Sakharov proposed the idea of induced gravity as an alternative theory of quantum gravity. Basically, his idea is there is no need to quantize the gravitational field. He observed that many condensed matter systems give rise to emergent phenomena which are identical to general relativity quantitatively. Crystal defects can look like torsion, for example. To him, this was not a coincidence. Andrei Sakharov, 1943 Andrei Dmitrievich Sakharov (Андре́й Дми́триевич Са́харов, May 21, 1921 – December 14, 1989), was a Russian nuclear physicist, dissident and human rights activist. ... Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... Jump to: navigation, search General relativity (GR) is the geometrical theory of gravity published by Albert Einstein in 1915. ... // Mathmatics In mathematics, the term torsion has several meanings, mostly unrelated to each other. ...

His idea was to start with an arbitrary background pseudo-Riemannian manifold (in modern treatments, possibly with torsion) and introduce quantum fields (matter) on it but not introduce any gravitational dynamics explicitly. This gives rise to an effective action which to one-loop order contains the Einstein-Hilbert action with a cosmological constant. In other words, general relativity arises as an emergent property of matter fields and is not put in by hand. On the other hand, such models typically predict huge cosmological constants. In differential geometry, a pseudo-Riemannian manifold is a smooth manifold equipped with a smooth, symmetric, tensor which is nondegenerate at each point on the manifold. ... Everything in the following article also applies to statistical mechanics. ... In general relativity, Einsteins field equations can be derived from an action principle starting from the Einstein-Hilbert action: where g is the (pseudo)Riemannian metric, R is the Ricci scalar, n is the number of spacetime dimensions and k is a constant which depends on the units chosen... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) occurs in Einsteins theory of general relativity. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) occurs in Einsteins theory of general relativity. ...