Do fermions and bosons produce the same gravitational field?

We examine some cosmological consequences of gravity coupling with different strength to fermions and bosons. We show that this leads to a different perturbation of the standard picture of primordial nucleosynthesis than the addition of extra neutrino types or overall scaling of the value of $G$. Observed abundances of deuterium and ${}^4\mathrm{H}\mathrm{e}$ place bounds on the ratio of the bosonic gravitational constant ($G_B$) to the fermionic gravitational constant ($G_F$) of $0.45<G_B/G_F<0.92$ at $1\sigma$ and $0.33<G_B/G_F<1.10$ at $2\sigma$. A value of $G_B<G_F$ can reconcile the current “tension” between the abundances of deuterium and ${}^4\mathrm{H}\mathrm{e}$ predicted by primordial nucleosynthesis. We comment briefly on other cosmological effects.

Figure 1

The $1-\sigma$ (solid) and $2-\sigma$ (dashed) contours in the ${\eta }_{10}$, $f_{BF}$ plane, where $\eta ={\eta }_{10}\times {10}^{-10}$ and $f_{BF}=G_B/G_F$.