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Higher order terms in the inflaton potential and the lower bound on the tensor to scalar ratio r

Abstract : The MCMC analysis of the CMB + LSS data in the context of the Ginsburg-Landau approach to inflation indicated that the fourth degree double-well inflaton potential in new inflation gives an excellent fit of the present CMB and LSS data. This provided a lower bound for the ratio r of the tensor to scalar fluctuations and as most probable value r ~= 0.05, within reach of the forthcoming CMB observations. In this paper we systematically analyze the effects of arbitrarily higher order terms in the inflaton potential on the CMB observables: spectral index ns and ratio r. Furthermore, we compute in close form the inflaton potential dynamically generated when the inflaton field is a fermion condensate in the inflationary universe. This inflaton potential turns out to belong to the Ginsburg-Landau class too. The theoretical values in the (ns, r) plane for all double well inflaton potentials in the Ginsburg-Landau approach (including the potential generated by fermions) fall inside a universal banana-shaped region B. The upper border of the banana-shaped region B is given by the fourth order double-well potential and provides an upper bound for the ratio r. The lower border of B is defined by the quadratic plus an infinite barrier inflaton potential and provides a lower bound for the ratio r. For example, the current best value of the spectral index ns = 0.964, implies r is in the interval: 0.021 < r < 0.053. Interestingly enough, this range is within reach of forthcoming CMB observations.
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Submitted on : Tuesday, August 2, 2022 - 1:30:53 PM
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C. Destri, Hector J. de Vega, Norma G. Sánchez. Higher order terms in the inflaton potential and the lower bound on the tensor to scalar ratio r. Annals of Physics, Elsevier Masson, 2011, 326, pp.578-603. ⟨10.1016/j.aop.2010.11.019⟩. ⟨hal-03742349⟩