Within conventional big bang cosmology, it has proven to be very difficult to understand why todays cosmological constant is so small. In this paper, we show that a cyclic model of the universe can naturally incorporate a dynamical mechanism that automatically relaxes the value of the cosmological constant, taking account of contributions to the vacuum density at all energy scales. Because the relaxation time grows exponentially as the vacuum density decreases, nearly every volume of space spends an overwhelming majority of the time at the stage when the cosmological constant is small and positive, as observed today.
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