Cosmological Constant and Maximum of Entropy for de Sitter Space

Abstract: There are at least two cosmological constants calling for explanation. The first one describes the quasi-de Sitter inflation in the early universe, and the second describes the current acceleration of the universe associated with dark energy. An approach to the computation of the inflationary cosmological constant in the early universe is proposed. The tunneling and no-boundary proposals suggest that the ground state of the early universe is the de Sitter space. In this paper it is argued that the radius of the de Sitter space, i.e. the cosmological constant, can be computed using the principle of maximum entropy. The universe emerges from ``nothing" that corresponds to a minimum of entropy. The entropy reaches its maximal value for the 4-dimensional de Sitter space with the inflationary cosmological constant $\Lambda=3\pi\,\exp{-\psi(3/2)}$, where $\psi$ is the digamma function, $\Lambda\approx 9.087$ in Planck units.