisotropy power spectra data of cosmic microwave background radiation (CMB) from Planck 2018 results. The observational constraints from the combining sample (SNe Ia + BAO + CMB) indicate that none of the three $\phi$CDM models exclude the $\Lambda$CDM model at $68.3\%$ confidence level. We find that the CMB anisotropy data have obvious advantages in constraining the dark energy models compared with other cosmological probes, which is particularly evident in the L-model. Furthermore, we apply the Bayesian evidence to compare the $\phi$CDM models and the $\Lambda$CDM model with the analysis of the combining sample. The concordance $\Lambda$CDM model is still the most supported one. In addition, among the three $\phi$CDM models, the IPL model is the most competitive one, while the L-model/Oscillatory tacker model is moderately/strongly disfavored., Comment: 18 pages, 4 figures, 1 table; Accepted for publication in Physics of the Dark Universe (PDU)