**RESEARCH > (A)dS/CFT Correspondence and Cosmology
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dS/CFT Correspondence and Cosmology
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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
[44]. 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 (AdS_{D+1})
Schwarzschild black hole background [45]. 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 AdS_{D+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 (dS_{D}), 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 (CFT_{D-1})
whose
central charges depend on the asymptotic Hubble constants. In the
case studied in [45], 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
AdS_{D+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
AdS_{D+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
AdS_{D+1}
black holes
interferes with the
dS_{D}/CFT_{D-1}
correspondence. Indeed,
the central charge of the CFT_{D-1}
is now related to the
energy of the black hole, thus entering the
Cardy-Verlinde formula [33] that gives the entropy of the
thermal CFT_{D}
dual to the black hole [34].

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 [36]. 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 [45] 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 [44] is by itself interesting and worthy
of further investigation.