2020/07/31 by D. M. Ghilencea · 1 citation
Physics and Astronomy · #hep-th #astro-ph.CO #gr-qc #hep-ph
paper · pdf · doi:10.1140/epjc/s10052-021-09226-1
25 pages, 7 figures, LaTeX; v3: Sections 1 and 3 expanded; improved presentation
arxiv created 2021/05/12 · arxiv updated 2021/06/30
We present a comparative study of inflation in two theories of quadratic gravity with \it 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 (wμ) 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 wμ), Planck scale and metricity emerge in the broken phase after wμ acquires mass (Stueckelberg mechanism), then decouples. In the presence of matter (ϕ1), 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 R2 term, both theories have a small tensor-to-scalar ratio (r∼ 10-3), larger in Palatini case. For a fixed spectral index ns, reducing the non-minimal coupling (ξ1) increases r which in Weyl theory is bounded from above by that of Starobinsky inflation. For a small enough ξ1≤ 10-3, unlike the Palatini version, Weyl theory gives a dependence r(ns) similar to that in Starobinsky inflation, while also protecting r against higher dimensional operators corrections.