Self-interacting holographic dark energy

We investigate a spatially flat Friedmann-Robertson-Walker (FRW) universe where dark matter exchanges energy with a self-interacting holographic dark energy (SIHDE). Using the ${\chi }^2$–statistical method on the Hubble function, we obtain a critical redshift that seems to be consistent with both BAO and CMB data. We calculate the theoretical distance modulus for confronting with the observational data of SNe Ia for small redshift $z\le 0.1$ and large redshift $0.1\le z\le 1.5$. The model gets accelerate faster than the $\mathrm{\Lambda }$CDM one and it can be a good candidate to alleviate the coincidence problem. We also examine the age crisis at high redshift associated with the old quasar APM 08279+5255.