Kunihito Uzawa

Dynamics of intersecting brane systems — Classification and their applications

We present dynamical intersecting brane solutions in higher-dimensional gravitational theory coupled to dilaton and several forms. Assuming the forms of metric, form fields, and dilaton field, we give a complete classification of dynamical intersecting brane solutions with/without M-waves and Kaluza-Klein monopoles in eleven-dimensional supergravity. We apply these solutions to cosmology and black holes. It is shown that these give FRW cosmological solutions and in some cases Lorentz invariance is broken in our world. If we regard the bulk space as our universe, we may interpret them as black holes in the expanding universe. We also discuss lower-dimensional effective theories and point out naive effective theories may give us some solutions which are inconsistent with the higher-dimensional Einstein equations.

Dynamical p-branes with a cosmological constant

We present a class of dynamical solutions in a D-dimensional gravitational theory coupled to a dilaton, a form field strength, and a cosmological constant. We find that for any D due to the presence of a cosmological constant, the metric of solutions depends on a quadratic function of the brane world volume coordinates, and the transverse space cannot be Ricci flat except for the case of 1-branes. We then discuss the dynamics of 1-branes in a D-dimensional spacetime. For a positive cosmological constant, 1-brane solutions with D>4 approach the Milne universe in the far-brane region. On the other hand, for a negative cosmological constant, each 1-brane approaches the others as the time evolves from a positive value, but no brane collision occurs for D>4, since the spacetime close to the 1-branes eventually splits into the separate domains. In contrast, the D=3 case provides an example of colliding 1-branes. Finally, we discuss the dynamics of 0-branes and show that for D>2, they behave like the Milne universe after the infinite cosmic time has passed.

Cosmology in p -brane systems

We present time-dependent solutions in the higher-dimensional gravity which are related to supergravity in the particular cases. Here, we consider p-branes with a cosmological constant and the intersections of two and more branes. The dynamical description of p-branes can be naturally obtained as the extension of static solutions. In the presence of a cosmological constant, we find accelerating solutions if the dilaton is not dynamical. In the case of intersecting branes, the field equations normally indicate that time-dependent solutions in supergravity can be found if only one harmonic function in the metric depends on time. However, if the special relation between dilaton couplings to antisymmetric tensor field strengths is satisfied, one can find a new class of solutions where all harmonic functions depend on time. We then apply our new solutions to study cosmology, with and without performing compactifications.

Dynamical solutions in the 3-form field background in the Nishino-Salam-Sezgin model

We investigate the dynamical 3-form flux compactifications and their implications for cosmology in our brane world in the six-dimensional Nishino-Salam-Sezgin model, which is usually referred to as the Salam-Sezgin model. We take the background of the 3-form field acting on the internal space and timelike dimensions without the U(1) gauge field strength. The first class of solutions we discuss is the dynamical generalization of the static solutions obtained recently. In this class, we find that the time evolution is restricted only in the azimuthal dimension of the internal space and not in the ordinary three-dimensional one, which does not give a cosmological evolution. The second class of solutions is obtained by exchanging the roles of the radial coordinate and the time coordinate from the assumptions in the first class. At the center of the internal space, there is a conical singularity which may be interpreted as our 3-brane world, but it is difficult to realize a warped structure in the direction of the ordinary 3-space. Except for the oscillating solutions, a dynamical evolution leads to expanding or contracting ordinary 3-space, depending on the choice of time direction. Furthermore, in the expanding solutions, there are decelerating and accelerating ones: In themorexa0» latter solution, the evolution is sustained for a finite proper time and the scale factor of the 3-space diverges.«xa0less

Warped de Sitter compactifications

A bstractWe show that the warped de Sitter compactifications are possible under certain conditions in D-dimensional gravitational theory coupled to a dilaton, a form field strength, and a cosmological constant. We find that the solutions of field equations give de Sitter spacetime with the warped structure, and discuss cosmological models directly obtained from these solutions. We also construct a cosmological model in the lower-dimensional effective theory. If there is a field strength having non-vanishing components along the internal space, the moduli can be fixed at the minimum of the effective potential where a de Sitter vacuum can be obtained.

Dynamical brane with angles: Collision of the universes

We present the time-dependent solutions corresponding to the dynamical D-brane with angles in ten-dimensional type II supergravity theories. Our solutions with angles are different from the known dynamical intersecting brane solutions in supergravity theories. Because of our ansatz for fields, all warp factors in the solutions can depend on time. Applying these solutions, we construct cosmological models from those solutions by smearing some dimensions and compactifying the internal space. We find the Friedmann-Lemaˆotre-Robertson-Walker (FLRW) cosmological solutions with power-law expansion. We also discuss the dynamics of branes based on these solutions. When the spacetime is contracting in ten dimensions, each brane approaches the others as the time evolves. However, for Dp-brane (p ≤ 7) without smearing branes, a singularity appears before branes collide. In contrast, the D6-D8 brane system or the smeared D(p − 2)-Dp brane system with one uncompactified extra dimension can provide an example of colliding branes (and collision of the universes), if they have the same charges.

Dynamics of partially localized brane systems

We study dynamical partially localized brane solutions in higher dimensions. We give new descriptions of the relevant solutions of dynamical branes which are localized along both the overall and relative transverse directions. The starting point is a system of p_r-branes ending on a p_s-brane with a time-dependent warp factor. This system can be related to Dp_r-Dp_s brane system in string theory, where one brane is localized at the delocalized other brane. We then show that these give Friedmann-Lemaitre-Robertson-Walker cosmological solutions. Our approach leads to a new and manifest description of the brane configurations near the delocalized branes, and new solutions in the wave or KK-monopole background in terms of certain partial differential equations in D dimensions including ten and eleven dimensions.

Dynamical Lifshitz-type solutions and aging phenomena

We consider time-dependent Lifshitz-type solutions in type IIB supergravity. The solutions describe a time evolution from Lifshitz spacetimes to AdS spaces. We argue the holographic relation of them to aging phenomena in condensed matter physics. The solutions have no time-translation invariance and possess the dynamical scaling symmetry with z_c=2. In addition, the time evolution corresponds to slow (nonexponential) dynamics from nonequilibrium states to the equilibrium. We also discuss a mechanism of quantum quench to generate nonequilibrium states.

Warped de Sitter compactifications in the scalar–tensor theory

Abstract We present new solutions of warped compactifications in the higher-dimensional gravity coupled to the scalar and the form field strengths. These solutions are constructed in the D -dimensional spacetime with matter fields, with the internal space that has a finite volume. Our solutions give explicit examples where the cosmological constant or 0-form field strength leads to a de Sitter spacetime in arbitrary dimensions.

Colliding

We discuss the dynamics of intersecting