On spin-driven inflation from inflaton fields in General Relativity and COBE data

Obukhov spin-driven inflation in General Relativity is extended to include inflaton fields.A de Sitter phase solution is obtained and new slow-rolling conditions for the spin potential are obtained.The spin potential reduces to Obukhov result at the present epoch of the Universe where the spin density is low with comparison to the Early Universe spin densities.A relation betwenn the spin density energy and the temperature fluctuation can be obtained which allow us to determine the spin density energy in terms of the COBE data for temperature fluctuations. Departamento de F́ısica Teórica Instituto de F́ısica UERJ Rua São Fco. Xavier 524, Rio de Janeiro, RJ, Maracanã, CEP:20550-003. Recently I showed [1]that COBE results on temperature fluctuations could be used to compute the spin-torsion density [2] at the inflation de Sitter phase of the Universe and at the present epoch.More recently Ramos and myself [3] investigated the role of spin-torsion on the chaotic phase of the Universe showing that the spin and torsion interactions are effectively only at the very first e-folds of inflation becoming quickly negligible and therefore not affecting the standard inflationary scenario nor the density perturbations.Earlier L.H.Ford [4] proposed a model of a vector driven inflation instead of the more usual models of scalar inflation proposed by Linde [5] and Guth [6]. More recently Obukhov [7] extended Ford’s work to include a spinning fluid like in torsion theories of gravity building a spin-driven inflation.In this letter we extend Obukhov idea to allow for a double vector-scalar inflation where the role of the scalar field is played by the inflaton and the vector role is played by the spin in the context of general relativity.This work can be further generalized if we also allow for the presence of torsion.But spin-torsion inflation with scalar field have been extensively investigated.Some interesting results appear from our model such as a new slow rolling condition for the spin potential in analogy to the slow rolling condition for the standard inflationary scenario. At the present epoch of the Universe both spin potentials coincide.Besides we compute the spin density energy from the COBE data of temperature fluctuations and found a result very similar to Obukhov one.Our dynamical equations are easily obtained from the Obukhov ones by the following prescription.We must substitute the spinning fluid pressure and matter densities by the following effective densities eeff = φ̇ 2 + V (φ) (1) and peff = φ̇ 2 − V (φ) (2) where φ is the inflaton potential and V (φ) is the inflaton potential which throughtout this work we shall take to be V (φ) = m φ 2 .Taking the usual Friedmann cosmological metric ds = dt − a(t)(dx + dy + dz) (3) Obukhov dynamical spinning fluid equations endowed with dilaton fields read 3 ȧ a = k(eeff + Vspin) (4)