Embedding inflation into the Standard Model - more evidence for classical scale invariance

TL;DR

This work investigates embedding cosmological inflation into the Standard Model under the principle of classical scale invariance, motivated by the BICEP2 detection of primordial tensor modes and the apparent absence of Planck-suppressed operators. It develops a minimal scale-free framework in which the inflaton and all mass scales are generated radiatively via dimensional transmutation, avoiding extra gauge symmetries and relying on a Coleman-Weinberg-type potential $V_{ m eff} = oldsymbol{ ext Λ}^4 + rac{eta_{ ext{λ}_ ext{φ}}}{4} igl|rac{ ext{φ}}{ ext{φ}_0}igr|^4$ (and its RG-improved form). The paper presents both a model-independent analysis showing a strong $n_s$–$r$ correlation with viable large-$r$ regimes, and a concrete minimal model with two singlets and right-handed neutrinos that realizes the dynamics and permits reheating and leptogenesis via inflaton decays. The framework predicts a testable range for $r$ that approaches the chaotic inflation limit in the trans-Planckian vev regime, and future precision measurements of $r$ and $n_s$ can potentially single out the underlying scale-free potential, offering a way to probe physics above the Planck scale.

Abstract

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 $M_{\rm P}$ induced operators. We show that classical 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 inflaton 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 $m^2φ^2$ 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.

Figures (6)

• Figure 1: The shape of scale-free inflaton potential. Both chaotic (red) and hilltop (blue) inflation are allowed.
• Figure 2: Predictions for tensor-to-scalar ratio $r$ as a function of $n_s$ for $N \in [50,60]$$e$-folds. The blue region represent the hilltop inflation configuration while the red one the chaotic inflation. For reference we also plot predictions of $\frac{m^2}{2} \phi^2$ (yellow) and $\l \phi^4$ (green) potentials. The $2\sigma$ BICEP2 band and $2\sigma,$$1\sigma$ Planck bounds are also presented.
• Figure 3: The predicted range for $r$ in function of $\phi_0$ producing $N \in [50,60]$$e$-folds of inflation in our model and in the $\frac{m^2}{2} \phi^2$ inflation. The colour code is the same as in previous figures.
• Figure 4: The range for $m_\phi$ and $\lambda^*$ corresponding to the results in Fig. \ref{['rvsn']}. The colour code is the same as in previous figures.
• Figure 5: The range for $\lambda^*$ and $\lambda_{\phi\eta}$. The colour code is the same as in previous figures.