Large Scale Structure and Supersymmetric Inflation without Fine Tuning

Abstract

We explore constraints on the spectral index $n$ of density fluctuations and the neutrino energy density fraction ${\Omega }_{HDM}$, employing data from a variety of large scale observations. The best fits occur for $n\approx 1$ and ${\Omega }_{HDM}\approx 0.15-0.30$, 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.

Comments: LaTEX, 14 pp. + 1 postscript figure appended