Higher derivative supersymmetric FRW cosmology
Date
2022-03-04
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Benemérita Universidad Autónoma de Puebla
Abstract
"Our aim in this work is quantum cosmology and we do not deal with perturbations, but instead consider a variant of homogeneous and isotropic, or FRW, universe. Under these symmetries, the gravitational field is represented by a single physical degree of freedom, the scale factor a(t). Considering only a cosmological constant, the dynamics is governed by the Friedmann and acceleration (or Raychaudhuri) equations. These can be derived from an effective one-dimensional (time) action that results from evaluating the four-dimensional, say Einstein-Hilbert, action at the FRW metric. As a remnant of general covariance, we still have time-reparameterization invariance, made manifest by the gauge field, N(t), called lapse. This gauge freedom gives rise to a constrained dynamics; since there is not preferred time parameter, the Hamiltonian is zero. Canonical quantization leads to a greatly simplified, although nontrivial, version of the Wheeler-DeWitt equation mentioned above. Configuration space is given by the possible values of the scale factor and some other (homogeneous) matter fields. It is, therefore, a space with a small number of dimensions, called generically mini-superspace. Since the wave function does not depend on time, it sets the problem of how to recover the notion of an evolving universe".
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