MSSM flat direction inflation: slow roll, stability, fine tunning and reheating

TL;DR

The paper develops a low-scale inflation model within the MSSM, driven by the udd or LLe flat directions near a saddle point of the scalar potential. It analyzes stability under radiative and supergravity corrections, showing radiative effects require modest fine-tuning while SUGRA corrections are negligible, and demonstrates a viable reheating history that avoids the gravitino problem. By solving the RG equations for the LLe direction, it connects the inflaton mass to slepton masses, offering potential collider tests at the LHC or a future Linear Collider. The work provides a concrete, testable link between early-Universe inflation and observable particle physics, without relying on Planck-scale dynamics or trans-Planckian field values.

Abstract

We consider low scale slow roll inflation driven by the gauge invariant flat directions {\bf udd} and {\bf LLe} of the Minimally Supersymmetric Standard Model at the vicinity of a saddle point of the scalar potential. We study the stability of saddle point and the slow roll regime by considering radiative and supergravity corrections. The latter are found to be harmless, but the former require a modest finetuning of the saddle point condition. We show that while the inflaton decays almost instantly, full thermalization occurs late, typically at a temperature $T\approx 10^{7}$ GeV, so that there is no gravitino problem. We also compute the renormalization group running of the inflaton mass and relate it to slepton masses that may be within the reach of LHC and could be precisely determined in a future Linear Collider experiment.

Figures (5)

• Figure 1: The colored curves depict the full potential, where $V(x)\equiv V(\phi)/(0.5~m_{\phi}^2 M_{\rm P}^2(m_{\phi}/M_{\rm P})^{1/2})$, and $x\equiv (\lambda_n M_{\rm P}/m_{\phi})^{1/4} (\phi/M_{\rm P})$. The black curve is the potential arising from the soft SUSY breaking mass term. The black dots on the colored potentials illustrate the gradual transition from minimum to the saddle point and to the maximum.
• Figure 2: The red curve depicts the potential, $V(x)\equiv V(\phi)/(0.5m_{\phi}^2M_{\rm P}^2(m_{\phi}/M_{\rm P})^{1/2})$, where $x\equiv (\lambda_n M_{\rm P}/m_{\phi})^{1/4}(\phi/M_{\rm P})$, for the saddle point (shown by the black dot) when $\delta=1$. The blue curve illustrates the potential when $\delta =1+\sqrt{40}/1000$, where the two black dots, one on right shows the minimum value $\phi_-$ and on the left shows the maximum value, $\phi_{+}$. The green curve portrays the potential for the opposite case when $\delta =1-\sqrt{40}/1000$. The black dot is the point of inflection.
• Figure 3: The tilt of the MSSM model as a function of the saddle point deviation parameter $\beta$ (3.16). We have plotted both cases $\delta < 1$ and $\delta > 1$. Note the allowed $2\sigma$ range coming from a combination of CMB and LSS observations.
• Figure 4: The running of $m^2_{\phi}$ for the $LLe$ inflaton when the saddle point is at $\phi_0 = 2.6 \times 10^{14}$GeV (corresponding to $n=6$, $m_{\phi}=1$ TeV and $\lambda = 1$). The three curves correspond to different values of the ratio of gaugino mass to flat direction mass at the GUT scale: $\xi = 2$ (dashed), $\xi = 1$ (solid) and $\xi = 0.5$ (dash-dot).
• Figure 5: The same as Fig. 1 but with $\phi_0 = 10^{14}$GeV (solid) and $\phi_0 = 10^{15}$GeV (dashed), and $\xi = 1$.