Minimal Inflation Luis ´ Alvarez-Gaum´ e $^{a}$, C´ esar G´ omez $^{b,a}$, Raul Jimenezc,a $^{a}$Theory Group, Physics Department, CERN, CH-1211, Geneva 23, Switzerland. $^{b}$Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, E-28049 Madrid, Spain. $^{c}$ICREA & Institute of Sciences of the Cosmos (ICC), University of Barcelona, 08028 Barcelona, Spain. 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. Abstract arXiv:1001.0010v1 [hep-th] 30 Dec 2009 Key words: SUSY; cosmology; inflation ber of new problems that appear [24], and we will discuss some of them later on. In spite of the enormous success of inflationary cosmol- ogy [1, 2, 3, 4, 5, 6, 7, 8, 9] at describing the observed properties of the Universe, we are still missing a deriva- tion from first principles where the inflaton field is iden- tified with one, or several, fundamental fields in particle physics. This manifests itself the in the fact that we still do not count with a natural way of identifying the inflaton field and the properties of its potential required to satisfy experimental constraints [10, 11]. Current observational constraints from CMB tempera- ture and polarization experiments and large-scale struc- ture limit the amount the inflaton field has moved to ap- proximately < 2 M$_{pl}$ [14], where M$_{pl}$ is the reduced Planck mass. Therefore, inflationary models that search for the inflaton at very large energies, like for example chaotic inflation, are severely constrained already by current ob- servations. With the current new generation of CMB ex- periments (Planck, EBEX, Spider, SPUDS etc...) it will be possible to further constraint how much the inflaton field has displaced during the inflationary period that gave rise to our current casual horizon. It is therefore useful to revisit again the problem of steep directions in SUGRA models to understand if a flat direction can be obtained at all. It was quickly realized after the inflationary scenario was proposed more than 30 years ago, that supersymmetry could provide a natural scenario with plenty of flat direc- tions which could lead to inflation [18, 19, 20, 21, 22, 23]. When the theory couples to supergravity, there are a num- In this paper we will suggest a natural embedding of in- flationary dynamics in the effective low-energy Lagrangian October 26, 2018 Preprint submitted to Physics Letters B Email addresses: Luis.Alvarez-Gaume@cern.ch (Luis ´ Alvarez-Gaum´ e), cesar.gomez@uam.es (C´ esar G´ omez), jimenez@icc.ub.edu (Raul Jimenez) 1. Introduction