Big-Bang Nucleosynthesis as a Probe of the Geometry of Superspace

We study the effect from a general ultralocal supermetric on primordial nucleosynthesis for Friedmann-Robertson-Walker Cosmology. The parameter $\lambda$ of the supermetric changes the effective number of degrees of freedom, $g_*$, which modifies the Friedmann equation. This modification produces variations in the production of primordial $^4He$. The observations of the primordial abundances of light elements ($^4He$, $D$, $^3He$ and $^7Li$) allow to estimate bounds on the values of $\lambda$ consistent with these observations. We obtain $0.87 \le \lambda \le 1.04$. In addition we analyze the importance of $\lambda < 1$ to explain possible incompatibilities in the standard Big-Bang nucleosynthesis.