LQC

Loop Quantum Cosmology (LQC) is a framework for applying the methods of Loop Quantum Gravity (LQG) to symmetry-reduced cosmological spacetimes, principally homogeneous and isotropic universes. It treats spacetime geometry as quantum, using holonomies of the Ashtekar-Barbero connection and fluxes of densitized triads, as in LQG, but with a finite number of degrees of freedom appropriate to cosmology. LQC is a major line of research within loop quantum gravity and seeks to derive quantum cosmological dynamics from first principles.

In LQC, the classical phase space is quantized using a polymer representation, and the quantum Hamiltonian constraint becomes a difference equation in a volume-like variable rather than a differential Wheeler-DeWitt equation. The underlying quantum geometry introduces a discrete evolution and a fundamental density scale, which together prevent the classical singularities encountered in general relativity.

A central result is the resolution of the Big Bang singularity via a quantum bounce: when the matter density reaches a critical value ρ_c (approximately 0.41 of the Planck density), the expansion rate vanishes and then reverses, connecting a contracting branch to an expanding one. Semi-classical, effective descriptions yield modified Friedmann equations, such as H^2 = (8πG/3) ρ [1 − ρ/ρ_c], which encode the bounce in a continuum form.

LQC has been developed for isotropic (FLRW) and anisotropic (e.g., Bianchi) models and includes improvements to the quantization scheme to ensure appropriate infrared behavior. It also explores consequences for early-universe inflation and potential observational signatures, though empirical confirmation remains the subject of ongoing research.

Relation to LQG: LQC is a symmetry-reduced application of LQG quantization methods and is not yet a complete theory of quantum gravity. It provides a testbed for quantum geometric effects and for connecting quantum gravity ideas with cosmological phenomenology.