## Extra space dimensions and Gravity

Why gravity is much weaker than Nature's other fundamental forces is still a mystery 3 centuries after Newton proposed his law of gravitation. Newton's theory is generalised by Einstein's General theory of Relativity (GR), where gravity is a consequence of the curvature of space-time, which is related to the density of matter and energy within it. The two theories explaining the infinitely large - General Relativity, and the infinitely small - the Standard Model (SM) of particle physics, based on quantum field theory, are incompatible. The SM successfully explains microscopic electromagnetic, weak and strong phenomena down to the distance scale of 10^{-19} m accessible at the LHC, corresponding to an energy of 10^{3} GeV. Gravity is expected to be as strong as the other forces at the Planck energy scale of ~ 10^{19} GeV corresponding to a distance of 10^{-34} m.

Gravity weakens with distance because, as it propagates, it gets spread out over an ever-larger boundary. In 3-dimensional space the boundary is 2-dimensional surface (of a sphere). This is the reason of the 1/r^{2} dependence of the gravitational force in Newton's law. If space had N extra dimensions, however, the surface would be (2+N)-dimensional and the law would go as 1/r^{(2+N)}.

It is hard to accept that the 1/r^{2} law will hold up to the Planck scale. A new law of gravity emerges from string theory, with the aim to establish an ultimate unified theory of nature. The theory predicts that the universe has extra space dimensions into which gravity, unlike other SM particles, may be able to escape. As conceived by string theory, gravitons, the mediators of gravity, like all particles, are ultimately the vibrations of tiny strings. Whereas the SM particles are vibrations of open-ended strings, like violin strings, the graviton is the vibration of a closed loop, like a rubber band. Open strings must be attached to a brane, our 3-dimensional space. In contrast, closed strings such as gravitons cannot get stuck. They are free to explore the full 10-dimensional space. Each vibration of the string presents a different fundamental particle.

Models exist where extra dimensions are (i) finite in size and wrapped up in small circles of sub-subatomic size, (ii) infinite in size but strongly curved, so that their volume is concentrated around our universe, or (iii) infinite in size and uncurved, just like our ordinary three dimensions. All models consider gravitons leaking into extra dimensions, making gravity weak in our 3-dimensional space.