Gauging scale symmetry and inflation: Weyl versus Palatini gravity

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 ($$w_\mu $$ w μ ) 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 $$w_\mu $$ w μ ), Planck scale and metricity emerge in the broken phase after $$w_\mu $$ w μ acquires mass (Stueckelberg mechanism), then decouples. In the presence of matter ($$\phi _1$$ ϕ 1 ), 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 $$R^2$$ R 2 term, both theories have a small tensor-to-scalar ratio ($$r\sim 10^{-3}$$ r ∼ 10 - 3 ), larger in Palatini case. For a fixed spectral index $$n_s$$ n s , reducing the non-minimal coupling ($$\xi _1$$ ξ 1 ) increases r which in Weyl theory is bounded from above by that of Starobinsky inflation. For a small enough $$\xi _1\le 10^{-3}$$ ξ 1 ≤ 10 - 3 , unlike the Palatini version, Weyl theory gives a dependence $$r(n_s)$$ r ( n s ) similar to that in Starobinsky inflation, while also protecting r against higher dimensional operators corrections.

Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in f(R) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background.

More stringy effects in target space from Double Field Theory

In Double Field Theory, the mass-squared of doubled fields associated with bosonic closed string states is proportional to NL + NR− 2. Massless states are therefore not only the graviton, anti-symmetric, and dilaton fields with (NL = 1, NR = 1) such theory is focused on, but also the symmetric traceless tensor and the vector field relative to the states (NL = 2, NR = 0) and (NL = 0, NR = 2) which are massive in the lower-dimensional non-compactified space. While they are not even physical in the absence of compact dimensions, they provide a sample of states for which both momenta and winding numbers are non-vanishing, differently from the states (NL = 1, NR = 1). A quadratic action is therefore here built for the corresponding doubled fields. It results that its gauge invariance under the linearized double diffeomorphisms is based on a generalization of the usual weak constraint, giving rise to an extra mass term for the symmetric traceless tensor field, not otherwise detectable: this can be interpreted as a mere stringy effect in target space due to the simultaneous presence of momenta and windings. Furthermore, in the context of the generalized metric formulation, a non-linear extension of the gauge transformations is defined involving the constraint extended from the weak constraint that can be uniquely defined in triple products of fields. Finally, we show that the above mentioned stringy effect does not appear in the case of only one compact doubled space dimension.

Properties of perturbations in beyond Horndeski theories

We study whether the approach of Deffayet et al. (DPSV) can be adopted for obtaining a derivative part of quadratic action for scalar perturbations in beyond Horndeski theories about homogeneous and isotropic backgrounds. We find that even though the method does remove the second and higher derivatives of metric perturbations from the linearized Galileon equation, in the same manner as in the general Horndeski theory, it gives incorrect result for the quadratic action. We analyze the reasons behind this property and suggest the way of modifying the approach, so that it gives valid results.

On perturbations in Horndeski theories

This research has been carried out in collaboration with R. Kolevatov, S. Mironov, V. Rubakov and N. Sukhov. We study the approach suggested by Deffayet et al. for obtaining a derivative part of the quadratic action for scalar perturbations in the cubic Horndeski theory. We analyse the validity of the approach and generalize it for the complete Horndeski theory. We explicitly check that the generalized method gives the correct result.

ADVANCES IN TERNARY AND OCTONIONIC GAUGE FIELD THEORIES

A ternary gauge field theory is explicitly constructed based on a totally antisymmetric ternary-bracket structure associated with a 3-Lie algebra. It is shown that the ternary infinitesimal gauge transformations do obey the key closure relations [δ1, δ2] = δ3. Invariant actions for the 3-Lie algebra-valued gauge fields and scalar fields are displayed. We analyze and point out the difficulties in formulating a nonassociative octonionic ternary gauge field theory based on a ternary-bracket associated with the octonion algebra and defined earlier by Yamazaki. It is shown that a Yang–Mills-like quadratic action is invariant under global (rigid) transformations involving the Yamazaki ternary octonionic bracket, and that there is closure of these global (rigid) transformations based on constant antisymmetric parameters Λab = - Λba. Promoting the latter parameters to space–time dependent ones Λab(xμ) allows one to build an octonionic ternary gauge field theory when one imposes gauge covariant constraints on the latter gauge parameters leading to field-dependent gauge parameters and nonlinear gauge transformations. In this fashion one does not spoil the gauge invariance of the quadratic action under this restricted set of gauge transformations and which are tantamount to space–time dependent scalings (homothecy) of the gauge fields.