Gravitino Production in the Inflationary Universe and the Effects on Big-Bang Nucleosynthesis

TL;DR

This work reassesses gravitino production and radiative decay in the inflationary era, deriving the most stringent reheating-temperature bounds by combining a precise gravitino production rate with a numerically solved high-energy photon spectrum from gravitino decays. By incorporating the full supergravity interactions for helicity $\pm\tfrac{3}{2}$ states and solving the cascade Boltzmann equations, the authors show that photo-dissociation of light elements during BBN constrains $T_R$ to roughly $10^{6}$–$10^{9}$ GeV for $m_{3/2}$ in the 100 GeV–1 TeV range, while photino-density considerations impose $T_R \lesssim (10^{11}$–$10^{12})$ GeV for $m_{\tilde{\gamma}}$ in the 10–100 GeV range irrespective of $m_{3/2}$. They also explore smaller radiative branching ratios $B_\gamma$, finding weaker, but still conservative, bounds. Together, these results place strong cosmological constraints on inflationary models in supergravity frameworks and highlight the importance of accurately modeling gravitino production and photon cascades.

Abstract

Gravitino production and decay in the inflationary universe are reexamined. Assuming that the gravitino mainly decays into a photon and a photino, we calculate the upperbound on the reheating temperature. Compared to previous works, we have essentially improved the following two points: (i) the helicity $\pm\frac{3}{2}$ gravitino production cross sections are calculated by using the full relevant terms in the supergravity lagrangian, and (ii) the high energy photon spectrum is obtained by solving the Boltzmann equations numerically. Photo-dissociation of the light elements (D, T, $^3$He, $^4$He) leads to the most stringent upperbound on the reheating temperature, which is given by ($10^{6}$--$10^{9}$)GeV for the gravitino mass 100GeV--1TeV. On the other hand, requiring that the present mass density of photino should be smaller than the critical density, we find that the reheating temperature have to be smaller than ($10^{11}$--$10^{12}$)GeV for the photino mass (10--100)GeV, irrespectively of the gravitino mass. The effect of other decay channels is also considered.

Figures (6)

• Figure 1: Typical spectra of photon (the solid lines) and electron (the dotted lines). We take the temperature of the background photon to be $T=100 {\rm keV} , 1 {\rm keV} , 10 {\rm eV}$, and the energy of the incoming high energy photon $\epsilon_{\gamma 0}$ is (a) 100GeV and (b) 10TeV. Normalization of the initial photon is given by $\epsilon_{\gamma 0}\times( \partial \tilde{f}_{\gamma}( \epsilon_{\gamma} )/\partial t)|_{\rm DE}=\delta( \epsilon_{\gamma} - \epsilon_{\gamma 0})~ {\rm GeV} ^{5}$.
• Figure 2: Photon spectrum derived from the fitting formula used in Ref.NPB373-399 is compared with our result. We take the temperature of the background photon to be $100$eV and the normalization of the incoming flux is the same as Fig.\ref{['fig:spectra']}. The solid line is the result of fitting formula, and the dotted line is our result with $\epsilon_{\gamma} =100 {\rm GeV}$.
• Figure 3: Contours for critical abundance of light elements in the $\eta_B - T_R$ plane for (a) $m_{3/2} = 10 {\rm GeV}$, (b) $m_{3/2} = 100 {\rm GeV}$, (c) $m_{3/2} = 1 {\rm TeV}$ and (d)$m_{3/2} = 10 {\rm TeV}$.
• Figure 4: Allowed regions in $m_{3/2} - T_R$ plane for (a) $B_{\gamma} =1$, (b)$B_{\gamma} =0.1$ and (c) $B_{\gamma} =0.01$. In the region above the solid curve $^3$He and D are overproduced, the abundance of $^4$He is less than 0.22 above the dotted curve and the abundance of D is less than $1.8\times 10^{-5}$ above the dashed curve.
• Figure 5: Contours for the upper limits of the reheating temperature in the $m_{3/2} - B_{\gamma}$ plane. The numbers in the figure denote the limit of the reheating temperature.