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We study baryogenesis in effective field theories where a $mathrm{U}(1)_{ B-L}$-charged scalar couples to gravity via curvature invariants. We analyze the general possibilities in such models, noting the relationships between some of them and existing models, such as Affleck-Dine baryogenesis. We then identify a novel mechanism in which $mathrm{U}(1)_{ B-L}$ can be broken by couplings to the Gauss-Bonnet invariant during inflation and reheating. Using analytic methods, we demonstrate that this mechanism provides a new way to dynamically generate the net matter-anti-matter asymmetry observed today, and verify this numerically.
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Weyl invariant theories of scalars and gravity can generate all mass scales spontaneously, initiated by a dynamical process of inertial spontaneous symmetry breaking that does not involve a potential. This is dictated by the structure of the Weyl current, $K_mu$, and a cosmological phase during which the universe expands and the Einstein-Hilbert effective action is formed. Maintaining exact Weyl invariance in the renormalised quantum theory is straightforward when renormalisation conditions are referred back to the VEVs of fields in the action of the theory, which implies a conserved Weyl current. We do not require scale invariant regulators. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential.
Over half century ago Carl Brans participated in the construction of a viable deformation of the Einstein gravity theory. Their suggestion involves expanding the tensor-based theory by a scalar field. But experimental support has not materialized. Nevertheless the model continues to generate interest and new research. The reasons for the current activity is described in this essay, which is dedicated to Carl Brans on his eightieth birthday.
We study anomalous chiral symmetry breaking in two-flavour QCD induced by gravitational and QCD-instantons within asymptotically safe gravity within the functional renormalisation group approach. Similarly to QCD-instantons, gravitational ones, associated to a K3-surface connected by a wormhole-like throat in flat spacetime, generate contributions to the t~Hooft coupling proportional to $exp(-1/g_N)$ with the dimensionless Newton coupling $g_N$. Hence, in the asymptotically safe gravity scenario with a non-vanishing fixed point coupling $g_N^*$, the induced t Hooft coupling is finite at the Planck scale, and its size depends on the chosen UV-completion. Within this scenario the gravitational effects on anomalous $U(1)_A$-breaking at the Planck scale may survive at low energy scales. In turn, fermion masses of the order of the Planck scale cannot be present. This constrains the allowed asymptotically safe UV-completion of the Gravity-QCD system. We map-out the parameter regime that is compatible with the existence of light fermions in the low-energy regime.
We discuss the local (gauged) Weyl symmetry and its spontaneous breaking and apply it to model building beyond the Standard Model (SM) and inflation. In models with non-minimal couplings of the scalar fields to the Ricci scalar, that are conformal invariant, the spontaneous generation by a scalar field(s) vev of a positive Newton constant demands a negative kinetic term for the scalar field, or vice-versa. This is naturally avoided in models with additional Weyl gauge symmetry. The Weyl gauge field $omega_mu$ couples to the scalar sector but not to the fermionic sector of a SM-like Lagrangian. The field $omega_mu$ undergoes a Stueckelberg mechanism and becomes massive after eating the (radial mode) would-be-Goldstone field (dilaton $rho$) in the scalar sector. Before the decoupling of $omega_mu$, the dilaton can act as UV regulator and maintain the Weyl symmetry at the {it quantum} level, with relevance for solving the hierarchy problem. After the decoupling of $omega_mu$, the scalar potential depends only on the remaining (angular variables) scalar fields, that can be the Higgs field, inflaton, etc. We show that successful inflation is then possible with one of these scalar fields identified as the inflaton. While our approach is derived in the Riemannian geometry with $omega_mu$ introduced to avoid ghosts, the natural framework is that of Weyl geometry which for the same matter spectrum is shown to generate the same Lagrangian, up to a total derivative.
We consider the electroweak phase transition in the conformal extension of the standard model known as SU(2)cSM. Apart from the standard model particles, this model contains an additional scalar and gauge field that are both charged under the hidden SU(2)$_X$. This model generically exhibits a very strong phase transition that proceeds after a large amount of supercooling. We estimate the gravitational wave spectrum produced in this model and show that its amplitude and frequency fall within the observational window of LISA. We also discuss potential pitfalls and relevant points of improvement required to attain reliable estimates of the gravitational wave production in this - as well as in more general - class of models. In order to improve perturbativity during the early stages of transition that ends with bubble nucleation, we solve a thermal gap equation in the scalar sector inspired by the 2PI effective action formalism.
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