When gravity is quantized, there inevitably exist quantum gravitational vacuum fluctuations which induce quadrupole moments in gravitationally polarizable objects and produce a quantum correction to the classical Newtonian interaction between them. Here, based upon linearized quantum gravity and the leading-order perturbation theory, we study, from a quantum field-theoretic prospect, this quantum correction between a pair of gravitationally polarizable objects treated as two-level harmonic oscillators. We find that the interaction potential behaves like r−11 in the retarded regime and r−10 in the near regime. Our result agrees with what were recently obtained in different approaches. Our study seems to indicate that linearized quantum gravity is robust in dealing with quantum gravitational effects at low energies.

We investigate the integrated Sachs–Wolfe (ISW) effect and its power spectra in the extended quintessence cosmological models in both the metric and Palatini formalisms. We find that the ISW effect depends on the Hubble function H(a), the growth function ${D}_{+}(a)$, the dimensionless matter density ${{\rm{\Omega }}}_{{\rm{m}}}(a)$ and the coupling function F(a). When the coupling constant of the extended quintessence is negative, the differences of the ISW effect and its power spectra between two different formalisms are negligibly small, and the deviation of the extended quintessence models from the ΛCDM is insignificant, which indicates that in this case the cosmological constant can be taken as a good approximation to the extended quintessence. However, a positive non-minimal coupling leads to an appreciable deviation from the ΛCDM, and the difference between two different formalisms is also very obvious.

We study the thermalization of an elementary quantum system modeled by a two-level atom interacting with stationary electromagnetic fields out of thermal equilibrium near a dielectric slab. The slab is held at a temperature different from that of the region where the atom is located. We find that when the slab is nonabsorbing and nondispersive, out-of-thermal-equilibrium effects exist only when its thickness is infinite. In other words, no out-of-thermal-equilibrium effects appear for a real dielectric slab of a finite thickness d. Furthermore, a finite thick dielectric slab with a tiny imaginary part in the relative permittivity Imε behaves like a half-space dielectric substrate if Imε√Reε−1dλ0>1 is satisfied, where λ0 is the transition wavelength of the atom. This condition can serve as a guide for an experimental verification, using a dielectric substrate of a finite thickness, of the effects that arise from out-of-thermal-equilibrium fluctuations with a half-space (infinite thickness) dielectric.

We use the spherical collapse method to investigate the nonlinear density perturbations of pressureless matter in the cosmological models with the extended quintessence as dark energy in the metric and Palatini formalisms. We find that for both formalisms, when the coupling constant is negative, the deviation from the ΛCDM model is the least according to the evolutionary curves of the linear density contrast δc and virial overdensity Δv, and it is less than 1%. And this indicates that, in the extended quintessence cosmological models in which the coupling constant is negative, all quantities dependent on δc or Δv are essentially unaffected if the linear density contrast or the virial overdensity of the ΛCDM model is used as an approximation. Moreover, we find that the differences between different formalisms are very small in terms of structure formation, and thus cannot be used to distinguish the metric and Palatini formalisms.

A check of the validity of the distance-duality relation (DDR) is necessary since a violation of one of the assumptions underlying this relation might be possible. In this paper, we test the DDR by combining the Union2.1 type Ia supernovae (SNIa) and five angular diameter distance data from the baryonic acoustic oscillation (BAO) measurements. We find that the DDR is consistent with the observations at the 2σ confidence level (CL) for the case of the Hubble constant h=0.7, and the consistency is improved to be 1σ CL when h=0.7 is replaced by the latest constraint from the Planck satellite, i.e., h=0.678, or h is marginalized. Our results show that the BAO measurement is a very powerful tool to test the DDR. With more and more BAO data being released in the future, we are expecting a better validity check of the DDR.

We study the emergent scenario, which is proposed to avoid the big bang singularity, in the Einstein-Cartan (EC) theory with a positive cosmological constant and a perfect fluid by analyzing the existence and stability of the Einstein static (ES) solutions. We find that there is no stable ES solution for a spatially flat or open universe. However, for a spatially closed universe, the stable ES solution does exist, and in the same existence parameter regions, there also exists an unstable one. With the slow decrease of the equation of state w of the perfect fluid, the stable and unstable critical points move close gradually and coincide once w reaches a critical value, so that the stable critical point becomes an unstable one. As a result, if w approaches a constant at t→−∞, the universe can stay at the stable ES state past eternally, and furthermore it can naturally exit from this state and evolve into an inflationary era if w decreases slowly as time goes forward. Therefore, the emergent scenario that avoids the big bang singularity can be successfully implemented in the EC theory of gravity.

We study the diamagnetic interaction between a ground-state atom, which is located at a distance z from a planar body, e.g., a perfect mirror or a nondispersive and nonabsorbing dielectric substrate, and the body-assisted electromagnetic fields from vacuum, equilibrium, and out of equilibrium thermal fluctuations. We find that the diamagnetic potential at zero temperature is always proportional to z−4 in both the retarded and the nonretarded zones, and the Casimir-Polder (CP) force is attractive. The CP potential due to the thermal fluctuations at equilibrium dominates over that due to the zero-point fluctuations in the long-distance or high-temperature limit and behaves like T/z3, and the corresponding force is attractive. However, in the case of out of thermal equilibrium, the CP potential exhibits a different behavior with slower dependence on the distance and stronger dependence on temperature in the same limit, and it decays like (T2e−T2s)/z2, where Te is the temperature of the environment and Ts is that of the substrate, yielding a CP force that can either be attractive or repulsive. Meanwhile, in the short-distance or low-temperature limit the CP potential is always dominated by the contribution due to the vacuum fluctuations.

The scenario of an emergent universe provides a promising resolution to the big bang singularity in universes with positive or negative spatial curvature. It however remains unclear whether the scenario can be successfully implemented in a spatially flat universe which seems to be favored by present cosmological observations. In this paper, we study the stability of Einstein static state solutions in a spatially flat Shtanov-Sahni braneworld scenario. With a negative dark radiation term included and assuming a scalar field as the only matter energy component, we find that the universe can stay at an Einstein static state past eternally and then evolve to an inflation phase naturally as the scalar field climbs up its potential slowly. In addition, we also propose a concrete potential of the scalar field that realizes this scenario.

In this paper, we quantify the ability of a future measurement of the Sandage-Loeb test signal from the Cosmic Dynamic Experiment-like spectrograph to constrain some popular modified gravity theories, including the Dvali-Gabadadze-Porrati braneworld scenario, f(R) modified gravity, and f(T) gravity theory. We find that the Sandage-Loeb test measurements are able to markedly break degeneracies between model parameters and thus greatly improve cosmological constraints for all concerned modified gravity theories when combined with the latest observations of the cosmic microwave background shift parameter. However, they yield almost the same degeneracy directions between model parameters as that from the distance ratio data derived from the latest observations of the cosmic microwave background and baryon acoustic oscillations. Moreover, for f(R) modified gravity, the Sandage-Loeb test could provide completely different bounded regions in model-parameter space as compared to cosmic microwave background and baryon acoustic oscillations and thus supplement strong complementary constraints.

Massive gravity is a modified theory of general relativity. In this paper, we study, using a method in which the scale factor changes as a particle in a “potential,” all possible cosmic evolutions in a ghost-free massive gravity. We find that there exists, in certain circumstances, an oscillating universe or a bouncing one. If the universe starts at the oscillating region, it may undergo a number of oscillations before it quantum mechanically tunnels to the bounce point and then expands forever. But going back to the singularity from the oscillating region is physically not allowed. So, the big bang singularity can be successfully resolved. At the same time, we also find that there exists a stable Einstein static state in some cases. However, the universe cannot stay at this stable state past eternally since it is allowed to quantum mechanically tunnel to a big-bang-to-big-crunch region and end with a big crunch. Thus, a stable Einstein static state universe cannot be used to avoid the big bang singularity in massive gravity.