Ya-Bo Wu

In this paper, in the Starobinsky gravity (SG) model, the gravitational wave (GW) luminosity distance $$d_L^{GW}(z)$$ d L GW ( z ) is analytically and numerically investigated by considering the dark matter as the two different kinds of shear viscous fluids in universe. Concretely, on the basis of the propagation equation of the metric perturbation derived by using transverse-traceless gauge for the linear perturbation of the metric in FRW background, we obtain the analytical expressions of the modified friction term $$\delta (z)$$ δ ( z ) and the ratio $$d_L^{GW}(z)/d_L^{EM}(z)$$ d L GW ( z ) / d L EM ( z ) of GW to electromagnetic (EM) wave luminosity distance, and find that they only depend on the SG model parameter $$\alpha $$ α and the shear viscous coefficient $$\eta $$ η , regardless of the bulk viscous coefficient $$\zeta $$ ζ . Evidently, both of them are affected by $$\alpha $$ α and $$\eta $$ η . It worth stressing that the results given by us can reduce to ones in documents [13, 22, 30]. It follows that we can extend the previous results as the special cases in our model. Furthermore, by combining the latest observational data, we more tightly constrain the values of related parameters and numerically analyze the influence of both $$\alpha $$ α and $$\eta $$ η on $$\delta (z)$$ δ ( z ) and $$d_L^{GW}(z)/d_L^{EM}(z)$$ d L GW ( z ) / d L EM ( z ) . We observe that, in the range of $$0< z\le 8.2$$ 0 < z ≤ 8.2 , the evolutionary curves of $$\delta (z)$$ δ ( z ) and $$d_L^{GW}(z)/d_L^{EM}(z)$$ d L GW ( z ) / d L EM ( z ) exhibit that $$\delta (z)$$ δ ( z ) ( $$d_L^{GW}(z)/d_L^{EM}(z)$$ d L GW ( z ) / d L EM ( z ) ) monotonically decrease (increase) as redshift rises, moreover there are always $$\delta (z)<0$$ δ ( z ) < 0 and $$d_L^{GW}(z)\ge d_L^{EM}(z)$$ d L GW ( z ) ≥ d L EM ( z ) , specially $$d_L^{GW}(0)=d_L^{EM}(0)$$ d L GW ( 0 ) = d L EM ( 0 ) in the limit of $$z\rightarrow 0$$ z → 0 , which means that detecting GW signals might represent a more efficient tool than detecting EM signals to test modified gravity model on the given scale of cosmic distances. It is worth noting that the numerical analyses to $$\delta (z)$$ δ ( z ) and $$d_L^{GW}(z)/d_L^{EM}(z)$$ d L GW ( z ) / d L EM ( z ) illustrate once again that the GW luminosity distance $$d_L^{GW}(z)$$ d L GW ( z ) is indeed influenced by $$\alpha $$ α and $$\eta $$ η , in particular more sensitive to $$\alpha $$ α than $$\eta $$ η in our model. In addition, by comparing the GW and EM luminosity distances of SG model with $$d_{L(GR)}$$ d L ( G R ) of Einstein GR, we find that the GW and EM signals in SG1 and SG2 change from stronger to weaker than the ones in GR as redshift increases and more difficultly to be detected in the same distance and detection sensitivity. Meanwhile, the EM signals change from strong to weak earlier than GW signals do. Finally, we confirm that $$\delta (z)$$ δ ( z ) and $$d_L^{GW}(z)$$ d L GW ( z ) of our model meet the constraints imposed by the standard siren GW170817 and its electromagnetic companion GRB170817A.

In this paper, in the framework of massive gravity, the holographic entanglement entropy (HEE) and holographic subregion complexity (HSC) are numerically investigated by means of the RT formula and the subregion CV conjucture for holographic superconductor with backreaction. We find that both the HEE and HSC exhibit discontinuity of slope at critical temperature, hence both of them are able to reflect the information of phase transition in the holographic superconducting system. Different from the previous studies, the HEE and HSC as function of strip-width are not always lower in the superconducting phase than ones in the normal phase, in particular the HSC decreases linearly as the subregion increases for positive coupling parameters. We notice that when the coupling parameters $$\alpha $$α and $$\beta $$β are taken as positive values, the HSC behaves in the same way as HEE, but when they are negative, the HSC has many different behaviors from HEE. Furthermore, we also observe that the HEE and HSC in the superconducting phase illustrate a tendency to converge to the same value as the temperature approaches zero, regardless of the coupling parameters of model. It is worth mentioning that in the massless gravity limit (the coupling parameters $$\alpha =0$$α = 0 and $$\beta =0$$β = 0 ), the results given by us are consistent with the case of holographic superconductor with backreaction from Einstein gravity.

The present work deals with two kinds of k-essence dark energy models within the framework of loop quantum cosmology (LQC). The two kinds of k-essence models originates from two forms of Lagrangians, i.e., ${\mathcal{L}}_1=F\left(X\right)V(\varphi )$ and ${\mathcal{L}}_2=F\left(X\right)-V(\varphi )$, where $F\left(X\right)$ and $V(\varphi )$ stand for the kinetic term and potential of the scalar field $\varphi$, respectively. Two models are based on different phase variables settings, and the general form of autonomous dynamical system is deduced for each Lagrangian. Then, the dynamical stabilities of the critical points in each model are analysed in different forms of $F\left(X\right)$ and $V(\varphi )$. Model I is a 3-dim system with four stable points, and Model II is a 4-dim system but reduced to a 3-dim system using the symmetry analysis, which has five stable points. Moreover, the corresponding cosmological quantities, such as ${\Omega }_{\varphi }$, $w_{\varphi }$ and q, are calculated at each critical point. To compare these with the case of the classical Einstein cosmology (EC), the dynamical evolutionary trajectories in the phase space and evolutionary curves of the cosmological quantities are drawn for both EC and LQC cases, which shows that the loop quantum gravity effects diminish in the late-time universe but are significant in the early time. Further, the effects of interaction $Q=\alpha H{\rho }_m$ on the evolutions of the universe are discussed. With the loop quantum gravity effects, bouncing universe is achieved in both models for different initial values of ${\varphi }_0$, ${\dot{\varphi }}_0$, $H_0$, ${\rho }_0$ and coupling parameter $\alpha$, which helps to avoid singularities. However, the interaction has little effect on bounce, although it is important to the stability of some critical points.

In recent years discrepancies have emerged in measurements of the present-day rate of expansion of the universe $H_0$ and in estimates of the clustering of matter $S_8$. Using the most recent cosmological observations we reexamine a novel model proposed to address these tensions, in which cold dark matter disintegrates into dark radiation. The disintegration process is controlled by its rate $Q = \alpha \mathcal{H} \rho_{\rm ddm}$, where $\alpha$ is a (constant) dimensionless parameter quantifying the strength of the disintegration mechanism and $\mathcal{H}$ is the conformal Hubble rate in the spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker universe and $\rho_{\rm ddm}$ is the energy density of the disintegrating cold dark matter. We constrain this model with the latest 2018 Planck temperature and polarization data, showing that there is no evidence for $\alpha \neq 0$ and that it cannot solve the $H_0$ tension below $3\sigma$, clashing with the result obtained by analyzing the Planck 2015 temperature data. We also investigate two possible extensions of the model in which the dark energy equation-of-state parameter $w \neq -1$. In this case it is possible to combine Planck data with the SH0ES measurement, and we demonstrate that in both these models the $H_0$ tension is resolved at the $1\sigma$ level, but the condition $w \neq -1$ exacerbates the $S_8$ tension. We also demonstrate that the addition of intermediate-redshift data (from the Pantheon supernova type Ia dataset and baryon acoustic oscillations) weakens the effectiveness of all these models to address the $H_0$ and $S_8$ tensions.

We investigate the cosmological evolution of the power law k-essence dark energy (DE) model with interaction in FRWL spacetime with the Lagrangian that contains a kinetic function $F(X)=-\sqrt{X}+X$. Concretely, the cosmological evolution in this model are discussed by the autonomous dynamical system and its critical points, together with the corresponding cosmological quantities, such as ${\mathsf{\Omega }}_{\varphi }$, $w_{\varphi }$, $c_s^2$, and q, are calculated at each critical point. The evolutionary trajectories are drawn in order to show the dynamical process on the phases plan around the critical points. The result that we obtained indicates that there are four dynamical attractors, and all of them correspond to an accelerating expansion of universe for certain potential parameter and coupling parameter. Besides that, the geometrical diagnostic by the statefinder hierarchy $S_3^{(1)}$ and $S_4^{(1)}$ of this scalar field model are numerically obtained by the phase components, as an extended null diagnostic for the cosmological constant. This diagnostic shows that both the potential parameter $\lambda$ and interaction parameter $\alpha$ play important roles in the evolution of the statefinder hierarchy.

At the probe approximation, we construct a holographic p-wave conductor/superconductor model in the five-dimensional Lifshitz black hole with the Weyl correction via both numerical and analytical methods, and study the effects of the Lifshitz parameter z as well as the Weyl parameter $$\gamma $$γ on the superconductor model. As we take into account one of the two corrections separately, the increasing z ( $$\gamma $$γ ) inhibits(enhances) the superconductor phase transition. When the two corrections are considered comprehensively, they display the obviously competitive effects on both the critical temperature and the vector condensate. In particular, the promoting effects of the Weyl parameter $$\gamma $$γ on the critical temperature are obviously suppressed by the increasing Lifshitz parameter. Meanwhile, in the case of $$z<2.35$$z < 2.35 ( $$z>2.35$$z > 2.35 ), the condensate at lower temperature decreases(increases) with the increasing Weyl parameter $$\gamma $$γ . What is more, the difference among the condensate with the fixed Weyl parameter( $$\gamma =-\frac{6}{100},0,\frac{4}{100}$$γ = - 6 100 , 0 , 4 100 ) decreases(increases) with the increasing Lifshitz parameter z in the region $$z<2.35$$z < 2.35 ( $$z>2.35$$z > 2.35 ). Furthermore, the increasing z obviously suppresses the real part of conductivity for all value of the Weyl parameter $$\gamma $$γ . In addition, the analytical results agree well with the ones from the numerical method.