Triple unification of inflation, dark matter, and dark energy using a single field

We construct an explicit scenario whereby the same material driving inflation in the early universe can comprise dark matter in the present universe, using a simple quadratic potential. Following inflation and preheating, the density of inflaton/dark matter particles is reduced to the observed level by a period of thermal inflation, of a duration already invoked in the literature for other reasons. Within the context of the string landscape, one can further argue for a nonzero vacuum energy of this field, thus unifying inflation, dark matter, and dark energy into a single fundamental field.

Figure 1

A schematic of the evolution of the densities throughout the Universe’s evolution. One (blue) line shows the density of the $\varphi$ field, and the other (black) line the combined density of all other materials. The latter changes shape depending whether this combined density is dominated by radiation or by the material driving thermal inflation. We also include a reheating period after thermal inflation. (To avoid confusing the diagram, we do not show the emergence of nonrelativistic baryons from the relativistic fluid at late times.)

Figure 2

The lines in both figures show the value of $\Gamma$ required to satisfy the abundance constraint Eq. (11), as a function of $\widehat{V}$, for some fixed values of $N_{\mathrm{TI}}$ (note that the value of $N_{\mathrm{TI}}$ itself depends on both $\widehat{V}$ and $\widehat{m}$) and the preheating coupling term $g^2$. Only models with large enough values of $N_{\mathrm{TI}}$ lie above the nucleosynthesis constraint line $\Gamma >{10}^{-42}{m}_{\mathrm{Pl}}$. We also show the thermal inflation estimation of the decay width $\Gamma$ (thin lines) for the cases $N_{\mathrm{TI}}=12$ (top) and $N_{\mathrm{TI}}=12.5$ (bottom); see text for details. As read from the crossing of the corresponding lines, models with flaton parameters of the order of $\widehat{m}\simeq {10}^3\mathrm{GeV}$ and ${\widehat{V}}^{1/4}\simeq {10}^8\mathrm{GeV}$ are able to satisfy all constraints.