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We investigate the linear cosmological perturbations in the context of the so-called energy-momentum squared gravity (EMSG) theory. Recent researches show that the EMSG theory can reproduce viable background cosmological evolution comparable to $\Lambda$CDM, while the matter-dominated era exhibits slight distinctions. In this paper, we mainly focus on the power-law EMSG models and derive the equations for the linear cosmological perturbations. We explore the propagation of the gravitational wave (GW) and the growth of matter density perturbation at the first order, and estimate the model parameters from the simulated GW data and the observed redshift space distortion data. Our analysis reveals that the model parameters should be small and positive in $1\sigma$ confidence interval, which indicates that the theory is in good agreement with the observational data and can be regarded as an alternative for the standard cosmological model., Comment: 11 pages, 2 figures

In this paper, we study the influence of the parameters for the accelerating Kerr-Newman black hole on the shadows and the constraints, extensively. We find that the rotating parameter $a$, the charge parameter $e$, and the inclination angle $\theta_0$ affect the shadow qualitatively similar to that of Kerr-Newman black holes. The result shows that the size of the shadow will scale down with the accelerating factor $A$. Besides, the factor $A$ also can affect the best viewing angles, which make the observations maximum deviate from $\theta_0=\frac{\pi}{2}$, and the degree of the deviations are less than $1\%$. Then, we assume the M87* as an accelerating Kerr-Newman black hole with the mass $M=6.5\times10^9M_\odot$ and the distance $r_0=16.8Mpc$. Combining the EHT observations, we find that neither the observations, circularity deviation $\Delta C$ or axial ratio $D_x$ can distinguish the accelerating black hole or not. However, the characteristic areal-radius of the shadow curve $R_a$ can give corresponding constraints on the parameters of the accelerating Kerr-Newman black hole. The results shows that the bigger accelerating factor $A$ is, the stronger constraints on the rotating parameter $a$ and charged parameter $e$. {The maximum range of the accelerating factor is $Ar_0\leq0.558$ for a accelerating Schwarzschild case with $(a/M=e/M=0)$, and for an extremely slow accelerating case $(Ar_0\leq0.01)$, the ranges of rotating parameter $a$ and charged parameter $e$ are $a/M\in(0,1)$ and $e/M\in(0,0.9)$., Comment: 9 pages, 16figures

In this paper, we present several explicit reconstructions for {the aether scalar tensor (AeST) theory} derived from the background of Friedmann-Lema$\hat{\text{\i}}$tre-Robertson-Walker cosmological evolution. It is shown that the Einstein-Hilbert Lagrangian with a positive cosmological constant is the only Lagrangian capable of accurately replicating the exact expansion history of the $\Lambda$ cold dark matter ($\Lambda$CDM) universe filled solely with dust-like matter. However, the $\Lambda$CDM-era can be produced within the framework of the AeST theory for some other fluids, including a perfect fluid with $p=-(1/3)\rho$, multifluids, and nonisentropic perfect fluids. Moreover, we demonstrate that the $\Lambda$CDM-era also can be replicated with no real matter field for the AeST theory. The cosmic evolution resulting from both the power-law and de-Sitter solutions also can be obtained.

As is well-known, black hole plays an important role in probing the quantum effects of gravity in the strong-field regime. In this paper, we focus on a polymerized black hole and investigate the quantum effects on the redshift, blueshift and gravitational redshift of photons emitted by massive particles revolving around this black hole. With a general relativistic formalism, we obtain two elegant and concise expressions for the mass of the black hole and the quantum parameter in terms of few direct observables, and find that all the frequency shifts of photons decrease with the quantum parameter. By expanding the total frequency shift for large orbit of the emitter, low peculiar redshift, and small azimuthal angle, we find that the leading contributions to the frequency shift are originated from the kinematic shift and peculiar shift, and the quantum effects make a negligible contribution. In addition, we study the effects of the plasma on the redshift/blueshift for the first time, and conclude that the presence of plasma results in the decrease of the redshift/blueshift., Comment: 8 pages, 2 figures; published in Physical Review D

Black hole shadow and gravitational lensing play important roles in testing gravitational theories in the strong field regime. As the first-order modifications from quantum gravity, the nonlocality can be manifested by black hole shadow and gravitational lensing. For example, the cut-off parameter introduced by nonlocality will affect the shape and size of the black hole shadow, and also affect the deflection angle of light rays. In this paper, we mainly investigate the effects of the nonlocality on the black hole shadow and the gravitational lensing for two types of rotating black holes in nonlocal gravity. It is found that the size of the black hole shadow decreases with the cut-off parameter since the nonlocality weakens the gravitational constant, and the shape of the shadow gets more deformed with the increase of the cut-off parameter. However, if the rotation parameter is small, the shape of the shadow is almost a circle even though the cut-off parameter approaches its maximum. The energy emission rate in both models is also studied. The results show that there is a peak for each curve and the peak decreases and shifts to the low frequency with the increase of the cut-off parameter. Besides, we also explore the shadow of both types of black holes surrounded by a nonmagnetized pressureless plasma which satisfies the separability condition. It is found that the plasma has a frequency-dependent dispersive effect on the size and shape of the black hole shadow. For the gravitational lensing, we find that the cut-off parameter of model A makes a positive contribution to the deflection angle, which can be compared with the contribution of the rotation parameter, while the cut-off parameter of model B makes a negative contribution which can be ignored. These results may be helpful for probing nonlocal gravity in future observations., Comment: 16 pages, 11 figures

It is well known that general relativity is an effective theory of gravity at low energy scale, and actually quantum effects cannot be ignored in the strong-field regime. As a strong gravitational object, black hole plays a key role in testing the quantum effects of gravity in the strong-field regime. In this paper, we focus on black hole in effective loop quantum gravity and investigate what the influences are of the quantum effects on the weak and strong bending angles of light rays. We find that this black hole could be a Schwarzschild black hole, a regular black hole, a one-way traversable wormhole, or a two-way traversable wormhole for the different values of the quantum parameter, and the strong bending angle for this compact object exhibits two different divergent behaviors, i.e., the logarithmic divergence and non-logarithmic divergence. There are a series of relativistic images on both sides of the optical axis. Only the outermost one can be resolved as a single image, and all others are packed together at the limiting angular position. It is interesting to note that the angular separation between the outermost relativistic image and the others initially increases and then decreases as the quantum parameter increases, indicating that there is a maximum in the angular separation. The maximum is reached after the black hole becomes a wormhole, which can be taken as a signal for the formation of the wormhole. Moreover, the limiting angular position decreases as the quantum parameter increases but a little bounce occurs after the formation of the wormhole, and the relative magnification in magnitudes first decreases and then increases as the quantum parameter increases., Comment: 14 pages, 6 figures; accepted for publication in Physical Review D

In this paper, we study the thick brane system in the so-called $f(Q)$ gravity, where the gravitational interaction was encoded by the nonmetricity $Q$ like scalar curvature $R$ in general relativity. With a special choice of $f(Q)=Q-b Q^n$, we find that the thick brane system can be solved analytically with the first-order formalism, where the complicated second-order differential equation is transformed to several first-order differential equations. Moreover, the stability of the thick brane system under tensor perturbation is also investigated. It is shown that the tachyonic states are absent and the graviton zero mode can be localized on the brane. Thus, the four-dimensional Newtonian potential can be recovered at low energy. Besides, the corrections of the massive graviton Kaluza-Klein modes to the Newtonian potential are also analyzed briefly.

In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory. By introducing two auxiliary super-potentials, we transform the second-order field equations of the system into a set of first-order equations. With this first-order formalism, several types of analytical thick brane solutions are obtained. Then, tensor and scalar perturbations are analysed. We find that both kinds of perturbations are stable. The effective potentials for the tensor and scalar perturbations are dual to each other. The tensor zero mode can be localized on the brane while the scalar zero mode cannot. Thus, the four-dimensional Newtonian potential can be recovered on the brane., Comment: 9 pages, 6 figures

Nonlinear electrodynamic (NLED) theories are well-motivated for their extensions to classical electrodynamics in the strong field regime, and have been extensively investigated in seeking for regular black hole solutions. In this paper, we focus on two spherically symmetric and static black hole solutions based on two types of NLED models: the Euler-Heisenberg NLED model and the Bronnikov NLED model, and calculate the weak deflection angle of light by these two black holes with the help of the Gauss-Bonnet theorem. We investigate the effects of the one-loop corrections to quantum electrodynamics on the deflection angle and analyse the behavior of the deflection angle by a regular magnetically charged black hole. It is found that the weak deflection angle of the electrically charged Einstein-Euler-Heisenberg black hole increases with the one-loop corrections and the regular magnetically charged black hole based on the Bronnikov NLED model has a smaller deflection angle than the singular one. Besides, we also calculate the deflection angle of light by the geodesic method for verification. In addition, we discuss the effects of a cold non-magnetized plasma on the deflection angle and find that the deflection angle increases with the plasma parameter.

Horndeski theory is the most general scalar-tensor theory retaining second-order field equations, although the action includes higher-order terms. This is achieved by a special choice of coupling constants. In this paper, we investigate thick brane system in reduced Horndeski theory, especially the effect of the non-minimal derivative coupling on thick brane. First, the equations of motion are presented and a set of analytic background solutions are obtained. Then, to investigate the stability of the background scalar profile, we present a novel canonically normalized method, and show that although the original background scalar field is unstable, the canonical one is stable. The stability of the thick brane under tensor perturbation is also considered. It is shown that the tachyon is absent and the graviton zero mode can be localized on the brane. The localized graviton zero mode recovers the four-dimensional Newtonian potential and the presence of the non-minimal derivative coupling results in a splitting of its wave function. The correction of the massive graviton KK modes to the Newtonian potential is also analyzed briefly.

It is known that the metric and Palatini formalisms of gravity theories have their own interesting features but also suffer from some different drawbacks. Recently, a novel gravity theory called hybrid metric-Palatini gravity was put forward to cure or improve their individual deficiencies. The action of this gravity theory is a hybrid combination of the usual Einstein-Hilbert action and a $f(\mathcal{R})$ term constructed by the Palatini formalism. Interestingly, it seems that the existence of a light and long-range scalar field in this gravity may modify the cosmological and galactic dynamics without conflicting with the laboratory and Solar System tests. In this paper we focus on the tensor perturbation of thick branes in this novel gravity theory. We consider two models as examples, namely, the thick branes constructed by a background scalar field and by pure gravity. The thick branes in both models have no inner structure. However, the graviton zero mode in the first model has inner structure when the parameter in this model is larger than its critical value. We find that the effective four-dimensional gravity can be reproduced on the brane for both models. Moreover, the stability of both brane systems against the tensor perturbation can also be ensured., Comment: 7 pages, 4 figures

We explore the tensor perturbation of the $f(T)$ brane embedded in an AdS$_5$ spacetime. With the transverse-traceless condition, we get the tensor perturbation equation of the $f(T)$ brane and show that the stability of this brane system can be ensured. In addition, we take $ f(T)=T+\alpha T^2$ as an example to analyse the localization problem of the graviton zero mode. It is shown that the graviton zero mode can be localized on the brane., Comment: 7 pages, 3 figures

Stability and localization of the gravitational perturbations for a special brane system in Eddington-inspired Born-Infeld (EiBI) gravity were studied in [Phys. Rev. D 85, 124053 (2012)]. In this paper, we show that the gravitational perturbations for a general brane system are stable, the four-dimensional graviton (massless KK graviton) can be localized on the brane, and the mass spectrum of massive KK gravitons are gapless and continuous. Two models are constructed as examples. In the first model, which is a generalization of [Phys. Rev. D 85, 124053 (2012)], the brane has no inner structure and there is no gravitational resonance (quasi-localized KK gravitons). In the second one, the background scalar field is a double-kink when the parameter in the model approaches its critical value. Correspondingly, the brane has inner structure and some gravitational resonances appear., Comment: 12 pages, 8 figures, improved version