General Relativity and Modified Gravity Theories

Einstein’s theory of relativity, i.e., general relativity, unifies 3-dimensional space and 1-dimensional time as 4-dimensional spacetime and describes gravity as the geometry of curved spacetime. This picture has been very successful in explaining and predicting many gravitational phenomena. In particular, the direct detection of gravitational waves from coalescing binary black holes was accomplished in 2015 for the first time in the history, and added an important piece of evidence for general relativity in a very strong gravitational field. A number of gravitational wave sources are expected to be detected in years to come, and the physics of general relativity in various extreme situations will be revealed.

Experimentally, however, we do not know how gravity behaves at distances shorter than 0.01 mm. At shorter distances, gravity may behave completely differently from what we expect. For example there may be hidden dimensions at short distances. Or the Universe might have been dictated by a completely different theory of gravity at its very early stage. In fact, many theories, including superstring theories and M-theory, require the existence of such extra dimensions. Extra dimensions may exist everywhere in our Universe, but they are somehow hidden from us. Although we cannot see extra-dimensions directly, we may hope to detect some indirect evidence of extra-dimensions in high-energy experiments or cosmological observations.

Gravity at very long distances (for example, on scales of billions of light-years) may also behave very differently from general relativity. Recent high precision observations revealed that the expansion of our universe is accelerating. If Einstein's theory is correct, this requires that more than 70% of our universe is filled with invisible energy with negative pressure. This energy is named dark energy, but we do not know what it really is. This situation reminds us of a story in the 19th century: when the perihelion shift of Mercury was discovered, some people hypothesized the existence of an invisible planet called Vulcan, a so-to-speak dark planet, to explain the anomalous behavior of Mercury. However, as we all know, the dark planet was not real and the correct explanation was to change gravity, from Newton’s theory to Einstein’s. With this in mind, we study if we can address the mystery of dark energy by modifying general relativity at very long distances. (Last update: 2018/05/08)