Inflation at the TeV scale with a PNGB curvaton

We investigate a particular type of curvaton mechanism, under which inflation can occur at Hubble scale of order 1 TeV. The curvaton is a pseudo Nambu-Goldstone boson, whose order parameter increases after a phase transition during inflation, triggered by the gradual decrease of the Hubble scale. The mechanism is studied in the context of modular inflation, where the inflaton is a string axion. We show that the mechanism is successful for natural values of the model parameters, provided the phase transition occurs much earlier than the time when the cosmological scales exit the horizon. Also, it turns our that the radial mode for our curvaton must be a flaton field. Inflation is the only compelling theory to date for the solution of the horizon and flatness problems of the big bang cosmology as well as for explaining structure formation in the Universe. Recent precise observations have confirmed the basic predictions of the inflationary paradigm by ascertaining the spatial flatness of the Universe and the approximate scale invariance of the density perturbations, which give rise to the anisotropy of the Cosmic Microwave Background Radiation (CMBR) and seed structure formation. These exciting developments have rendered the inflationary paradigm a necessary extension to the hot big bang standard cosmology. In the light of precision data, inflation model-building can be upgraded beyond the simple single-field stage of its early beginnings. Indeed, more complex and realistic models of inflation, with tighter connections to the theory, less fine tunning and enhanced predictability and falsifiability are now possible to construct, making use of the rich content of particle physics. A first such example is the well-known hybrid inflation model [1], which couples the inflaton field to the Higgs field of a Grand Unified Theory (GUT) in order to obtain without tunning the desired false vacuum energy scale [2]. In hybrid inflation the inflationary period is terminated through the dynamics of this other field. In an analogous manner, one can attribute the generation of density perturbations during inflation to a field other than the inflaton [3]. This so-called curvaton field allows inflation to take place at a much lower energy scale than the typically required GUT-scale [4] and, in general, may relax a number of constraints regarding inflation model-building [5]. Low-scale inflation can revamp a number of inflation models that are well motivated on particle physics grounds [4]. It is important to stress here that the curvaton is not an ad hoc additional degree of freedom introduced “by hand”, but it may be a realistic field, already present in simple extensions of the standard model. Indeed, many such examples exist in the literature [6, 7]. However, even when a curvaton field is considered, there exists a lower bound for the inflationary scale, which, for generic curvaton models, can be quite tight [8]. This lower bound can be substantially relaxed for certain types of curvaton models [9], which enables inflation to be directly connected to realistic, beyond the standard model physics. In this letter I present a curvaton model which allows inflation at a Hubble scale as low as 1 TeV. The curvaton field is a pseudo Nambu-Goldstone boson (PNGB), whose order parameter is substantially increased after the cosmological scales exit the horizon during inflation. As shown in [9], the result of this increase is to amplify the curvaton’s perturbations. This enables even low-scale inflation to generate density perturbations of the observed amplitude. In the curvaton model presented, the increase of the PNGB order parameter follows a phase transition during inflation, which releases the radial mode from the top of the potential hill. The use of a PNGB curvaton is highly motivated because such a curvaton can be naturally light during inflation, since its mass is protected by the global U(1) symmetry [7]. This dispenses with the danger imposed by supergravity corrections, which typically lift the flatness of the scalar potential [10]. We investigate the performance of the curvaton model in the context of modular inflation, which corresponds to Hubble scale of order 1 TeV. Modular inflation is a well motivated model, which uses a string axion as the inflaton [11]. Let us begin by presenting the amplification mechanism for the curvature perturbations. We discuss here the case of an PNGB curvaton, whose order parameter has a different (larger) expectation value in the vacuum than during inflation and, in particular, when the cosmological scales exit the horizon. Thus, the potential for the curvaton field σ is V (σ) = (vm̃σ) [1− cos(σ/v)] ⇒ V (|σ| < v) ≃ 1 2 m̃σσ , (1) where v = v(t) is the order parameter determined by the expectation value of the radial field |φ| and m̃σ = m̃σ(v) is the mass of the curvaton at a given moment. In the true vacuum we have v = v0 and m̃σ = mσ with v0 being the vacuum expectation value (VEV) of the radial field and mσ being the mass of the curvaton in the vacuum. Let us demonstrate that the curvaton perturbations can be amplified by the non-trivial evolution of the radial field. We begin by using the fact that [3]: ζ ∼ Ωdecζσ , (2)