Effects of the Gravitino on the Inflationary Universe

TL;DR

This work analyzes how gravitinos influence the inflationary universe, deriving cosmological bounds on the reheating temperature $T_R$ via BBN and present-day density arguments. It advances the analysis by incorporating complete gravitino production cross sections from local SUSY Lagrangians, solving high-energy photon spectra numerically through Boltzmann equations, and evolving light-element abundances with a modified Kawano code. The study distinguishes unstable and stable gravitino scenarios, showing that gravitino decays can severely constrain $T_R$ (via photodissociation of light elements) or, in the stable case, impose closure bounds on gravitino relics. Overall, the results connect early-universe dynamics, SUSY breaking, and cosmological observations to delimit viable inflationary and SUSY-breaking models.

Abstract

Gravitino problem is discussed in detail. We derive an upperbound on the reheating temperature from the constraints of the big-bang nucleosynthesis and the present mass density of the universe. Compared to previous works, we have improve the following three points; (i) the gravitino production cross sections are calculated by taking all the relevant terms in the supergravity lagrangian into account, (ii) high energy photon spectrum is obtained by solving the Boltzmann equations numerically, and (iii) the evolutions of the light elements (D, T, $^3$He, $^4$He) at the temperature lower than $\sim$1MeV are calculated by using modified Kawano's computer code.

Figures (28)

• Figure 1: Quadratically divergent Feynman diagrams for the $H_{2}$ mass. Diagram with CF (CB, GB, GF) is the contribution from chiral fermion (chiral boson, gauge boson, gauge fermion) loop. Dashed lines in external lines represent $H_{2}$. Notice that the diagram with $H_2$ loop (lower-left) originates to the gauge $D$-term, and hence we classify it as the contribution of gauge boson.
• Figure 2: Renormalization group flow of the coupling constants of ${\rm SU(3)}_{C}$, ${\rm SU(2)}_{L}$ and ${\rm U(1)}_{Y}$ gauge group for the case of (a) the MSSM, and (b) the standard model. Here, we use two loop renormalization group equations, and take the SUSY scale at 1TeV for the MSSM case.
• Figure 3: The predicted value of the running bottom-quark mass $m_b(m_b)$ is shown as a function of $\tan\beta$ for $\alpha_3(m_Z)=0.11$ and 0.12. Here, we take the (on-shell) top-quark mass at 174GeV.
• Figure 4: Feynman rules for the interactions of gravitino.
• Figure 5: Feynman diagrams for the processes (a) $\psi_\mu \rightarrow \lambda + A_\mu$, and (b) $\psi_\mu \rightarrow \phi^i + \overline{\chi}^i$.