ar X iv : h ep - t h / 04 12 18 6 v 1 16 D ec 2 00 4 Radiative corrections to scalar masses in de Sitter space

Quantum field theory in an inflating universe is thought to be the playground of the physical processes that took place during the early Universe [1]. However little has yet been explicitly computed for self interacting fields [2]. Any light bosonic fields with non minimal coupling that exist during an inflationary phase is bound to produce, together with the inflaton field, superhorizon fluctuations that eventually might be visible in mechanisms such as isocurvature modes generation from multi-field inflation [3, 4, 5, 6], curvaton models [7, 8], bent trajectory inflationary models [9, 10] or modulated fluctuations [11]. If such fields are self interacting, for instance with a quartic potential, such fluctuations might develop significant non-Gaussian features that in turn could be detected (see ref.[12] for a review). This would be only possible however if the radiative corrections do not render the particle too massive, e.g. with a mass larger than the Hubble constant H , to develop any fluctuations at all. One question then raised by phenomenological investigations of this physics is whether the mass of a self interacting bosonic field can be protected against radiative corrections. Of course one expects such a theory to be renormalizable but it implies that the fundamental bare theory has to be fine-tuned. The radiative correction to the mass of a self interacting boson should indeed be naively of the order of δm ∼ λM Pl (λ being the coupling constant). This question has been investigated in [22] in the case of the inflaton field. In this case λ is generically small since, for the inflaton field λM Pl has to be of the order of H . In the case we are interested in, however, we have no such constraints on λ which can then be close to unity. For such values of the coupling constant the scalar field becomes too heavy to develop significant fluctuations unless the cancellation is precise over ten orders of magnitude since H/M Pl ∼ 10 during inflation. On the other hand light scalar fields are expected to be associated with fermions as parts of super-multiplets in supersymmetric theories such as in D or F -term inflation models [13, 14]. From the Minkowskian behavior, one expects the largest divergences coming from the fermionic and bosonic loops to cancel out. The aim of this paper is precisely to compute the radiative corrections to a test boson mass embedded in a chiral multiplet and when it lives in an inflating universe. The test model will be the Wess-Zumino Lagrangian in an expanding universe, not necessarily assumed to be de Sitter. The background evolution of the Universe is assumed to be driven by an other sector of the theory. We set up the formalism in section II. In section III we compute the two-point function to get the one loop effective masses of the fields in any spacially flat Friedman-Lemâitre-Robertson-Walker (FLRW) spacetime. The ultraviolet and infrared behaviors are discussed in section IV. We show in particular that the infrared divergences can be apprehended in a classical approach. In the ultraviolet domain, the correction to the mass is found to be logarithmically divergent and proportional to the spacetime curvature and the coupling constant. It shows that masses of light scalar fields do not get a large contribution compared to the Hubble scale. Our results are put into perspective in the conclusion.