Gravity waves and the LHC: Towards high-scale inflation with low-energy SUSY

TL;DR

The paper investigates whether high-scale inflation can coexist with low-energy SUSY in string-inspired supergravity by examining the KL problem and presenting a dynamical mechanism in which the superpotential expectation value W decreases during inflation, decoupling the Hubble scale from the gravitino mass. It constructs a toy model with an extra field X and a stabilized modulus that yields an F_X-dominated inflationary potential V(φ) ∼ α^2 φ^{2n}, showing m_{3/2} can be much smaller than H during inflation while avoiding decompactification. However, when constraining the model to TeV-scale SUSY after inflation, the no-decompactification condition and cosmological data force n to be large, which is incompatible with observed n_s and r, implying TeV gravitino is not viable in this setup. The study thus suggests that the KL tension is not universal across string-inspired inflation models, but achieving realistic SUSY scales with high-scale inflation remains an open challenge requiring further top-down modeling.

Abstract

It has been argued that rather generic features of string-inspired inflationary theories with low-energy supersymmetry (SUSY) make it difficult to achieve inflation with a Hubble scale H > m_{3/2}, where m_{3/2} is the gravitino mass in the SUSY-breaking vacuum state. We present a class of string-inspired supergravity realizations of chaotic inflation where a simple, dynamical mechanism yields hierarchically small scales of post-inflationary supersymmetry breaking. Within these toy models we can easily achieve small ratios between m_{3/2} and the Hubble scale of inflation. This is possible because the expectation value of the superpotential <W> relaxes from large to small values during the course of inflation. However, our toy models do not provide a reasonable fit to cosmological data if one sets the SUSY-breaking scale to m_{3/2} < TeV. Our work is a small step towards relieving the apparent tension between high-scale inflation and low-scale supersymmetry breaking in string compactifications.

Figures (4)

• Figure 1: The $|F/W|^2$-ratios plotted as functions of the inflaton $\varphi$ with $X$ and $T$ adiabatically tracking their instantaneous minima.
• Figure 2: The vev of the superpotential $|\langle W\rangle|=|\langle W(\varphi,X(\varphi),T(\varphi))\rangle|$ plotted as a function of the inflaton $\varphi$ with $X$ and $T$ adiabatically tracking their instantaneous minima.
• Figure 3: Minimum value of $n$ in the inflaton potential $V(\varphi)\sim \varphi^{2n}$ necessary to achieve a given $\delta\equiv \delta\rho/\rho$, at fixed $W_0=-10^{-15}$, satisfying the no-decompactification-constraint eq. (\ref{['fconstraint']}). Points are labelled in the format $(n,\mathcal{O}(|W_i|/|W_0|))$, where $W_i=\langle W(\varphi_{60},X(\varphi_{60}),T(\varphi_{60}))\rangle$ is the initial superpotential (and ${\cal O}(|x|)$ here denotes the order of magnitude of $|x|$).
• Figure 4: Minimum value of $n$ in the inflaton potential $V(\varphi)\sim \varphi^{2n}$ necessary to achieve a given post-inflationary vacuum VEV of the superpotential $W_0$, at fixed $\delta\equiv\delta\rho/\rho=2\times 10^{-5}$, satisfying the no-decompactification-constraint eq. (\ref{['fconstraint']}). Points are labelled in the format $(n,\mathcal{O}(|W_i|/|W_0|))$, where $W_i=\langle W(\varphi_{60},X(\varphi_{60}),T(\varphi_{60}))\rangle$ is the initial superpotential (and ${\cal O}(|x|)$ here denotes the order of magnitude of $|x|$).