RESEARCH > (A)dS/CFT Correspondence and Cosmology
dS/CFT Correspondence and Cosmology
If the dS/CFT correspondence resembles at all its successful cousin - the AdS/CFT correspondence - then the possibility arises for a quantum field theoretical description of the cosmological evolution . Namely, considering that the cosmological evolution in D spacetime dimensions is modeled by a (flat) metric of the Friedman-Robertson-Walker (FRW) form such that the Hubble constant approaches distinct values in the infinite past and future, respectively, then the cosmological evolution could be viewed as a ``holographic'' renormalization-group (RG) flow between the two Euclidean CFTs dual to the asymptotic de-Sitter regimes in the infinite past and future. Such an evolution from the infinite past to the infinite future would correspond to a dual RG flow from the infrared (IR) to the ultraviolet (UV).
Motivated by the above, as well as from the puzzling rareness of string/M-theory compactifications to de Sitter space, Dr. Siopsis and his collaborator, Dr. A. C. Petkou, considered branes moving in a (D+1)-dimensional anti-de Sitter (AdSD+1) Schwarzschild black hole background . When the brane tension exceeded a critical value, they found solutions in which the induced metric on the brane was of the general FRW form and approached de Sitter space in the infinite past and future.
An interesting class of solutions are those where the brane radius is always greater than the event horizon of the AdSD+1 black hole and stretches to infinity both at the infinite past and future. In this case the brane metric is asymptotically a D-dimensional de Sitter space (dSD), with the same Hubble constant in the past and future infinity. The dS/CFT correspondence applied to the asymptotic de-Sitter regimes of the above brane metrics implies the existence of dual (D-1)-dimensional CFTs (CFTD-1) whose central charges depend on the asymptotic Hubble constants. In the case studied in , the latter depended generically only on the brane tension, hence it seems that their values have nothing to do with any properties of the bulk AdSD+1 black hole. Phrased differently, the brane excitations induced by the thermal bulk seem to be ``orthogonal'' to ``holographic'' de-Sitter RG flows. Nevertheless, these brane configurations break down when the mass of the bulk AdSD+1 black holes reaches a critical value that depends on the brane tension. At this critical point, the solution interpolates between a dS space and a space with Hubble constant zero and corresponds to non-singular evolution on the brane (no Big Bang or Big Crunch). It appears therefore that at this critical point the thermodynamics of the AdSD+1 black holes interferes with the dSD/CFTD-1 correspondence. Indeed, the central charge of the CFTD-1 is now related to the energy of the black hole, thus entering the Cardy-Verlinde formula  that gives the entropy of the thermal CFTD dual to the black hole .
The above discussion leads to the interesting possibility of studying properties of the dS/CFT correspondence in embedded spaces (i.e., branes), using results of the AdS/CFT correspondence. One could extend this result to asymptotically flat brane cosmologies in which case one expects that one should use the Cardy-Verlinde entropy formula for black holes with flat horizons discussed in . Notice that at the critical point the evolution on the brane leads to an infinite ratio of the Hubble constants in the infinite future and infinite past, respectively. It would be interesting to perturb this symmetric state and obtain a large but finite ratio of Hubble constants as observed in our Universe. In that sense, a natural extension of the investigation in  would be to consider more complicated black hole solutions of supergravity and study the influence of the bulk fields on possible asymptotic dS regimes on the brane. Introducing explicitly thermal conformal fields on the brane would also be a possible way forward. In any case, the idea of viewing the cosmological expansion as a RG flow  is by itself interesting and worthy of further investigation.
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401 Nielsen Physics Bldg., The University of Tennessee, Knoxville, TN 37996-1200, U.S.A.