Physicists Paul Steinhardt at Princeton University, in New Jersey, US, and Neil Turok at Cambridge University in the UK, claim today's universe is part of an endless cycle of big bangs and big crunches, with each cycle lasting about a trillion years:
At every big bang, the amount of matter and radiation in the universe is reset, but the cosmological constant is not. Instead, the cosmological constant gradually diminishes over many cycles to the small value observed today.
The physicists' calculations show that the cosmological constant decreases in steps, through a series of quantum transitions. Crucially, the higher the value of the constant, the more rapid the transitions, says Turok. But as the constant reaches lower levels, it changes more slowly, lingering on the lowest positive value for an extremely long time. That means that today's universe is most likely to have a small cosmological constant, just as we currently observe, says Turok.
The physicists say this explains way the cosmological constant is a googol smaller than predicted by particle physics theories. They claim this problem can be solved by looking at the universe as a cyclic model in which time didn't start with the big bang. More details over here.