Nonvanishing Cosmological Constant of Flat Universe in Brane-World Scenario

The finite temperature effect is examined in Randall-Sundrum brane-world scenario with inclusion of the matter fields on the brane. At zero temperature it is found that the theory on the brane is conformally invariant, which guarantees AdS/CFT. At 4d effective action we derived a temperature-dependent nonvanishing cosmological constant at the flat spacetime limit of brane worldvolume. At the cosmological temperature 3K the cosmological constant is roughly (0.0004eV )4 which is within the upper bound of the recent experimental value (0.01eV )4 ∗Email:[email protected] †Email:[email protected] ‡Email:[email protected] 1 The recent astronomical observations [1–3] indicate that our universe is flat and has a nonvanishing positive cosmological constant. In this letter we will show that these important features of our universe can be implemented within the Randall-Sundrum(RS) brane-world scenario [4,5] if the effect of nonzero temperature is properly involved. In the RS brane-world scenario our universe is treated as a three dimensional brane embedded in the higher dimensional spacetime. This picture and its variants are used to solve the various long-standing puzzles such as gauge hierarchy [4], Newton gravity [5,6], cosmological constant [7,8], and black holes [9,10]. It is also shown that the brane-world scenario supports a non-static cosmological solution [11–13] which leads to the conventional Friedmann equation by introducing bulk and brane cosmological constants and imposing a particular fine-tuning condition between them. The RS bulk spacetime is two copies of AdS5 glued in a Z2-symmetric way along a boundary which is interpreted as the three-brane world-volume. This fact is very useful to re-interpret the RS scenario within AdS/CFT or holography principle [14]. From the fact that RS picture yields similar results to those of the Horava-Witten scenario [15] one can imagine that it is somehow related to the string theories. In this context it is interesting to examine whether or not the similarity of RS scenario to AdS/CFT is maintained at finite temperature. It is well-known that AdS5 in AdS/CFT is extended to the Schwarzschild-AdS5 [16] at nonzero temperature by taking a non-extremal limit of black 3-brane solution of the string theories. Therefore the similarity of RS picture with AdS/CFT strongly suggests that the RS bulk spacetime at finite temperature is two copies of the Schwarzschild-AdS5 attached along the boundary as follows ds = e [