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A Modified Holographic Dark Energy Model with Infrared Infinite Extra Dimension(s)

We propose a modified holographic dark energy (MHDE) model with the Hubble scale as the infrared (IR) cutoff. Introducing the infinite extra dimension(s) at very large distance scale, we consider the black hole mass in higher dimensions as the ultraviolet cutoff. Thus, we can probe the effects of the IR infinite extra dimension(s). As a concrete example, we consider the Dvali-Gabadadze-Porrati (DGP) model and its generalization. We find that the DGP model is dual to the MHDE model in five dimensions, and the $Λ$CDM model is dual to the MHDE model in six dimensions. Fitting the MHDE model to the observational data, we obtain that $Ω_{m0}=0.269^{+0.030}_{-0.027}$, $Ω_{k0}=0.003^{+0.011}_{-0.012}$, and the number of the spatial dimensions is $N=4.78^{+0.68}_{-0.44}$. The best fit value of $N$ implies that there might exist two IR infinite extra dimensions.