Sailing with three nonzero vev scalars in the wind of Adimensional gravity, Planck Mass excursion : 250

Is it enough to circumnavigating the grand loop of physics?
Today is the Winter solstice. Younger I would spend the shortest day and part of its longest night in a sofa reading the Treasure Island. Nowadays I am old enough to indulge myself : dreaming of a different kind of quest where gold coins have been traded for quanta of heavy scalar fields, taking part in a mutiny against the TeV scale physics doxa, looking for broader theoretical horizons and a clearer phenomenological outlook... Here is my last reading for the ending year 2015 :
The current treatment is devoted to simultaneously address a number of these problems within a unified and consistent classically scale invariant framework. Specifically, an analysis of the slow-roll inflationary paradigm, dark matter, and the neutrino mass generation mechanism is presented, in which the various scales are free of the mutual quadratic destabilizations [1a, 1b]. 
The model concerns the minimal addition of a complex gauge singlet to the SM content, in a scale- and CP symmetric manner. It has been previously demonstrated [2] that, within such an extended scalar sector, the ColemanWeinberg mechanism [3] may be successfully realized, while accommodating the recently discovered 125 GeV Higgslike state [4a,4b], and, therefore, remedy the failure of the mechanism within the ordinary SM scalar sector. In particular, the dynamical generation of a nonzero VEV for the CP-even component of the complex singlet scalar via this mechanism can be transmitted to the electroweak sector via the Higgs portal operators, inducing the nonzero VEV for the SM Higgs boson, and thereby giving rise to a successful spontaneous breaking of the electroweak symmetry. The classical scale symmetry, subsequently, guarantees the absence of any quadratic destabilization between the singlet and the electroweak scales. The CP-odd singlet component cannot decay due to the imposed CP-invariance, and constitutes a dark matter candidate. In addition, incorporating the see-saw mechanism [5] within this framework, by including three flavors of the right-handed Majorana neutrinos, yields nonzero masses for the SM neutrinos. The dark matter and collider phenomenology of the theory around the TeV scale were studied in [6, 7], whereas the possibility for realizing a strongly first-order electroweak phase transition, important for the baryogenesis paradigm, was exhibited in [8]. Hence, this technically-natural (minimal and yet comprehensive) framework presents an extremely promising and economical theoretical route to pursue, from a model-building perspective. 
In this analysis, we further investigate incorporating the slow-roll inflationary paradigm within the described framework, while additionally accounting for the gravitational effects by utilizing a renormalizable and scale symmetric theory of gravity, known as the Agravity [9]. Within this fully scale invariant framework, the dynamically-generated nonzero VEV of the CP-even singlet scalar induces the Planck scale via the scalar non-minimal couplings, in addition to the aforementioned generation of the electroweak scale via the Higgs portal operators. These induced scales are, then, shown to be free of quadratic divergences, and thus stable, as a consequence of the scale symmetry. The availability of a renormalizable gravitational UV-completion candidate, consistent with the symmetries of theory, allows for the proper trans-Planckian field excursions, while the stability of the vacuum and the perturbativity of the couplings are satisfied to large trans-Planckian energies. Identifying the pseudo-Nambu-Goldstone boson of the (approximate) scale symmetry with the inflaton field, we explore the viability of the inflationary paradigm according to the latest observational values by the Planck collaboration [10],[ Studies of the classically scale-invariant inflation, in various contexts, are available within the literature. See, e.g. [11, 12]]  and the reheating of the Universe due to the decay of the inflaton. Moreover, we demonstrate that the aforementioned pseudoscalar dark matter candidate constitutes a WIMPzilla [13], satisfying the observed relic abundance [10]. Hence, several important and pressing issues, faced by the contemporary physics, are captured within a single consistent framework.
... within the framework under consideration, it is sufficient to demand that the gauge, fermionic, and scalar couplings remain perturbative up to at least an energy scale of 250 {times the reduced Planck massP, where the internal consistency of the theory is guaranteed...  
In our developed model, the sole relevant scalar degree of freedom along the flat direction with a non-vanishing (loop-induced) potential is the σ boson. In this section we analyze the consequences of identifying this degree of freedom, in its canonical form, with the inflaton... and confront our model with the available cosmological data. For this purpose, we consider the slow-roll inflation paradigm...
The nS − r plane, incorporating several observational data sets by the Planck collaboration [10] at 68% C.L. (darker region) and at 95% C.L. (lighter region). Model’s predictions for both the small and large field inflation scenarios are also depicted (dashed lines) for the e-folding numbers, N = 60, 80, and the full range of the mixing angle, sin ω2 {between scalar singlet (σ) and gravity (κ) sectors}. Near the sin ω2 → 0 limit, the model reduces to the ordinary chaotic inflation scenario, indicated by the diagonal line labeled as “ϕ2 -model” within the plot

Marginalized probability distributions displayed within the sin ω2 − M/M¯P plane (left) and the N − M/P  plane (right), with 68% C.L. (darker inner region) and 95% C.L. (lighter outer region), obtained by the parameter estimation using the Planck TT+lowP (red) and Planck TT, TE, EE+lowP (blue) data sets {N stands for the e-folding number, M for a mass scale related to the σ singlet mass and for the reduced Planck mass}.

The best-fit locations in the parameter space are determined as ... (log10(M/P), log10 sinω2, N) = (−1.42, −1.01, 65.05) ... for the Planck TT, TE, EE+lowP data set. One deduces from this statistical analysis that the most likely value of the mixing angle compatible with the observation is limited to sinω2∼0.1, whereas the corresponding most-favorable value of the mass combination lies around M∼1017 GeV, with a most-likely e-folding number in the vicinity of N∼65.


Dominant final state products of the χ WIMPzilla pair-annihilation. Various scalar final states (including non-identical pairs) are obtained via the contact interactions, as well as the s, t, u-channel processes (diagrams in the top row from left to right), whereas the fermionic and vector boson final states only proceed through the s-channel (bottom row). The relevant mediator(s) are indicated within each diagram. Note that the tree-level σσh, σσκ, σσσ, and σκh couplings are absent due to the classical scale symmetry
... the pseudoscalar dark matter, χ, constitutes a WIMPzilla candidate [13], with a mass much larger than the reheating temperature, which becomes non-relativistic at the time of the reheating. As the inflaton mass is also larger than the reheating temperature, hence, only a sufficiently light scalar graviton, κ, can thermalize and contribute to {the effective number of thermalized relativistic degrees of freedom at Treh equal to} 107.75 for Mκ  Treheating... 
Furthermore, one observes that the WIMPzilla mass, compatible with the dark matter relic abundance, is confined below ∼1013 GeV. This (rather general) result is a direct consequence of the constraints imposed by the inflation, combined with the WIMPzilla nature of the dark matter. In particular, the small amplitude of the primordial scalar perturbations, As∼10-9, implies an accordingly small amplitude for the inflaton potential,... M < 0.1P, within vast regions of the parameter space... This, in turn, introduces a relatively light inflaton..., with a mass several orders of magnitude below the reduced Planck mass, which results in moderate reheating temperatures ... Within the WIMPzilla paradigm, the dark matter mass satisfies the condition Mχ < 2000 Treh, and hence may not be too heavy for moderate reheating temperatures. In addition, small values of M, as favored by the inflationary constraints, require the masses of the bosonic and fermionic degrees of freedom to reside in the relative vicinity of one another...
We have identified the viable regions of the parameter space, which simultaneously accommodate {the perturbativity and vacuum stability, inflation, and the dark matter constraints}... In particular, we have reached the important (and rather general) conclusion that within a classically scale invariant framework in which the pseudo-Nambu-Goldstone boson of the (approximate) scale symmetry is identified with the inflaton, the masses of the inflaton and the WIMPzilla, as well as the resulting reheating temperature are (much) smaller than the reduced Planck scale, while satisfying the inflationary and the relic abundance observational values.

(Submitted on 18 Dec 2015)

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