Graviton Cosmology in Universal Extra Dimensions

TL;DR

The paper analyzes gravitons in universal extra dimensions by deriving KK graviton couplings for torus and orbifold compactifications and computing NLKP decay widths into LKP gravitons, establishing lifetimes of order $10^{5}$–$10^{8}$ s that impact BBN. It then shows that primordial production of the KK gravitons is dramatically enhanced by the KK tower, yielding a gravitons abundance scaling as $\zeta_G \sim \frac{m_{\text{KK}}^2}{M_4} \left( \frac{T_{\text{RH}}}{m_{\text{KK}}} \right)^{2+3d/2}$, which imposes stringent bounds on the reheat temperature $T_{\text{RH}}$ (typically $\lesssim 1$–$10$ TeV for $m_{\text{KK}} \sim 100$ GeV–1 TeV). Despite these constraints, there exists a window with $T_{\text{RH}} \sim m_{\text{KK}}$ that yields the correct thermal relic densities for KK WIMP and superWIMP dark matter, making KK gravitons a viable dark sector component in certain cosmologies. The findings have broad implications for dark matter phenomenology, as well as for leptogenesis and inflation models constrained by low reheating temperatures.

Abstract

In models of universal extra dimensions, gravity and all standard model fields propagate in the extra dimensions. Previous studies of such models have concentrated on the Kaluza-Klein (KK) partners of standard model particles. Here we determine the properties of the KK gravitons and explore their cosmological implications. We find the lifetimes of decays to KK gravitons, of relevance for the viability of KK gravitons as dark matter. We then discuss the primordial production of KK gravitons after reheating. The existence of a tower of KK graviton states makes such production extremely efficient: for reheat temperature T_RH and d extra dimensions, the energy density stored in gravitons scales as T_RH^{2+3d/2}. Overclosure and Big Bang nucleosynthesis therefore stringently constrain T_RH in all universal extra dimension scenarios. At the same time, there is a window of reheat temperatures low enough to avoid these constraints and high enough to generate the desired thermal relic density for KK WIMP and superWIMP dark matter.

Figures (1)

• Figure 1: Bounds on the reheat temperature $T_{\text{RH}}$ as a function of $m_{\text{KK}}$ from the overclosure constraint $\Omega_G < 0.23$ and the BBN constraint $\zeta_G < 10^{-12}~\text{GeV}$ for $D=5,7$, as indicated. We assume $g_*^{KK} = 200$; the range in each bound arises from varying $C$ from $0.001$ to $0.1$ (see text). In the region with $T_{\text{RH}} < m_{\text{KK}}/25$, $T_{\text{RH}}$ is too low to generate the thermal relic abundance for WIMPs. The vertical bands delimit regions where the $B^1$ thermal relic abundance is too low ($\Omega_{\text{WIMP}} < 0.1$), approximately right, and too high ($\Omega_{\text{WIMP}} > 0.3$).