At Ars Technica:
... And since it has energy, it should curve space and time. In other words, the vacuum of space should contain enough energy to curl the Universe up into a tight little ball or blow it apart so fast that no stars could ever form (it depends on whether the energy is positive or negative).
Given our current data, there's no argument over the approximate value of the cosmological constant: it is small and positive. So why doesn't the vacuum energy bend space and time? When physicists bolt the quantum vacuum energy on to general relativity, they get absurd results unless some kind of correction factor (to the tune of 10120) is carefully added to counteract the vacuum. This fine-tuning bothers people because there is simply no way to obtain these numbers naturally.
Enter the new work by Nemanja Kaloper (UC-Davis) and Antonio Padilla (University of Nottingham), who have proposed a modification to general relativity that naturally generates a small cosmological constant. According to the researchers, the cosmological constant should be treated as the average of the vacuum contribution over all space and time. When this happens, the local vacuum energy contributions appear twice in the equations with opposite signs. No matter what energy the vacuum has right now, it can't bend space and time—think of it as pushing with one hand and pulling with the other.
The residual cosmological constant is a kind of historical average. That is, all the fluctuations in the vacuum from the beginning of time up to this moment contribute to the cosmological constant we observe now. In the early Universe, this created a large cosmological constant that drove inflation. Later, as the Universe cooled, the cosmological constant became small. Even later, it may change signs, causing the Universe to begin contraction.
One other implication is that the Universe has to be finite in both space and time.