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We discuss the phenomenological implications of hybrid natural inflation models in which the inflaton is a pseudo-Goldstone boson but inflation is terminated by a second scalar field. A feature of the scheme is that the scale of breaking of the Goldstone symmetry can be lower than the Planck scale and so gravitational corrections are under control. We show that, for supersymmetric models, the scale of inflation can be chosen anywhere between the Lyth upper bound and a value close to the electroweak breaking scale. Unlike previous models of low scale inflation the observed density perturbations and spectral index are readily obtained by the choice of the free parameters.
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A spontaneously broken global discrete symmetry may have pseudo Goldstone modes associated with the spontaneous breaking of the approximate continuous symmetry of the low dimension terms in the Lagrangian. These provide natural candidates for an inflaton that can generate slow roll inflation. We show that, in the case of a non Abelian discrete symmetry, the pseudo Goldstone modes readily couple to further scalar fields in a manner that the end of inflation is determined by these additional scalar fields, generating hybrid inflation. We give a simple parameterisation of the inflationary potential in this case, determine the inflationary parameters resulting, and show that phenomenological successful inflation is possible while keeping the scale of symmetry breaking sub-Plankian. Unlike natural inflation the inflation scale can be very low. We construct two simple hybrid inflation models, one non supersymmetric and one supersymmetric. In the latter case no parameters need be chosen anomalously small.
We discuss the hybrid inflation model where the inflaton field is nonminimally coupled to gravity. In the Jordan frame, the potential contains $phi^4$ term as well as terms in the original hybrid inflation model. In our model, inflation can be classified into the type (I) and the type (II). In the type (I), inflation is terminated by the tachyonic instability of the waterfall field, while in the type (II) by the violation of slow-roll conditions. In our model, the reheating takes place only at the true minimum and even in the case (II) finally the tachyonic instability occurs after the termination of inflation. For a negative nonminimal coupling, inflation takes place in the vacuum-dominated region, in the large field region, or near the local minimum/maximum. Inflation in the vacuum dominated region becomes either the type (I) or (II), resulting in blue or red spectrum of the curvature perturbations, respectively. Inflation around the local maximum can be either the type (I) or the type (II), which results in the red spectrum of the curvature perturbations, while it around the local minimum must be the type (I), which results in the blue spectrum. In the large field region, to terminate inflation, potential in the Einstein frame must be positively tilted, always resulting in the red spectrum. We then numerically solve the equations of motion to investigate the whole dynamics of inflaton and confirm that the spectrum of curvature perturbations changes from red to blue ones as scales become smaller.
In hybrid inflation, the inflaton generically has a tadpole due to gravitational effects in supergravity, which significantly changes the inflaton dynamics in high-scale supersymmetry. We point out that the tadpole can be cancelled if there is a supersymmetry breaking singlet with gravitational couplings, and in particular, the cancellation is automatic in no-scale supergravity. We consider the LARGE volume scenario as a concrete example and discuss the compatibility between the hybrid inflation and the moduli stabilization. We also point out that the dark radiation generated by the overall volume modulus decay naturally relaxes a tension between the observed spectral index and the prediction of the hybrid inflation.
We introduce a minimal and yet comprehensive framework with $CP$- and classical scale-symmetries, in order to simultaneously address the hierarchy problem, neutrino masses, dark matter, and inflation. One complex gauge singlet scalar and three flavors of the right-handed Majorana neutrinos are added to the standard model content, facilitating the see-saw mechanism, among others. An adimensional theory of gravity (Agravity) is employed, allowing for the trans-Planckian field excursions. The weak and Planck scales are induced by the Higgs portal and the scalar non-minimal couplings, respectively, once a Coleman-Weinberg dynamically-generated vacuum expectation value for the singlet scalar is obtained. All scales are free from any mutual quadratic destabilization. The $CP$-symmetry prevents a decay of the pseudoscalar singlet, rendering it a suitable WIMPzilla dark matter candidate with the correct observational relic abundance. Identifying the pseudo-Nambu-Goldstone boson of the (approximate) scale symmetry with the inflaton field, the model accommodates successful slow-roll inflation, compatible with the observational data. We reach the conclusion that a pseudo-Nambu-Goldstone inflaton, within a classically scale-symmetric framework, yields lighter WIMPzillas.
Scalar fields, $phi_i$ can be coupled non-minimally to curvature and satisfy the general criteria: (i) the theory has no mass input parameters, including the Planck mass; (ii) the $phi_i$ have arbitrary values and gradients, but undergo a general expansion and relaxation to constant values that satisfy a nontrivial constraint, $K(phi_i) =$ constant; (iii) this constraint breaks scale symmetry spontaneously, and the Planck mass is dynamically generated; (iv) there can be adequate inflation associated with slow roll in a scale invariant potential subject to the constraint; (v) the final vacuum can have a small to vanishing cosmological constant (vi) large hierarchies in vacuum expectation values can naturally form; (vii) there is a harmless dilaton which naturally eludes the usual constraints on massless scalars. These models are governed by a global Weyl scale symmetry and its conserved current, $K_mu$ . At the quantum level the Weyl scale symmetry can be maintained by an invariant specification of renormalized quantities.
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