The variable cosmological constant and dynamics of dark energy

We study the variable cosmological constant model with the interaction between dark energy and matter. By constructing the dark energy component as an effective quintessence scalar field, we give an upper limit of parameter m with weak gravity conjecture which requires that the variation of the scalar field Δϕ should be less than the Planck mass Mp. On the other hand, we constrain the model parameters with recent type Ia supernovae and WMAP five-year observation, which gives a consistent result with weak gravity conjecture. The combination of these observational data restricts the model parameters within narrow ranges with Ωm0=0.276−0.017+0.020, 0⩽m⩽0.075, showing that weak interaction between dark energy and matter is favored in this model. The involving behaviors of relative densities Ωm(z), Ωde(z) and decelerated parameter q(z) are also studied with the constrained parameters.