We investigate the particle content of parity-preserving Weyl gauge theories of gravity (WGT$^+$) about a Minkowski background. Within a subset of the full theory, we use a systematic method previously presented in [arXiv:1812.02675] to determine 862 critical cases for which the parameter values in the action lead to additional gauge invariances. We find that 168 of these cases are free of ghosts and tachyons, provided the parameters satisfy certain conditions that we also determine. We further identify 40 of these cases that are also power-counting renormalizable and determine the corresponding conditions on the parameters. Of these theories, 11 have only massless tordion propagating particles, 23 have only a massive tordion propagating mode, and 6 have both. We also repeat our analysis for WGT$^+$ with vanishing torsion or curvature, respectively. We compare our findings with the very few previous results in the literature.
A systematic method is presented for determining the conditions on the parameters in the action of a parity-preserving gauge theory of gravity for it to contain no ghost or tachyon particles. The technique naturally accommodates critical cases in which the parameter values lead to additional gauge invariances. The method is implemented as a computer program, and is used here to investigate the particle content of parity-conserving Poincaré gauge theory, which we compare with previous results in the literature. We find 450 critical cases that are free of ghosts and tachyons, and we further iden…
We present 48 further examples, in addition to the 10 identified in [1], of ghost-and-tachyon-free critical cases of parity-conserving Poincaré gauge theories of gravity (PGT$^+$) that are also power-counting renormalizable (PCR). This is achieved by extending the range of critical cases considered. Of the new PCR theories, seven have 2 massless degrees of freedom (d.o.f.) in propagating modes and a massive $0^-$ or $2^-$ mode, eight have only 2 massless d.o.f., and 33 have only massive mode(s). We also clarify the treatment of nonpropagating modes in determining whether a theory is PCR.
Could a conformal Galileon be describing a gauge mode of a broader diffeomorphism invariant theory? We answer this question affirmatively in 3D by using a coset construction for a nonlinearly realized conformal symmetry. In particular, we show that the conformal Galileon emerges as a Stückelberg field of a local Weyl symmetry. The coset construction gives us a diffeomorphism and Weyl invariant 3D theory containing first, second, and third powers of the curvatures, their couplings to certain tensors made of the Galileon and its derivatives, and the conformal Galileon terms. In a theory with a b…
We study the viability conditions for the absence of ghost, gradient and tachyonic instabilities, in scalar-torsion $f(T,ϕ)$ gravity theories in the presence of a general barotropic perfect fluid. To describe the matter sector, we use the Sorkin-Schutz action and then calculate the second order action for scalar perturbations. For the study of ghost and gradient instabilities, we found that the gravity sector keeps decoupled from the matter sector and then applied the viability conditions for each one separately. Particularly, we verified that this theory is free from ghost and gradient instab…
Weyl-invariant extensions of three-dimensional New Massive Gravity, generic n-dimensional Quadratic Curvature Gravity theories and three-dimensional Born-Infeld gravity theory are analyzed in details. As required by Weyl-invariance, the actions of these gauge theories do not contain any dimensionful parameter; therefore the local symmetry is spontaneously broken in (Anti) de Sitter vacua in analogy with the Standard Model Higgs mechanism. About the flat vacuum, symmetry breaking mechanism is more complicated: The conformal symmetry is radiatively broken (at two loop level in 3-dimensions and a…
The tachyonic instability is associated with the unboundedness of the Hamiltonian from below and results in an unstable low-$k$ regime. In the cosmological exploration of modified gravity, it is seldom taken into account, with more focus given to the popular no-ghost and no-gradient conditions. The latter though are intrinsically high-$k$ statements. Here we combine all three conditions into a full set of requirements that we show to guarantee stability on the whole range of cosmological scales. We then explore the impact of the different conditions on the parameter space of scalar-tensor grav…
All Quiet on the Vector Front: Scalar Growth and Perturbative Control in Horndeski--Weyl-squared Gravity
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Institute for Theoretical Physics, Leibniz University Hannover（汉诺威莱布尼茨大学理论物理研究所）；Max Planck Institute for Gravitational Physics, Albert Einstein Institute（马克斯·普朗克引力物理研究所爱因斯坦研究所）；Dipartimento di Fisica e Astronomia “G. Galilei”, Università degli Studi di Padova（帕多瓦大学伽利略物理与天文系）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
Weyl conformal geometry may play a role in early cosmology where effective theory at short distances becomes conformal. Weyl conformal geometry also has a built-in geometric Stueckelberg mechanism: it is broken spontaneously to Riemannian geometry after a Weyl gauge transformation (of "gauge fixing") while Stueckelberg mechanism re-arranges the degrees of freedom, conserving their number ($n_{df}$). The Weyl gauge field ($ω_μ$) of local scale transformations acquires a mass after absorbing a compensator (dilaton), decouples, and Weyl connection becomes Riemannian. Mass generation has thus a dy…
