Unified emergence of energy scales and cosmic inflation

Abstract

In the quest for unification of the Standard Model with gravity, classical scale invariance can be utilized to dynamically generate the Planck mass MPl. However, the relation of Planck scale physics to the scale of electroweak symmetry breaking μH requires further explanation. In this paper, we propose a model that uses the spontaneous breaking of scale invariance in the scalar sector as a unified origin for dynamical generation of both scales. Using the Gildener-Weinberg approximation, only one scalar acquires a vacuum expectation value of υS ∼ (1016−17) GeV, thus radiatively generating $$ {M}_{\mathrm{P}1}\approx {\beta}_S^{1/2}{\upsilon}_S $$ M P 1 ≈ β S 1 / 2 υ S and μH via the neutrino option with right handed neutrino masses mN = yMυS ∼ 107 GeV. Consequently, active SM neutrinos are given a mass with the inclusion of a type-I seesaw mechanism. Furthermore, we adopt an unbroken Z2 symmetry and a Z2-odd set of right-handed Majorana neutrinos χ that do not take part in the neutrino option and are able to produce the correct dark matter relic abundance (dominantly) via inflaton decay. The model also describes cosmic inflation and the inflationary CMB observables are predicted to interpolate between those of R2 and linear chaotic inflationary model and are thus well within the strongest experimental constraints.

Pre-Inflationary Bounce Effects on Primordial Gravitational Waves of $f(R)$ Gravity

“…This approach is much simpler and offers insights toward understanding the inflationary era. To our opinion a synergistic approach that combines scalars and higher order curvature terms, is the most complete approach from many aspects, and there are many examples of this sort in the literature [23][24][25][26][27][28][29][30][31][32][33]. But as we said, studies of theories containing either scalar or only higher order curvature terms offer a simple path toward understanding the fundamental physics and problems of inflation.…”

“…Regarding the redshifts z i and z b we shall calculate them using Eq. (30). Specifically, for the redshift z i which corresponds to the beginning of inflation, we shall take the corresponding temperature to be the temperature of inflation, so T inf ∼ 10 15 GeV, hence by using Eq.…”

Inflation and dark matter after spontaneous Planck scale generation by hidden chiral symmetry breaking

“…(i) In this part of the model, a robust energy scale is generated, which is the unified origin of energy scales of other sectors. Instead of the Coleman-Weinberg mechanism [1] which has been used for the unified origin of energy scales in [13], we employ here a stronglyinteracting, QCD-like theory in which chiral symmetry is dynamically broken [2][3][4] and as a result a robust energy scale is generated. This part is described by…”

“…GeV to obtain a desired size of the radiative correction to µ 2 H [33][34][35][36] for triggering the electroweak symmetry breaking and at the same to make the type-I seesaw mechanism [39][40][41][42] viable -a scenario dubbed the "Neutrino option" [13,32,38,[49][50][51][52][53][54]. In this scenario it is assumed that the radiative correction is the dominant contribution to µ 2 H while the tree-level contribution λ HS v 2 S /4 is negligibly small [38,50].…”

“…The nonminimalcoupling term S 2 R generates the effective Einstein-Hilbert term, where S is a real scalar field and R is the Ricci scalar. This scenario incorporates inflation while identifying the scalar field as inflaton [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In this case, the Planck mass is dynamically generated during or before inflation.…”