Loop Quantum Cosmology and Spin Foams

Details Loop Quantum Cosmology and Spin Foams Loop Quantum Cosmology and Spin Foams

2009-09-23

arxiv.org/abs/0909.4221v1

Phys.Lett.B681:347-352,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, no figures

Scientific paper

10.1016/j.physletb.2009.10.042

Loop quantum cosmology (LQC) is used to provide concrete evidence in support of the general paradigm underlying spin foam models (SFMs). Specifically, it is shown that: i) the physical inner product in the timeless framework equals the transition amplitude in the deparameterized theory; ii) this quantity admits a %convergent vertex expansion a la SFMs in which the $M$-th term refers just to $M$ volume transitions, without any reference to the time at which the transition takes place; iii) the exact physical inner product is obtained by summing over just the discrete geometries; no `continuum limit' is involved; and, iv) the vertex expansion can be interpreted as a perturbative expansion in the spirit of group field theory. This sum over histories reformulation of LQC also addresses certain other issues which are briefly summarized.

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