Baryon density of the Universe : an imprint of a scalar field ?

Abstract

The baryon density of our Universe, $\Omega_{b}h^{2}=0.0224\pm 0.0009$, as inferred from the WMAP first year of observations is used to predict the primordial abundances of light elements produced during Big Bang Nucleosynthesis (BBN). Such a baryon density, and a gravitation described by General Relativity, lead to predictions for the abundances of $^{4}$He and D in very good agreement with the observed ones; but they lead to a significant discrepancy between the calculated and the observed $^{7}$Li abundances. Supposing that the standard non gravitational sector is not modified, we consider scalar-tensor theories of gravity, and study their impact on the $^7$Li abundance. It is shown that an expansion of the Universe slower than in General Relativity at the beginning of BBN, and faster at the end both solves the lithium problem and leads to predictions for $^4$He and D abundances consistent with the observational constraints. Moreover, this behaviour is shown to be compatible with a convergence mechanism of the theory towards General Relativity at late times. This kind of behaviour is obtained thanks to numerous models, both without and with self-interactions for the scalar field.