bes how space-time is deformed and stretched by whatever it holds and, in return, the different constituents of the universe will coast along the bends and warps of space-time. If we apply Einstein's idea to the whole of space-time, we find that the universe expands according to the underlying geometry of space itself.
The geometry of the universe can take three possible forms, each of which is intimately related to the total amount of matter and energy in each unit-volume of space. If there is too much stuff, the universe will have a positive curvature. This means it curves like the surface of a ball and may collapse in a big crunch. Too little and the curvature will be negative: the universe will curve like a saddle, flying apart unfettered by the gravitational pull (see diagram below).
Only if the universe has exactly the right density, corresponding to a few protons per cubic metre, will it be flat and have zero curvature. It will continue expanding forever because the energy of all the constituents that are flying apart carefully balances their gravitational pull.
Because it is so central to the evolution of the universe, understanding the curvature of space is one of cosmology's great goals. Before the late 1990s, we suspected that the universe had to be almost flat. Otherwise it would have either flown apart or collapsed very early on in its existence.
But all we had was a rough idea and little else. In fact, at any given conference on cosmology at the time, a few different models would be discussed: one with flat geometry and full of dark matter, another, also flat and containing dark energy, and yet another one which was emptier than all the others and so had negative curvature. Every now and then, the possibility that we lived in a positively curved universe would be mooted but without firm, precise observations, there was much rhetoric and no conclusions.
This changed as measurements of the cosmic microwave background (CMB), the radiation left over from the big bang, became more accurate and a simple method to use them took hold. In the late 1960s, a group led by Yakov Zel'Dovich in the Soviet Union, published a short paper showing that an accurate map of CMB radiation would have very distinct features: it should consist of randomly distributed hot and cold spots with a characteristic size.
Zel'Dovich's group calculated how large the spots were when they formed 370,000 years after the big bang, an era in cosmic history known as recombination. How large the spots appear to us today depends on how fast the universe has expanded since then (see diagram below). Under reasonably simple assumptions about what the universe is made of, we can determine the distance to recombination with some accuracy. Knowing this, and assuming the universe is flat, we can use standard trigonometry to work out the angular size of the spots in the sky.
I said "assuming the universe is flat". If the universe is not flat, then we have to use a different set of rules. The typical size of hot and cold spots in a flat universe should be about 1 degree across the sky, approximately twice the angular size of the moon as seen from the ground. If the hot and cold spots look bigger to us, then space has positive curvature. If they look smaller, then the curvature is negative.
In 1992, NASA's COBE satellite provided the first all-sky map of the hot and cold spots. The pictures were simply too blurred to pin down the universe's geometry, but they triggered a gold rush as teams vied with each to take clearer pictures of the CMB, hoping to home in on that magical angular scale of about 1 degree.
In 1995, I moved to the University of California, Berkeley, where cosmologists were hard at work on the coalface of research into the CMB. I had started life as a theorist, but with COBE and the potential for true discovery I decided to roll up my sleeves and get my hands dirty. For me, this involved preparing for the launch and then analysing the signals collected by two experiments carried aloft by balloons: Maxima and Boomerang.
Both experiments carried a