Getting the math of the Universe to cancel out

The vacuum of space isn't actually "empty"; it teems with particles that pop in and out of existence, giving the vacuum an energy of its own. But here's an embarrassing fact about that energy: it predicts that the cosmological constant (which provides a measure of the rate of the expansion of the Universe) should be 10¹²⁰ times larger than we think it actually is.

Most scientists prefer things to be a bit more accurate than this. Still, the main question on cosmologists' minds is not why the predicted and real values appear to be so different, but how it is that the vacuum energy does so little. An answer of sorts has recently appeared in Physical Review Letters. But before we get to the paper, let's delve into the nature of the problem it's trying to solve.

An expanding Universe

When Einstein was first formulating a new theory of gravity, his solutions predicted that the Universe was expanding. At the time, the Universe was widely regarded to be static, so Einstein added a constant that counteracted the expansion and kept the Universe unchanging. Everyone rejoiced—electromagnetism, space, time, and gravity could all live together in harmony.

Later, Edwin Hubble took advantage of a new generation of telescopes to measure the speed at which distant galaxies were moving. He found that the further away a galaxy was, the faster away from us it was moving. The conclusion was inescapable: the Universe was expanding. Everyone chuckled over Einstein's big goof and got on with the business of crashing the economy and going to live in Hooverville.

Fast forward to the turn of the century, where yet another generation of telescopes—combined with an excellent understanding of how a particular type of supernova worked—allowed scientists to measure whether the rate at which the Universe expands is constant or not. Turns out it's not; every day, the Universe expands a bit faster than it did the day before. Inflation, it seems, is a physical as well as an economic universal, and Einstein's cosmological constant was back (albeit in altered form).

Funnily enough, it wouldn't have mattered whether the new cosmological constant was positive, negative, or zero—problems were going to arise. This is because Einstein's work had also established that mass and energy are two sides of the same coin. Since mass causes space and time to warp, so too should energy. At the time, no one gave the issue a second thought because we thought that most of space was empty vacuum.

Unfortunately, it turns out that the vacuum is anything but empty. 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.

A new idea

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.

Now, it might be possible to separate this idea out from all the others by trying to piece together the history of the expansion of the Universe in more detail. Alternatively, we can wait about 100 billion years to see if the expansion of the Universe begins to slow. Otherwise, it's going to be very difficult to generate observational evidence to support the idea.

Physical Review Letters, 2014, DOI: 10.1103/PhysRevLett.112.091304