T. Padmanabhan, Hamsa Padmanabhan
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 \Lambda 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 = 4\pi. On the other hand, N is related to ln (\Lambda 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_\gamma / n_m) ~ 4.3 x 10^{10} and E_{inf} ~ 10^{15} GeV, our postulate N =4\pi 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.
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http://arxiv.org/abs/1302.3226
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