https://doi.org/10.1140/epjc/s10052-020-08722-0
Regular Article – Theoretical Physics
Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation
Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering, 077125, Bucharest, Romania
Received:
26
October
2020
Accepted:
27
November
2020
Published online:
12
December
2020
We study quadratic gravity 
in the Palatini formalism where the connection and the metric are independent. This action has a gauged scale symmetry (also known as Weyl gauge symmetry) of Weyl gauge field 
, with 
(
) the trace of the Palatini (Levi-Civita) connection, respectively. The underlying geometry is non-metric due to the 
term acting as a gauge kinetic term for 
. We show that this theory has an elegant spontaneous breaking of gauged scale symmetry and mass generation in the absence of matter, where the necessary scalar field (
) is not added ad-hoc to this purpose but is “extracted” from the 
term. The gauge field becomes massive by absorbing the derivative term 
of the Stueckelberg field (“dilaton”). In the broken phase one finds the Einstein–Proca action of of mass proportional to the Planck scale 
, and a positive cosmological constant. Below this scale decouples, the connection becomes Levi-Civita and metricity and Einstein gravity are recovered. These results remain valid in the presence of non-minimally coupled scalar field (Higgs-like) with Palatini connection and the potential is computed. In this case the theory gives successful inflation and a specific prediction for the tensor-to-scalar ratio 
for current spectral index 
(at 
CL) and 
efolds. This value of r is mildly larger than in inflation in Weyl quadratic gravity of similar symmetry, due to different non-metricity. This establishes a connection between non-metricity and inflation predictions and enables us to test such theories by future CMB experiments.
© The Author(s) 2020
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