We study a nonminimal derivative coupling of scalar field, where the scalar field is coupled to curvature tensor in the five dimensional bulk in the context of universal extra dimension model. We apply the Einstein equation in the bulk and show that the acelerated expanding solution for the four dimensional scale factor a(t) is exist. Then, we study four different cases of the solution which is correspond to four different types of evolution of the extra dimension scale factor b.

The brane-world cosmological model in higher-dimensional spacetime with a bulk scalar field is investigated. We derive the $(4+n)$-dimensional gravitational field equations for the scalar field on the $(3+n)$-brane in a $(5+n)$-dimensional bulk with Einstein gravity plus a self-interacting scalar field. The $(4+n)$-dimensional gravitational field equations can be formulated to standard form with the extra component. Using this formalism we study the Kaluza-Klein brane cosmology. We derive the Friedmann equation and a possible energy leak out of the brane into the bulk. We present some exact solutions corresponding to vacuum brane and matter on the brane.

This paper provides a study of some aspects of flat and curved BPS domain walls together with their Lorentz invariant vacua of four-dimensional chiral N = 1 supergravity. The scalar manifold can be viewed as a one-parameter family of Kahler manifolds generated by a Kahler-Ricci flow equation. Consequently, a vacuum manifold characterized by (m, lambda) where m and lambda are the dimension and the index of the manifold, respectively, does deform with respect to the flow parameter related to the geometric soliton. Moreover, one has to carry out the renormalization group analysis to verify the existence of such a vacuum manifold in the ultraviolet or infrared regions. At the end, we discuss a simple model with linear superpotential on U(n) symmetric Kahler-Ricci orbifolds.

We study two (4 + n)-dimensional branes embedded in (5 + n)-dimensional spacetime. Using the gradient expansion approximation, we find that the effective theory is described by (4 + n)-dimensional scalar-tensor gravity with a specific coupling function. Based on this theory we investigate the Kaluza-Klein two-brane-worlds cosmology at low energy, in both the static and the nonstatic internal dimensions. In the case of the static internal dimensions, the effective gravitational constant in the induced Friedmann equation depends on the equations of state of the brane matter, and the dark radiation term naturally appears. In the nonstatic case we take a relation between the external and internal scale factors of the form b(t) = alpha(gamma)(t) in which the brane world evolves with two scale factors. In this case, the induced Friedmann equation on the brane is modified in the effective gravitational constant and the term proportional to alpha(-4 beta). For dark radiation, we find gamma = -2(1 + n). Finally, we discuss the issue of conformal frames which naturally arises with scalar-tensor theories. We find that the static internal dimensions in the Jordan frame may become nonstatic in the Einstein frame.

We investigate the weak-field, post-Newtonian expansion to the solution of the field equations in scalar-vector-tensor theory of gravity. hi the calculation we restrict ourselves to the first post Newtonian. The parameterized post Newtonian (PPN) parameters are determined by expanding the modified field equations in the metric perturbation. Then, we compare the solution to the PPN formalism in first PN approximation proposed by Will and Nordtvedt and read of the coefficients (the PPN parameters) of post Newtonian potentials of the theory. We find that the values of gamma(PPN) and beta(PPN) are the same as in General Relativity but the coupling functions beta(1), beta(2), and beta(3) are the effect of the preferred frame.

We study some aspects of spherical symmetric dyonic non-supersymmetric black holes in 4d N=1 supergravity coupled to chiral and vector multiplets on Kähler-Ricci solitons. Then, we have a family of dyonic non-supersymmetric black holes deformed with respect to the flow parameter related to the Kähler-Ricci soliton, which possibly controls the nature of black holes, such as their asymptotic and near horizon geometries. Two types of black holes are discussed, namely a family of dyonic Reissner-Nordström-like black holes and Bertotti-Robinson-like black holes where the scalars are freezing all over spacetime and at the horizon, respectively. In addition, the corresponding vacuum structures for such black holes are also studied in the context of Morse-(Bott) theory. Finally, we give some simple P^n-models whose superpotential and gauge couplings have a linear form.

We study BPS domain walls of N=1 supergravity coupled to a chiral multiplet and their Lorentz invariant vacua which can be viewed as critical points of BPS equations and the scalar potential. Supersymmetry further implies that gradient flows of BPS equations controlled by a holomorphic superpotential and the Kaehler geometry are unstable near local maximum of the scalar potential, whereas they are stable around local minimum and saddles of the scalar potential. However, the analysis using RG flows shows that such gradient flows do not always exist particularly in infrared region.

Randall-Sundrum single brane system (RS II) is investigated systematically, with an emphasis of the effective equation of motion on the brane, by using a low energy expansion method (gradient expansion method) in the bulk. Through the junction condition, we deduce in the zeroth order fine tuning for RS model. The modified Einstein equation, as well as Friedmann equation with dark energy radiation on the brane is derived from the first order expansion. We also clarify the emergence of the AdS/CFT correspondence for the case of the higher order expansion in a low energy iteration scheme.