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The curvaton scenario in supersymmetric theories

Marieke Postma

TL;DR

This work analyzes the curvaton mechanism within supersymmetric theories, highlighting that generic SUSY-breaking during inflation induces soft masses of order the Hubble scale, which disrupt scale-invariant perturbations unless protected by symmetries. It assesses three protection schemes—no-scale gravity, D-term inflation, and pseudo-Goldstone bosons—along with the impact of non-renormalizable operators and thermal/nucleosynthesis constraints, to map viable parameter regions for curvaton candidates. The study derives explicit relations for perturbation amplitudes and spectral tilt, and rigorously outlines the bounds on mass, coupling $h$, and inflationary scale required for successful conversion of isocurvature to adiabatic perturbations. The results show that only narrowly tuned or specially protected SUSY realizations can realize the curvaton scenario in the early universe, often demanding very small couplings ($h\lesssim 10^{-8}$) and careful control of higher-order operators. These findings guide model-building for early-universe cosmology and the role of SUSY fields in generating observable CMB perturbations.

Abstract

We analyze the curvaton scenario in the context of supersymmety. Supersymmetric theories contain many scalars, and therefore many curvaton candidates. To obtain a scale invariant perturbation spectrum, the curvaton mass should be small during inflation $m \ll H$. This can be achieved by invoking symmetries, which suppress the soft masses and non-renormalizable terms in the potential. Other constraints on the curvaton model come from nucleosynthesis, gravitino overproduction, and thermal evaporation. The curvaton coupling to matter should be very small to satisfy these constraints ({\it e.g.} $h \lesssim 10^{-8}$ for typical soft masses $m \sim \TeV$).

The curvaton scenario in supersymmetric theories

TL;DR

This work analyzes the curvaton mechanism within supersymmetric theories, highlighting that generic SUSY-breaking during inflation induces soft masses of order the Hubble scale, which disrupt scale-invariant perturbations unless protected by symmetries. It assesses three protection schemes—no-scale gravity, D-term inflation, and pseudo-Goldstone bosons—along with the impact of non-renormalizable operators and thermal/nucleosynthesis constraints, to map viable parameter regions for curvaton candidates. The study derives explicit relations for perturbation amplitudes and spectral tilt, and rigorously outlines the bounds on mass, coupling , and inflationary scale required for successful conversion of isocurvature to adiabatic perturbations. The results show that only narrowly tuned or specially protected SUSY realizations can realize the curvaton scenario in the early universe, often demanding very small couplings () and careful control of higher-order operators. These findings guide model-building for early-universe cosmology and the role of SUSY fields in generating observable CMB perturbations.

Abstract

We analyze the curvaton scenario in the context of supersymmety. Supersymmetric theories contain many scalars, and therefore many curvaton candidates. To obtain a scale invariant perturbation spectrum, the curvaton mass should be small during inflation . This can be achieved by invoking symmetries, which suppress the soft masses and non-renormalizable terms in the potential. Other constraints on the curvaton model come from nucleosynthesis, gravitino overproduction, and thermal evaporation. The curvaton coupling to matter should be very small to satisfy these constraints ({\it e.g.} for typical soft masses ).

Paper Structure

This paper contains 12 sections, 37 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Constraints
  3. Density perturbations
  4. Initial conditions
  5. Domination
  6. Thermal constraints
  7. Various models
  8. Negative mass squared --- no-scale inflation
  9. Positive mass squared --- no-scale inflation and Goldstone bosons
  10. Positive mass squared --- non-renormalizable terms
  11. D-term inflation
  12. Conclusions

Figures (4)

  • Figure 1: Parameter space for the curvaton model in no-scale type gravities with a soft mass term $\delta m^2 \approx - 10^{-2} h^2 H^2$ during inflation, for the parameters $M/\sqrt{\lambda} =M_{\rm P}'$, $n=2$, and $\Gamma_I >m$. The curvaton scenario works for masses and couplings in the shaded area.
  • Figure 2: Parameter space for models with a positive mass squared during inflation, for $\Gamma_I >m$. The curvaton scenario works for masses and couplings in the shaded area.
  • Figure 3: Constraints from gravitino production for $T_I =10^7 \,\hbox{GeV}$
  • Figure 4: Parameter space when the effective mass is set by higher order terms $\phi^6$ ($n=2$), $\phi^8$ ($n=4$), or $\phi^{10}$ ($n=4$). Here $M = M_{\rm P}$, $\lambda =1$, $\Gamma_I > m$, and $\kappa \to 1$. The dashed line corresponds to the $r=1$ line in the absence of higher order terms (from Fig. 2), which is added for comparison.