Shin'Ichi Nojiri

We calculate the difference of one-loop vacuum energies for massive scalar field in five-dimensional AdS black hole. (The same is done in five-dimensional deSitter space). In each case this difference is specified by the boundary conditions corresponding to the double-trace operator (massive term) and it describes RG flow in the manner discussed by Gubser-Mitra for pure AdS space. For AdS black hole there occurs instability which is the manifestation of the Hawking-Page phase transition. For stable phase of AdS black hole as well as for deSitter bulk, c-function found beyond the leading order approximation shows the monotonic behaviour consistent with c-theorem.

The role of quantum effects in brane-world cosmology is investigated. It is shown in time-independent formulation that quantum creation of deSitter branes in five-dimensional (A)dS bulk occurs with also account of brane quantum CFT contribution. The surface action is chosen to include cosmological constant and curvature term. (The time-dependent formulation of quantum-corrected brane FRW equations is shown to be convenient for comparison with Supernovae data). The particles creation on deSitter brane is estimated and is shown to be increased due to KK modes. The deSitter brane effective potential due to bulk quantum matter on 5d AdS space is found. It may be used to get the observable cosmological constant in the minimum of the potential (stabilization). The appearence of the entropy bounds from bulk field equation is also mentioned.

Five-dimensional braneworld cosmology with deSitter (inflationary) brane universe induced by classical and quantum matter is discussed. It is shown that negative energy phantom field with quantum CFT supports the creation of deSitter universe. On the same time, pure phantom or dust with quantum effects, or Chaplygin gas with quantum effects may naturally lead to the occurence of Anti-deSitter brane universe but not deSitter one. It is also interesting that unlike to four-dimensional gravity, for phantom with (or without) quantum contribution the standard cosmological energy conditions may be effectively satisfied.

We consider deSitter universe and Nariai universe induced by quantum CFT with classical phantom matter and perfect fluid. The model represents the combination of trace-anomaly driven inflation and phantom driven deSitter universe. The similarity of phantom matter with quantum CFT indicates that phantom scalar may be the effective description for some quantum field theory. It is demonstrated that it is easier to achieve the acceleration of the scale factor preserving the energy conditions in such unified model. Some properties of unified theory (anti-gravitating solutions, negative ADM mass Nariai solution, relation with steady state) are briefly mentioned.

The bulk gauge fields on 5d AdS black hole are discussed. We construct the bulk (and the corresponding brane) gauge propagator when black hole has large radius. The properties of gauge and ghost propagators are studied in both, minkowski or euclidean signature. In euclidean formulation the propagator structure corresponds to the one of theory at finite temperature (which depends on coordinates). The decoupling of KK modes and localization of gauge fields on flat brane is demonstrated. We show that with such a bulk there is no natural solution of hierarchy problem.

Thermodynamics of 5d SdS black hole is considered. Thermal fluctuations define the (sub-dominant) logarithmic corrections to black hole entropy and then to Cardy-Verlinde formula and to FRW brane cosmology. We demonstrate that logarithmic terms (which play the role of effective cosmological constant) change the behavior of 4d spherical brane in dS, SdS or Nariai bulk. In particularly, bounce Universe occurs or 4d dS brane expands to its maximum and then shrinks. The entropy bounds are also modified by next-to-leading terms. Out of braneworld context the logarithmic terms may suggest slight modification of standard FRW cosmology.

We calculate the holographic conformal anomaly and brane Newton potential when bulk is 5d AdS BH. It is shown that such anomaly is the same as in the case of pure AdS or (asymptotically) dS bulk spaces, i.e. it is (bulk) metric independent one. While Newton potential on the static brane in AdS BH is different from the one in pure AdS space, the gravity trapping still occurs for two branes system. This indicates to metric independence of gravity localization.

Using graviton correlator on deSitter (dS) brane in 5d AdS or dS bulk we calculate the four-dimensional Newton potential. For flat brane in AdS bulk the Randall-Sundrum result is recovered. For flat brane in dS bulk the sign of subleading ($1/r^3$) term in Newton potential is negative if compare with AdS bulk. In accordance with dS/CFT correspondence this indicates that dual CFT should be non-unitary (for example, higher derivative conformal theory).

In the first part of this work we review the equations of motion for the brane presented in Friedmann-Robertson-Walker (FRW) form, when bulk is five-dimensional (A)dS Black Hole. The spacelike (timelike) FRW brane equations are considered from the point of view of their representation in the form similar to two-dimensional CFT entropy, so-called Cardy-Verlinde (CV) formula. The following five-dimensional gravities are reviewed: Einstein, Einstein-Maxwell and Einstein with brane quantum corrections. The second part of the work is devoted to study FRW brane equations and their representation in CV form, brane induced matter and brane cosmology in Einstein-Gauss-Bonnet (GB) gravity. In particular, we focus on the inflationary brane cosmology. The energy conditions for brane matter are also analyzed. We show that for some values of GB coupling constant (bulk is AdS BH) the brane matter is not CFT. Its energy density and pressure are not always positive.