Gravitation and Cosmology

(Claes Uggla, Marcus Berg)

Of the four known fundamental forces (the strong and weak nuclear forces, the electromagnetic force, and the gravitational force) only gravity affects everything. And gravity affects everything in the same way, though its strength gradually decreases with distance. As a consequence, even though gravity is the weakest of all forces, it is gravity that determines how planets move, how large stars die, how large scale structures like galaxies and clusters of galaxies form, and how the university as a whole develops.

Taking the above properties of gravity as his starting point, and combining this with his theory of special relativity, Einstein came up with the idea that gravity could be described by means of curved spacetime geometry instead of a force in 1907, an idea Einstein considered to be his best idea ever. After 8 years of additional struggles, Einstein finally managed to describe how matter curves spacetime geometry in 1915 when he presented what is now known as Einstein's field equations and the theory of general relativity. This led to the picture that matter tells spacetime how to curve, and spacetime curvature tells matter how to move.

Already from the outset Einstein used his theory of general relativity to make observable predictions that differed from those of Newtonian gravitational theory. Observations quickly showed Einstein to be right, but it took time for Einstein's theory to make a large impact. One of the predictions of Einstein's theory is that time is affected by gravity and that time passes more slowly in a strong gravitational field than in a weaker one. As a consequence, your feet age slower than your head, by slightly less than a billionth of a second every year (gravity decreases with height), an effect that was confirmed by experiments around 1960. This might sound abstract, but it is real: scientists need to be aware of this effect when guiding satellites that explore the solar system, to minimize their fuel consumption, which to a large extent determines the cost for such missions.

This framework is also relevant for more down-to-earth applications like GPS, which is used everywhere from bus and car navigation, to precision agriculture in the Värmland region (the picture on the right shows satellite-aided farming). The GPS system is based on satellites that keep track of locations on the surface of the Earth. Not only does motion affect time according to special relativity, but these satellites orbit in a gravitational field that is weaker than the one at Earth's surface, which leads to time flowing differently, and scientists need to produce technological solutions that take into account that Newton's equations, for which time is not affected by anything, receive relativistic correction terms. (See this review for more details.)

Today Einstein's theory also plays a major role in astronomy; it is needed for astronomical predictions about neutron stars, black holes, the connection between gigantic galactic black holes and galaxy formation, gravitational radiation, and the universe itself, i.e. for cosmology. Observations tell us the universe is expanding, i.e., space on sufficiently large scales is getting larger and larger, which is understandable within Einstein's theory, but doesn't make much sense in Newton's. Moreover, the rate of expansion is increasing, the universe is said to be accelerating (Nobel Prize 2011). If we imagine the universe as a movie and play it backwards, this means that the universe would contract, and matter is squeezed together. Going further backwards in time, eventually the matter density becomes infinite everywhere, so the curvature of spacetime also becomes infinite. According to present observations this happened 13.7 billon years ago, at a moment called Big Bang, when spacetime, matter, and natural laws were created. To ask what happened before Big Bang is nonsensical according to Einstein's theory, it is like asking "what is north of the North Pole?".

However, no one expects general relativity to be correct when gravity, and hence spacetime curvature, becomes infinitely large. When approaching these scales general relativity has to be generalized to also take into account quantum mechanical effects (quantum mechanics is the physical theory that describes microscopic phenomena such as atoms and elementary particles) to produce a new theory of quantum gravity, something no one has succeeded with so far. There are several attempts, like loop quantum gravity and string theory, where the latter also has the ambition to unify all forces and quantum mechanics into a single description of nature as we know it. The future will tell us if our quest for a better understanding of the world we live in will succeed or not, but for sure we will fail if no one makes the attempt.