Loop Quantum Cosmology

Abstract

Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time.Electronic Supplementary MaterialSupplementary material is available for this article at 10.12942/lrr-2008-4.

Inflationary universe in loop quantum cosmology

“…with the critical density given by 8) where ρ Pl = G −2 is the Planck density. The modified Friedmann equation provides an effective description for LQC which very well approximates the underlying discrete quantum dynamics.…”

“…Given the effective energy density and pressure, the effective equation of state is defined naturally as 8) where x is defined as dimensionless density, x = ρ/ρ crit , so we have 0 < x < 1. From Eq.…”

“…The underlying geometry in LQG is discrete and the continuum spacetime can be obtained from the quantum geometry in a large eigenvalue limit. Loop quantum cosmology (LQC) focuses on symmetry reduced models (with homogeneous and isotropic space) but inherits quantization scheme and techniques from LQG [8]. Investigations of LQC has led to important insights on the resolution of singularities in various situations [9,10,11].…”

Effective dynamics of the closed loop quantum cosmology

“…General prediction of this approach, called Loop Quantum Cosmology (LQC) [2], is avoidance of the initial singularity. Namely in LQC singularity is replaced by the phase of bounce.…”

Improved constraints on violations of the Einstein equivalence principle in the electromagnetic sector with complementary cosmic probes

“…Among such new theories we can cite massive gravity theories [1], modified Newtonian dynamic (MOND) [2], f (R, T ) theories [3], models with extra dimensions, as brane world models, Kaluza-Klein theories, string and loop quantum cosmology theories [4,5,6]. Nevertheless, some of these new theories naturally break the Einstein equivalence principle (EEP), leading to observational consequences that deserve to be tested and verified.…”