In the absence of CMB precision measurements, a Taylor expansion has often been invoked to parametrize the Hubble flow function during inflation. The standard "horizon flow" procedure implicitly relies on this assumption. However, the recent Planck results indicate a strong preference for plateau inflation, which suggests the use of Padé approximants instead. We propose a novel method that provides analytic solutions of the flow equations for a given parametrization of the Hubble function. This method is illustrated in the Taylor and Padé cases, for low order expansions. We then present the results of a full numerical treatment scanning larger order expansions, and compare these parametrizations in terms of convergence, prior dependence, predictivity and compatibility with the data. Finally, we highlight the implications for potential reconstruction methods.
We assess the range of validity of sgoldstino-less inflation in a scenario of low energy supersymmetry breaking. We first analyze the consistency conditions that an effective theory of the inflaton and goldstino superfields should satisfy in order to be faithfully described by a sgoldstino-less model. Enlarging the scope of previous studies, we investigate the case where the effective field theory cut-off, and hence also the sgoldstino mass, are inflaton-dependent. We then introduce a UV complete model where one can realize successfully sgoldstino-less inflation and gauge mediation of supersymmetry breaking, combining the α-attractor mechanism and a weakly coupled model of spontaneous breaking of supersymmetry. In this class of models we find that, given current limits on superpartner masses, the gravitino mass has a lower bound of the order of the MeV, i.e. we cannot reach very low supersymmetry breaking scales. On the plus side, we recognize that in this framework, one can derive the complete superpartner spectrum as well as compute inflation observables, the reheating temperature, and address the gravitino overabundance problem. We then show that further constraints come from collider results and inflation observables. Their non trivial interplay seems a staple feature of phenomenological studies of supersymmetric inflationary models. arXiv:1705.06788v2 [hep-th] 9 Aug 2017Contents Recently there has been renewed interest in models of inflation in supergravity [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The inflationary paradigm for the very early universe is indeed supported by more and more experimental evidence, and the high energy scales that it naturally involves beg for its embedding in supergravity, as a first step towards a more complete quantum treatment in string theory models. 1 Models where the sgoldstino itself is the inflaton exist [24][25][26][27], though it has been more popular to consider an inflaton superfield together with a stabilizer superfield [28], which can cure most of the problems of SUGRA inflation, and/or together with a supersymmetry breaking sector [29][30][31].2 There are models where the inflaton resides directly into the hidden sector [34][35][36][37][38][39], though there seem to be difficulties in getting towards low supersymmetry breaking scales.
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