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.