https://doi.org/10.1140/epjc/s10052-021-09226-1
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
Received:
16
December
2020
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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