Sergei D. Odintsov

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.

We discuss the bulk Casimir effect (effective potential) for a conformal or massive scalar when the bulk represents five-dimensional anti–de Sitter (AdS) or de Sitter (dS) space with one or two four-dimensional dS branes, which may correspond to our Universe. Using zeta regularization, the interesting conclusion is reached that for both bulks in the one-brane limit the effective potential corresponding to the massive or to the conformal scalar is zero. The radion potential in the presence of quantum corrections is found. It is demonstrated that both the dS and the AdS braneworlds may be stabilized by using the Casimir force only. A brief study indicates that bulk quantum effects are relevant for brane cosmology, because they do deform the de Sitter brane. They may also provide a natural mechanism yielding a decrease of the four-dimensional cosmological constant on the physical brane of the two-brane configuration.

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 discuss the bulk Casimir effect (effective potential) for a conformal or massive scalar when the bulk represents five-dimensional AdS or dS space with two or one four-dimensional dS brane, which may correspond to our universe. Using zeta-regularization, the interesting conclusion is reached, that for both bulks in the one-brane limit the effective potential corresponding to the massive or to the conformal scalar is zero. The radion potential in the presence of quantum corrections is found. It is demonstrated that both the dS and the AdS braneworlds may be stabilized by using the Casimir force only. A brief study indicates that bulk quantum effects are relevant for brane cosmology, because they do deform the de Sitter brane. They may also provide a natural mechanism yielding a decrease of the four-dimensional cosmological constant on the physical brane of the two-brane configuration.

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.

The occurence of 5d de Sitter space with 4d de Sitter brane is discussed on classical and quantum level. It is shown that quantum effects maybe produced by dual CFT living on the brane. Moreover, gravity trapping on the brane is proved via the presentation of 5d dS gravity as 4d gravity coupled with gauge theory. This supports the dS/CFT correspondence. Some open questions in 5d dS/4d CFT correspondence are briefly discussed.