Title: Why the cosmological constant is small and positive Authors: Paul J. Steinhardt, Neil Turok

Within conventional big bang cosmology, it has proven to be very difficult to understand why today's 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.

A cyclic universe, which bounces through a series of big bangs and "big crunches", could solve the puzzle of our cosmological constant.

The cosmological constant represents the energy of empty space, and is thought to be the most likely explanation for the observed speeding up of the expansion of the universe. But its measured value is a googol (1 followed by 100 zeroes) times smaller than that predicted by particle physics theories. It is a discrepancy that gives cosmologists a real headache. In the 1980s, physicists considered the possibility that an initially large cosmological constant could decay down to the value measured today. But this theory was abandoned when calculations showed that it would take far longer than 14 billion years – the time since the big bang – for the constant to reach the level seen today. Now physicists Paul Steinhardt at Princeton University, in New Jersey, US, and Neil Turok at Cambridge University in the UK, are resurrecting the idea. They point out that if time stretches back beyond the big bang, the problem could be solved. At that is just what is predicted by their cyclic model of the universe – an alternative to the Standard Big Bang theory – which the pair first developed in 2002. According to Steinhardt and Turok, 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.

However, there are other cosmic coincidences that the cyclic model cannot explain, like why the size of the cosmological constant is so similar to the density of matter in the universe today.

And of course, a big crunch scenario is ruled out by current observations on the expansion rates.