Solution to the cosmological constant problem

The current, accelerated, phase of expansion of our universe can be modeled in terms of a cosmological constant. A key issue in theoretical physics is to explain the extremely small value of the dimensionless parameter Λ L_P^2 ~ 3.4 x 10^-122, where L_P is the Planck length. We show that this value can be understood in terms of a new dimensionless parameter N, which counts the number of modes inside a Hubble volume crossing the Hubble radius, from the end of inflation until the beginning of the accelerating phase. Theoretical considerations suggest that N = 4π. On the other hand, N is related to ln (Λ L_P^2) and two other parameters which will be determined by high energy particle physics: (a) the ratio between the number densities of photons and matter and (b) the energy scale of inflation. For realistic values of (n_γ / n_m) ~ 4.3 x 10^10 and E_inf ~ 10^15 GeV, our postulate N =4π leads to the observed value of the cosmological constant. This provides a unified picture of cosmic evolution relating the early inflationary phase to the late accelerating phase.