Radiative corrections set up inflation: dynamical models

We establish the possibility that the initial configuration of fields for an inflationary period in the early universe can be set up by radiative corrections to the tree-level potential. A maximum of the radiatively-corrected potential can occur at an energy scale just above the Planck scale; we consider that the scalar (inflaton}) field rolls down from this maximum. In a model, we find that the radiative corrections also induce a minimum in the potential at a non–zero value of the energy scale somewhat below the Planck scale.     

Chaotic inflation

We investigate the conditions under which the chaotic inflationary model can provide sufficient inflation to solve the usual cosmological problems. We use a mixture of analytic and numerical techniques to examine the success of the model in cases where spatial curvatures of the background metric are large and when the scalar field lagrangian includes contributions from velocity terms and spatial gradients. Using the simplest natural measure on the space of initial conditions, we calculate the probability of obtaining sufficient inflation given random initial conditions when velocity terms and curvature terms are included. We find this probability to be large in all cases considered. We also derive conditions under which scalar field inhomogeneities will not affect the viability of inflation.     

Fluxbrane inflation

As a first step towards inflation in genuinely F-theoretic setups, we propose a scenario where the inflaton is the relative position of two 7-branes on holomorphic 4-cycles. Non-supersymmetric gauge flux induces an attractive inter-brane potential. The latter is sufficiently flat in the supergravity regime of large volume moduli. Thus, in contrast to brane-antibrane inflation, fluxbrane inflation does not require warping. We calculate the inflaton potential both in the supergravity approximation and via an open-string one-loop computation on toroidal backgrounds. This leads us to propose a generalisation to genuine Calabi-Yau manifolds. We also comment on competing F-term effects. The end of inflation is marked by the condensation of tachyonic recombination fields between the 7-branes, triggering the formation of a bound state described as a stable extension along the 7-brane divisor. Hence our model fits in the framework of hybrid D-term inflation. We work out the main phenomenological properties of our D-term inflaton potential. In particular, our scenario of D7/D7 inflation avoids the familiar observational constraints associated with cosmic strings.     

Ultraviolet-protected inflation

In natural inflation, the inflaton is a pseudo-Nambu-Goldstone boson which acquires a mass by explicit breaking of a global shift symmetry at scale f. In this case, for small field values, the potential is flat and stable under radiative corrections. Nevertheless, slow roll conditions enforce f ? M(p), making the validity of the whole scenario questionable. In this Letter, we show that a coupling of the inflaton kinetic term to the Einstein tensor allows f ? M(p) by enhancing the gravitational friction acting on the inflaton during inflation. This new unique interaction (a) keeps the theory perturbative in the whole inflationary trajectory, (b) preserves the tree-level shift invariance of the pseudo-Nambu-Goldstone boson, and (c) avoids the introduction of any new degrees of freedom with respect to standard natural inflation.     

Flavon inflation

We propose an entirely new class of particle physics models of inflation based on the phase transition associated with the spontaneous breaking of family symmetry responsible for the generation of the effective quark and lepton Yukawa couplings. We show that the Higgs fields responsible for the breaking of family symmetry, called flavons, are natural candidates for the inflaton field in new inflation, or the waterfall fields in hybrid inflation. This opens up a rich vein of possibilities for inflation, all linked to the physics of flavour, with interesting cosmological and phenomenological implications. Out of these, we discuss two examples which realise flavon inflation: a model of new inflation based on the discrete non-Abelian family symmetry group A₄$A_4$ or Δ₂₇${\mathrm{\Delta }}_{27}$, and a model of hybrid inflation embedded in an existing flavour model with a continuous SU(3)$\mathit{SU}(3)$ family symmetry. With the inflation scale and family symmetry breaking scale below the Grand Unification Theory (GUT) scale, these classes of models are free of the monopole (and similar) problems which are often associated with the GUT phase transition.     

Minimal inflation

Using the universal X-superfield that measures in the UV the violation of conformal invariance we build up a model of multifield inflation. The underlying dynamics is the one controlling the natural flow of this field in the IR to the goldstino superfield once SUSY is broken. We show that flat directions satisfying the slow-roll conditions exist only if R-symmetry is broken. Naturalness of our model leads to scales of SUSY breaking of the order of 10^11–13 GeV, a nearly scale-invariant spectrum of the initial perturbations and negligible gravitational waves. We obtain that the inflaton field is lighter than the gravitino by an amount determined by the slow-roll parameter η. The existence of slow-roll conditions is directly linked to the values of supersymmetry and R-symmetry breaking scales. We make cosmological predictions of our model and compare them to current data.     

Extranatural inflation

We present a new model of inflation in which the inflaton is the extra component of a gauge field in a 5D theory compactified on a circle. The chief merit of this model is that the potential comes only from nonlocal effects so that its flatness is not spoiled by higher-dimensional operators or quantum gravity corrections. The model predicts a red spectrum (n approximately 0.96) and a significant production of gravitational waves (r approximately 0.11). We also comment on the relevance of this idea to quintessence.