Gravitational Baryogenesis

We show that a gravitational interaction between the derivative of the Ricci scalar curvature and the baryon-number current dynamically breaks $CPT$ in an expanding Universe and, combined with baryon-number-violating interactions, can drive the Universe towards an equilibrium baryon asymmetry that is observationally acceptable.

Figure 1

The range of $T_{\mathrm{R}\mathrm{D}}$, $M_B$, and $w$ that can generate an observationally acceptable $B$-asymmetry, assuming a dimension five ($n=1$) $B$-violating operator and no significant entropy production after decoupling, is shown in dark gray and light gray. In supersymmetric theories, where the gravitino decays rapidly to an LSP with ${\mathrm{m}}_{\mathrm{L}\mathrm{S}\mathrm{P}}\approx 100\mathrm{G}\mathrm{e}\mathrm{V}$, the allowed region is restricted to the dark gray region only to avoid overclosure of the Universe by LSP’s. Both light and dark gray regions are allowed if the ${\mathrm{m}}_{\mathrm{L}\mathrm{S}\mathrm{P}}\ll 100\mathrm{G}\mathrm{e}\mathrm{V}$, if the LSP decays, if the gravitino is lighter than keV, or if there is no supersymmetry.

Figure 2

The range of $T_{\mathrm{R}\mathrm{D}}$, $M_B$, and $w$ that can generate an observationally acceptable $B$-asymmetry and avoid overclosure of the Universe by stable LSP’s expands to cover essentially both the light and dark gray regions in Fig. 1 if we allow for entropy to be produced after the B-violating interactions and gravitinos decouple. For each $w$, the allowed line in Fig. 1 becomes an allowed strip (shown for two cases in the Figure) because we now include the possibility that the $B$-asymmetry may be overproduced at decoupling to some degree and brought to its proper value by entropy production after decoupling. For the case $w=0.5$, we indicate along the strip the values of $n_B/s$ before dilution. The additional entropy reduces the gravitino/LSP density, thereby opening up the allowed range of $T_{\mathrm{R}\mathrm{D}}$ and $M_B$.