Planck mass and inflation as consequences of dynamically broken scale invariance

Abstract

Classical scale invariance represents a promising framework for model building beyond the Standard Model. However, once coupled to gravity, any scale-invariant microscopic model requires an explanation for the origin of the Planck mass. In this paper, we provide a minimal example for such a mechanism and show how the Planck mass can be dynamically generated in a strongly coupled gauge sector. We consider the case of hidden SU (Nc) gauge interactions that link the Planck mass to the condensation of a scalar bilinear operator that is nonminimally coupled to curvature. The effective theory at energies below the Planck mass contains two scalar fields: the pseudo-Nambu-Goldstone boson of spontaneously broken scale invariance (the dilaton) and a gravitational scalar degree of freedom that originates from the R 2 term in the effective action (the scalaron). We compute the effective potential for the coupled dilaton-scalaron system at one-loop order and demonstrate that it can be used to successfully realize a stage of slow-roll inflation in the early Universe. Remarkably enough, our predictions for the primordial scalar and tensor power spectra interpolate between those of standard R 2 inflation and linear chaotic inflation. For comparatively small gravitational couplings, we thus obtain a spectral index ns 0.97 and a tensor-to-scalar ratio as large as r 0.08. Contents

Type I seesaw mechanism as the common origin of neutrino mass, baryon asymmetry, and the electroweak scale

“…Here, the cosh (2z I ) factor is a consequence of the relation yy † II ∝ cosh (2z I ), while the cubic power of the RHN mass follows from the two powers of M 1 in Eq. (48) contour lines are also generated by our numerical code, we are able to confirm that they can be reproduced to excellent precision by the analytical expressions in Eqs. (58) and (68).…”

“…In recent years, it has been applied as a tool for BSM model building in a variety of scenarios, ranging from neutrino physics over dark matter to inflation (see, e.g., Refs. [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]).…”

“…This dependence is a direct consequence of the neutrino-option constraint in Eq. (48), which can also be written as…”

Quasi-conformal models and the early universe

“…The "quasi" of "quasi-conformal" is important. It reminds us that the Einstein-Hilbert term and other Weyl-breaking parameters can be present in the Lagrangian, generated, for example, through dimensional transmutation and various quantum effects [3,6,[15][16][17][18][19][20][21][22][23]. Note that an exactly Weyl invariant model would not be physically different from a Weyl-breaking one; indeed, any exactly conformal model can be written as a non-conformal one by fixing a gauge for Weyl symmetry and, conversely, any model of gravity coupled to an arbitrary matter sector can always be made exactly Weyl invariant 4 .…”

Dilaton-assisted generation of the Fermi scale from the Planck scale

“…1(b). This somewhat surprising behavior is due to the asymptotics (32). The latter, in turn, are traced back to the sign of the dilaton kinetic term in eq.…”