MSSM inflation, dark matter, and the LHC

Inflation can occur near a point of inflection in the potential of flat directions of the minimal supersymmetric standard model (MSSM). In this paper we elaborate on the complementarity between the bounds from cosmic microwave background measurements, dark matter, and particle physics phenomenology in determining the underlying parameters of MSSM inflation by specializing to the minimal supergravity scenario. We show that the future measurements from the Large Hadron Collider in tandem with all these constraints will significantly restrict the allowed parameter space. We also suggest a new perspective on the fine tuning issue of MSSM inflation. With quantum corrections taken into account, the necessary condition between the soft supersymmetry breaking parameters in the inflaton potential can be satisfied at scales of interest without a fine tuning of their boundary values at a high scale. The requirement that this happens at the inflection point determines a dimensionless coupling, which is associated with a nonrenormalizable interaction term in the Lagrangian and has no bearing for phenomenology, to very high accuracy.

Figure 1

The green band shows the acceptable region in the $m_{\varphi }-{\varphi }_0$ plane where MSSM inflation generates density perturbations compatible with the $2\sigma$ region allowed by WMAP data. The dark curve at the center corresponds the central value of $n_s$.

Figure 2

The ratio ($40m_{\varphi }^2/A^2$) as a function of $\mathrm{Log}[\frac{\mu }{\mathrm{GeV}}]$ in the case of the $udd$ flat direction. The curves are for $M_{\mathrm{GUT}}$ boundary values $m_{\varphi }=150$, 200, 250, 300 GeV (respectively from left to right), and $A=1.6\mathrm{TeV}$.

Figure 3

The ratio ($40m_{\varphi }^2/A^2$) as a function of $\mathrm{Log}[\frac{\mu }{\mathrm{GeV}}]$ in the case of the $udd$ flat direction. The curves are for $M_{\mathrm{GUT}}$ boundary values $A_{udd}=1.6$, 1.8, 2.0, 2.2 TeV (respectively from top to bottom), and $m_{\varphi }=400\mathrm{GeV}$.

Figure 4

The dots show the scale $\mu$ (horizontal axis) at which $A^2=40m_{\varphi }^2$, with the vertical axis representing the value of $40m_{\varphi }^2/A^2$ at $M_{\mathrm{GUT}}$, in the case of the $udd$ flat direction. It is seen that for a large number of points the scale is within the interesting range ${10}^{14}–{10}^{15}\mathrm{GeV}$.

Figure 5

The $m_{\varphi }-{\varphi }_0$ plane for the mSUGRA scenario, assuming $udd$ flat direction as the inflaton, with $A_0=0$ and $\tan \beta =10(50)$ in the upper (lower) panel. The $g_{\mu }-2$ bounds, denoted by D and T, are from [27, 28] respectively. The contours and shadings are described in the text.

Figure 6

The same as Fig. 5 for $\tan \beta =10(50)$ and $A_0=0$, assuming the $LLe$ flat direction as the inflaton.

Figure 7

The allowed regions in the $m_{\varphi }-{\varphi }_0$ plane as a result of mass measurement at the LHC, for the mSUGRA scenario with $\tan \beta =40$ and $A_0=0$. Here, $m_0=210\pm 4\mathrm{GeV}$ and $m_{1/2}=350\pm 4\mathrm{GeV}$, with uncertainties due to experimental uncertainty in the masses.