Manipulating lightcone fluctuations in an analogue cosmic string

We study the flight time fluctuations in an anisotropic medium inspired by a cosmic string with an effective fluctuating refractive index caused by fluctuating vacuum electric fields, which are analogous to the lightcone fluctuations due to fluctuating spacetime metric when gravity is quantized. The medium can be realized as a metamaterial that mimics a cosmic string in the sense of transformation optics. For a probe light close to the analogue string, the flight time variance is $\nu$ times that in a normal homogeneous and isotropic medium, where $\nu$ is a parameter characterizing the deficit angle of the spacetime of a cosmic string. The parameter $\nu$, which is always greater than unity for a real cosmic string, is determined by the dielectric properties of the metamaterial for an analogue string. Therefore, the flight time fluctuations of a probe light can be manipulated by changing the electric permittivity and magnetic permeability of the analogue medium. We argue that it seems possible to fabricate a metamaterial that mimics a cosmic string with a large $\nu$ in laboratory so that a currently observable flight time variance might be achieved.Comment: 13 pages, 1 figur

Quantum gravitational interaction between a polarizable object and a boundary

We investigate the interaction caused by quantum gravitational vacuum fluctuations between a gravitationally polarizable object and a gravitational boundary, and find a position-dependent energy shift of the object, which induces a force in close analogy to the Casimir-Polder force in the electromagnetic case. For a Dirichlet boundary, the explicit form of the quantum gravitational potential for the polarizable object in its ground-state is worked out and is found to behave like $z^{-5}$ in the near regime, and $z^{-6}$ in the far regime, where $z$ is the distance to the boundary. Taking a Bose-Einstein condensate as a gravitationally polarizable object, we find that the relative correction to the radius caused by fluctuating quantum gravitational waves in vacuum is of order $10^{-21}$. Although far too small to observe in comparison with its electromagnetic counterpart, it is nevertheless of the order of the gravitational strain caused by a recently detected black hole merger on the arms of the LIGO.Comment: 11 pages, no figure

Quantum correction to classical gravitational interaction between two polarizable objects

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 was 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.Comment: 10 pages. Accepted for publication in PL

Interaction between two gravitationally polarizable objects induced by thermal bath of gravitons

The quadrupole-quadrupole interaction between a pair of gravitationally polarizable objects induced by vacuum fluctuations of the quantum linearized gravitational field is first obtained with a relatively simple method, which is then used to investigate the contribution of thermal fluctuations of a bath of gravitons to the interaction at temperature $T$. Our result shows that, in the high temperature limit, the contribution of thermal fluctuations dominates over that of vacuum fluctuations and the interaction potential behaves like $T/ r^{10}$, where $r$ is the separation between the objects, and in the low temperature limit, the contribution of thermal fluctuations is proportional to $T^{10}/r$, which only provides a small correction to the interaction induced by zero-point fluctuations.Comment: 11 pages. Accepted by PR