### How many scalars for a quantum ladder to climb up the top of the Planck column ?

**Dilaton, inflaton, majoron and darkon: the four Horsemen of the grand unification?**

If cosmological inflation is due to a slowly rolling single inflation field taking trans-Planckian values as suggested by the BICEP2 measurement of primordial tensor modes in CMB, embedding inflation into the Standard Model challenges standard paradigm of effective field theories. Together with an apparent absence of Planck scale contributions to the Higgs mass and to the cosmological constant, BICEP2 provides further experimental evidence for the absence of large MPlanck induced operators. We show thatclassical scale invariance – the paradigm that all fundamental scales in Nature are induced by quantum effects – solves the problem and allows for a remarkably simple scale-free Standard Model extension with [two real singlet scalar fields φand ηand threeheavy singlet right-handed neutrinos]... without extending the gauge group. Due to trans-Planckian inflaton values and vevs, a dynamically induced Coleman-Weinberg-type inflaton potential of the model can predict tensor-to-scalar ratio r in a large range, converging around the prediction of chaotic m²φ² inflation for a large trans-Planckian value of the inflaton vev. Precise determination of r in future experiments will single out a unique scale-free inflation potential, allowing to test the proposed field-theoretic framework.

Embedding inflation into the Standard Model - more evidence for classical scale invariance, Kristjan Kannike, Antonio Racioppi, Martti Raidal (Submitted on 15 May 2014)

We propose that inflation and dark matter have a common origin, connected to the neutrino mass generation scheme. As a model we consider spontaneous breaking of global lepton number within the seesaw mechanism. We show that it provides an acceptable inflationary scenario consistent with the recent CMB B-mode observation by the BICEP2 experiment. The scheme may also account for the baryon asymmetry of the Universe through leptogenesis for reasonable parameter choices.

... Here we consider the simplest type-I seesaw scenario... of neutrino mass generation in which lepton number is promoted to a spontaneously broken symmetry, within the standard SU(3)c⊗SU(2)L⊗U(1)Y gauge framework... In order to consistently formu- late the spontaneous violation of lepton number within the SU(3)c⊗SU(2)L⊗U(1)Y model,one requires the presence of a lepton-number-carrying complex scalar singlet, σ, coupled to the singlet “right-handed” neutrinos νR. The real part of σ drives inﬂation through a Higgs potential... while the imaginary part, which is the associated Nambu-Goldstone boson, is assumed to pick up a mass due to the presence of small explicit soft lepton number violation terms in the scalar potential, whose origin we need not specify at this stage.For suitable masses such a majoron can account for the dark matter..., consistent with the CMB observations...

(Submitted on 11 Apr 2014)

We revisit a single field inflationary model based on Coleman-Weinberg potentials. We show that in small field Coleman-Weinberg inflation, the observed amplitude of perturbations needs an extremely small quartic coupling of the inflaton, which might be a signature of radiative origin. However, the spectral index obtained in a standard cosmological scenario turns out to be outside the 2σ region of the Planck data. When a non-standard cosmological framework is invoked, such as brane-world cosmology in the Randall-Sundrum model, the spectral index can be made consistent with Planck data within 1σ, courtesy of the modification in the evolution of the Hubble parameter in such a scheme. We also show thatthe required inflaton quartic coupling as well as a phenomenologically viable B-L symmetry breaking together with a natural electroweak symmetry breaking can arise dynamically in a generalized B-L extension of the Standard Model where the full potential is assumed to vanish at a high scale.

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