We perform the UV deformation of the Green's function in free scalar field theory using a discrete heat kernel method. It is found that the simplest UV deformation based on the discretized diffusion equation leads to the well-known Pauli-Villars effective Lagrangian. Furthermore, by extending assumptions on the discretized equation, we find that the general higher derivative theory is derived from the present UV deformation. In some specific cases, we also calculate the vacuum expectation values of the scalar field squared in nontrivial background spaces and examine their dependence on the UV cutoff constant.

We evaluate the quantum expectation values in nonsimply connected spaces by using UV improved Green’s functions proposed by Padmanabhan, Abel, and Siegel. It is found that the results from these three types of Green’s functions behave similarly under changes of scales, but have minute differences. Prospects in further applications are briefly discussed.

For an extension of the previous work on gravitational lensing by massless braneworld black holes, we investigate their microlensing phenomena and shadows and discuss how to distinguish them from standard Schwarzschild black holes and Ellis wormholes. Microlensing is known as the phenomenon in which luminosity amplification appears when a bright object passes behind a black hole or another massive object. We find that, for the braneworld black hole as well as for the Ellis wormhole, there appears luminosity reduction just before and after the amplification. This means that observation of such a reduction would indicate the lens object is either a braneworld black hole or a wormhole, though it is difficult to distinguish one from the other by microlensing solely. Therefore, we next analyze the optical images, or shadows of the braneworld black hole surrounded by optically thin dust, and compare them to those of the Ellis wormhole. Because the spacetime around the braneworld black hole possesses unstable circular orbits of photons, a bright ring appears in the image, just as in Schwarzschild spacetime or in the wormhole spacetime. This indicates that the appearance of a bright ring does not solely confirm a braneworld black hole, a Schwarzschild, nor an Ellis wormhole. However, we find that only for the wormhole is the intensity inside the ring larger than that the outsider intensity. Therefore, with future high-resolution observations of microlensing and shadows together, we could identify the braneworld black holes if they exist.

We consider a D-dimensional cosmological model with a dilaton field and two (D− d−1)-form field strengths which have nonvanishing fluxes in extra dimensions. Exact solutions for the model with a certain set of couplings are obtained by separation of three variables. Some of the solutions describe accelerating expansion of the d-dimensional space. Quantum cosmological aspects of the model are also briefly mentioned.

We study classical and quantum noncommutative cosmology with a Liouville-type scalar degree of freedom. The noncommutativity is imposed on the minisuperspace variables through a deformation of the Poisson algebra. In this paper, we investigate the effects of noncommutativity of minisuperspace variables on the accelerating behavior of the cosmic scale factor. The probability distribution in noncommutative quantum cosmology is also studied and we propose a novel candidate for interpretation of the probability distribution in terms of noncommutative arguments.