Decay of the cosmological constant by Hawking radiation as quantum   tunneling
  We calculate the emission rate of Hawking radiation from the cosmological horizon by quantum tunneling approaches. Using the Hamilton-Jacobi and the null geodesic methods, two typical observations are obtained. First, the spectrum of radiation is not strictly pure thermal. Second, the value of the cosmological constant decreases. Our calculation is different from other similar works about Hawking radiation from the cosmological horizon in that the horizon does not shrink but expands by taking into account the back-reaction effect. We show that when a positive frequency particle is materialized near the cosmological horizon, the contribution of a negative frequency partner to the background geometry lowers the value of the cosmological constant. We also touch upon thermodynamics of de Sitter space and the quantum creation of universe. 
Yuichi Sekiwa