We report on the detection of strongly varying intergalactic HeII absorption in HST/COS spectra of two z~3 quasars. From our homogeneous analysis of the HeII absorption in these and three archival sightlines, we find a marked increase in the mean HeII effective optical depth from tau~1 at z~2.3 to tau>5 at z~3.2, but with a large scatter of 2< tau <5 at 2.7< z <3 on scales of ~10 proper Mpc. This scatter is primarily due to fluctuations in the HeII fraction and the HeII-ionizing background, rather than density variations that are probed by the co-eval HI forest. Semianalytic models of HeII absorption require a strong decrease in the HeII-ionizing background to explain the strong increase of the absorption at z>2.7, probably indicating HeII reionization was incomplete at z>2.7. Likewise, recent three-dimensional numerical simulations of HeII reionization qualitatively agree with the observed trend only if HeII reionization completes at z=2.7 or even below, as suggested by a large tau>3 in two of our five sightlines at z<2.8. By doubling the sample size at 2.7< z <3, our newly discovered HeII sightlines for the first time probe the diversity of the second epoch of reionization when helium became fully ionized.
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