Classically scale invariant inflation, supermassive WIMPs, and adimensional gravity

Abstract

We introduce a minimal and yet comprehensive framework with CP -and classical scalesymmetries, in order to simultaneously address the hierarchy problem, neutrino masses, dark matter, and inflation. One complex gauge singlet scalar and three flavors of the right-handed Majorana neutrinos are added to the standard model content, facilitating the see-saw mechanism, among others. An adimensional theory of gravity (Agravity) is employed, allowing for the trans-Planckian field excursions. The weak and Planck scales are induced by the Higgs portal and the scalar non-minimal couplings, respectively, once a Coleman-Weinberg dynamically-generated vacuum expectation value for the singlet scalar is obtained. All scales are free from any mutual quadratic destabilization. The CP -symmetry prevents a decay of the pseudoscalar singlet, rendering it a suitable WIMPzilla dark matter candidate with the correct observational relic abundance. Identifying the pseudoNambu-Goldstone boson of the (approximate) scale symmetry with the inflaton field, the model accommodates successful slow-roll inflation, compatible with the observational data. We reach the conclusion that a pseudo-Nambu-Goldstone inflaton, within a classically scale-symmetric framework, yields lighter WIMPzillas.

Inflationary perturbations in no-scale theories

“…24) 25) where H ≡ a /a (related to H ≡ȧ/a by H = a H) and a prime denotes a derivative with respect to η, while a dot is a derivative with respect to t. The equations for the scalar fields are instead…”

“…They lead to naturally flat inflationary potentials [3,[7][8][9][10][11][12][13] and dark matter candidates [10,[14][15][16][17] and represent an interesting framework to address the hierarchy problem [3,4,10,14,16,[18][19][20][21][22][23][24][25]. This no-scale principle has also the virtue of being predictive as only dimension-four operators are allowed in the classical Lagrangian, which can be viewed as a strong constraint on the allowed free parameters.…”

Agravity up to infinite energy

“…Another simple and useful form of L¨Ẅ eyl can be obtained from (8) as follows. We define L = e σ and complete the square rewriting Eq.…”

“…The weak scale, the QCD scale and the Planck scale can be dynamically generated [4] from vacuum expectation values or from condensates. Perturbative dimensionless theories automatically give slow-roll inflation [4][5][6][7][8][9] (see also refs. [10,11] for related studies).…”

The Higgs of the Higgs and the diphoton channel

“…What makes the dynamical generation of masses attractive is the fact that it can lead to a separation of scales, which depends exponentially on dimensionless couplings. Therefore, this specific setup allows us to justify why the weak scale is many orders of magnitude smaller than the Planck scale, which itself might be generated by dimension-less dynamics, with important implications for inflation [3][4][5][6][7][8][9][10][11].…”