PHYS08200605006 D.K. Hazra - Homi Bhabha National Institute

CHAPTER 7. IMPRINTS OF PRIMORDIAL NON-GAUSSIANITY IN THE LY-ALPHA FOREST
k min (Mpc −1 ) ¯n (Mpc −2 ) S/N ∆f NL
∆b 1
2×10 −3 2.2×10 −3 5 228.84 1.1×10 −2
1×10 −3 2.2×10 −3 5 161.81 7.7×10 −3
5×10 −4 2.2×10 −3 5 114.42 5.5×10 −3
8×10 −4 1.0×10 −3 5 272.95 1.5×10 −2
8×10 −4 2.2×10 −3 5 144.73 6.9×10 −3
8×10 −4 5.0×10 −3 5 91.65 3.5×10 −3
8×10 −4 2.2×10 −3 2 263.52 1.5×10 −2
8×10 −4 2.2×10 −3 3 182.83 9.5×10 −3
8×10 −4 2.2×10 −3 4 156.56 7.7×10 −3
Ideal case
5×10 −4 1 5 23.72 2.1×10 −4
Table 7.1: The bounds on (f NL
,b 1 ) obtained from a Fisher analysis for various combinations
of(k min ,¯n,S/N).
∆f NL
∼ 23 in the equilateral limit.
We tabulate our results for varying sky coverage
[k −3
min = V/(2π)3 ], Poisson noise (∼ 1/¯n) and pixel noise (S/N) in Table 7.1. As expected
we have tighter constraints on (f NL
,b 1 ) with increasing survey volume, ¯n and S/N. The
values of the survey parameters chosen are reasonable and achievable by future Ly-α
surveys. Exploiting the entire sky coverage of SDSS we find that one can obtain a bound
onf NL
∼ 100 (in the equilateral configuration) for a survey with ¯n = 5×10 −3 Mpc −2 when
the spectra are measured at5-σ level [149].
Our analysis has largely focussed on the equilateral configuration. However we find
that the Cramer-Rao bound for f NL
in the squeezed limit (k 3