Regular Article - Theoretical Physics
Gauging scale symmetry and inflation: Weyl versus Palatini gravity
Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering, 077125, Bucharest, Romania
Accepted: 9 May 2021
Published online: 9 June 2021
We present a comparative study of inflation in two theories of quadratic gravity with gauged scale symmetry: (1) the original Weyl quadratic gravity and (2) the theory defined by a similar action but in the Palatini approach obtained by replacing the Weyl connection by its Palatini counterpart. These theories have different vectorial non-metricity induced by the gauge field () of this symmetry. Both theories have a novel spontaneous breaking of gauged scale symmetry, in the absence of matter, where the necessary scalar field is not added ad-hoc to this purpose but is of geometric origin and part of the quadratic action. The Einstein-Proca action (of ), Planck scale and metricity emerge in the broken phase after acquires mass (Stueckelberg mechanism), then decouples. In the presence of matter (), non-minimally coupled, the scalar potential is similar in both theories up to couplings and field rescaling. For small field values the potential is Higgs-like while for large fields inflation is possible. Due to their term, both theories have a small tensor-to-scalar ratio (), larger in Palatini case. For a fixed spectral index , reducing the non-minimal coupling () increases r which in Weyl theory is bounded from above by that of Starobinsky inflation. For a small enough , unlike the Palatini version, Weyl theory gives a dependence similar to that in Starobinsky inflation, while also protecting r against higher dimensional operators corrections.
© The Author(s) 2021
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