Cartan Gravity and Equivalent Scalar-Tensor Theory
arXiv:2204.01255 · doi:10.3390/sym14091830
Abstract
We investigate the Cartan formalism in gravity. gravity has been introduced as a theory to explain cosmological accelerated expansion by replacing the Ricci scalar in the Einstein-Hilbert action with a function of . As is well-known, gravity is rewritten as a scalar-tensor theory by using the conformal transformation. Cartan gravity is described based on the Riemann-Cartan geometry formulated by the vierbein. In the Cartan formalism, the Ricci scalar is divided into two parts, one derived from the Levi-Civita connection and the other from the torsion. Assuming the spin connection independent matter action, we have successfully rewritten the action of Cartan gravity into the Einstein-Hilbert action and a scalar field with canonical kinetic and potential terms without any conformal transformations. The resulting scalar-tensor theory is useful in applying the usual slow-roll scenario. As a simple case, we employ the Starobinsky model and evaluate fluctuations in the cosmological microwave background radiation.
8 pages
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