Large Scale Structure and Supersymmetric Inflation without Fine Tuning

TL;DR

The paper tests large-scale structure data against inflationary cosmologies, focusing on the spectral index n and the hot dark matter fraction Ω_HDM using COBE, IRAS, bulk flows, cluster normalization, and quasar counts. The analysis shows n ≈ 1 and a mixed cold+hot dark matter model across H0 in 40–60 km s^-1 Mpc^-1, with n constrained near unity. The authors then realize a natural hybrid inflation scenario within supersymmetric GUTs based on G = SU(3)_c × SU(3)_L × SU(3)_R, where the inflaton sector is fixed by particle physics and avoids fine-tuning; the scalar density fluctuations scale as (M_X/M_P)^2, yielding n ≈ 0.98. This framework resolves the gauge hierarchy via an R-symmetry, predicts M_X ≈ 10^15.5 GeV and κ ≈ 10^-2 with negligible tensor modes, and provides a viable baryogenesis route and a bino-like LSP as cold dark matter, while allowing a see-saw neutrino sector.

Abstract

We explore constraints on the spectral index $n$ of density fluctuations and the neutrino energy density fraction $Ω_{HDM}$, employing data from a variety of large scale observations. The best fits occur for $n\approx 1$ and $Ω_{HDM} \approx 0.15 - 0.30$, over a range of Hubble constants $40-60$ km s$^{-1}$ Mpc$^{-1}$. We present a new class of inflationary models based on realistic supersymmetric grand unified theories which do not have the usual `fine tuning' problems. The amplitude of primordial density fluctuations, in particular, is found to be proportional to $(M_X /M_P)^2$, where $M_X (M_P)$ denote the GUT (Planck) scale, which is reminiscent of cosmic strings! The spectral index $n = 0.98$, in excellent agreement with the observations provided the dark matter is a mixture of `cold' and `hot' components.