Loopquantum cosmology (LQC)[1][2][3][4][5] is afinite,symmetry-reduced model ofloop quantum gravity (LQG) that predicts a "quantum bridge" between contracting and expandingcosmological branches.
The distinguishing feature of LQC is the prominent role played by thequantum geometry effects of loop quantum gravity (LQG). In particular,quantum geometry creates a brand new repulsive force which is totally negligible at low space-time curvature but rises very rapidly in thePlanck regime, overwhelming the classical gravitational attraction and thereby resolvingsingularities of general relativity. Once singularities are resolved, the conceptual paradigm ofcosmology changes and one has to revisit many of the standard issues—e.g., the "horizon problem"—from a new perspective.
Since LQG is based on a specific quantum theory ofRiemannian geometry,[6][7] geometric observables display a fundamental discreteness that play a key role inquantum dynamics: While predictions of LQC are very close to those of quantumgeometrodynamics (QGD) away from thePlanck regime, there is a dramatic difference once densities and curvatures enter thePlanck scale. In LQC theBig Bang is replaced by aquantum bounce.
Study of LQC has led to many successes, including the emergence of a possible mechanism forcosmic inflation, resolution ofgravitational singularities, as well as the development of effective semi-classicalHamiltonians.
This subfield originated in 1999 byMartin Bojowald, and further developed in particular byAbhay Ashtekar andJerzy Lewandowski, as well asTomasz Pawłowski andParampreet Singh, et al. In late 2012 LQC represented a very active field inphysics, with about three hundred papers on the subject published in the literature. There has also recently been work byCarlo Rovelli, et al. on relating LQC tospin foam cosmology.
However, the results obtained in LQC are subject to the usual restriction that a truncated classical theory, then quantized, might not display the true behaviour of the full theory due to artificial suppression of degrees of freedom that might have large quantum fluctuations in the full theory. It has been argued that singularity avoidance in LQC is by mechanisms only available in these restrictive models and that singularity avoidance in the full theory can still be obtained but by a more subtle feature of LQG.[8][9]
Due to the quantum geometry, the Big Bang is replaced by a big bounce without any assumptions on the matter content or any fine tuning. An important feature of loop quantum cosmology is the effectivespace-time description of the underlying quantum evolution.[10] The effective dynamics approach has been extensively used in loop quantum cosmology to describe physics at the Planck scale and the very early universe. Rigorous numerical simulations have confirmed the validity of the effective dynamics, which provides an excellent approximation to the full loop quantum dynamics.[10] It has been shown that only when the states have very large quantum fluctuations at late times, which means that they do not lead to macroscopic universes as described by general relativity, that the effective dynamics has departures from the quantum dynamics near bounce and the subsequent evolution. In such a case, the effective dynamics overestimates the density at the bounce, but still captures the qualitative aspects extremely well.[10]
If the underlying spacetime geometry with matter has ascale invariance, which has been proposed to resolve theproblem of time,Immirzi ambiguity[11] and hierarchy problem of fundamental couplings,[12] then the resulting loop quantum geometry has no definitive discrete gaps or a minimum size.[13][14] Consequently, in scale-invariant LQC, the Big Bang is shown not to be replaced by a quantum bounce.[13]