Abstract
There are many dark energy models having been investigated with constraint from observational data. The best dark energy candidate is ΛCDM model. In this work, our model has extended to include AdS/CFT correspondent, where the AdS black hole boundary exhibit the FLRW metric foliated with four-dimensional gravity theory, can lead to a modified Friedmann Equation contains extra parameter coming from 5D AdS (hairy) black hole, where such extension to ACDM can be considered. We obtained modified Friedmann equation from both 5D hairless and scalar hair black hole. The effect from extra dimension in hairless black hole solutions can be observed in the form of radiation. Also, it is interesting to see a non-trivial term emerges in scalar hair solution case. However in this study, we only consider Hairless black hole case for data constraint by using a join analysis of Supernovae, CMB and H0 measurement to obtain $ \chi _{\min }^2 $ . As a result, we compare this particular case with ACDM using AIC and BIC statistics.
Highlights
New terms associated with the charge Q emerge in this scalar hair solution which has not been observed in RN-AdS black hole
Schwarzschild black hole case shows that we obtained smaller χ2min and AIC than ΛCDM
It is usually the case when a model has more parameter, it can lead to smaller χ2min which is the reason why information criterion is needed to penalize the extra parameter. ∆AIC we obtained shows that our model is not ruled out by current data, but instead is competitive with ΛCDM from the perspective of data fitting
Summary
F (r)g(r) g(r) f (r) dr, we obtain a metric in the Eddington-Finkelstein(EF) coordinates ds2 = 2dvdr − f (r)dv2 + Σ(r)2dΩ23,. Introduce Fefferman-Graham(FG) coordinates (This coordinate can have well-defined stress-energy tensor in dual CFT). Comparing (EF) and (FG) coordinate, we should find the relation for metric component in FG coordinate in terms of black hole information from EF coordinate by expansion near boundary. EF will ensure that we will have FLRW metric behavior near the boundary of Black Hole, while FG will ensure that we may have a well-defined dual field theory for 4D gravity. Notice that TμCνFT can be obtained from AdS/CFT correspondent. Method can be found in [2, 3]
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