Cosmological evolution with a logarithmic correction in the dark energy entropy

In a thermodynamical model of cosmological FLRW event horizons for the dark energy (DE), we consider a logarithmic corrective term in the entropy to which corresponds a new term in the DE density. This model of $\Lambda (t)$ in an interacting two-component cosmology with cold dark matter (DM) as second component leads to a system of coupled equations, yielding, after numerical resolution, the evolutions of $\Lambda (t)$, the Hubble $H(t)$, vacuum density $\Omega \_{\Lambda}(t)$, deceleration $q(t)$ and statefinder $R(t)$ and $S(t)$ parameters. Its results, compatible with an initial inflation and the current observations of the so-called "concordance model", predict a graceful exit of early inflation and the present acceleration and solve in the same time the age and coincidence problems. Moreover they account for the low-$l$ CMBR power spectrum suppression.