# Loop Quantum Cosmology

**Martin Bojowald
**

Institute for Gravitation and the Cosmos

The Pennsylvania State University

University Park, PA 16802, U.S.A.

and

Max Planck Institute for Gravitational Physics

(Albert Einstein Institute)

Am Mühlenberg 1, 14476 Potsdam, Germany

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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.