This paper investigates anthropic bounds on the vacuum energy Lambda by considering alternate starting assumptions. We first consider the possibility of cosmic observers existing at any random time (including the future) for constant Lambda, and take into account the suppression of new structure formation as the universe approaches its eternal de Sitter (DS) geometry. Structures that collapse prior to the era of Lambda-domination will lose causal contact with our Hubble volume within a finite (short) conformal time tau(*). Any remnants within our Hubble volume then suffer a cosmological heat death after the universe becomes DS. The probability for finding observers by random measurements in the volume bound by the de Sitter horizon is proportional to the rate of change in the ratio of the 3-volume V-3(tau) to the 4-volume V-4(tau), so that P similar or equal to 0. This vanishing probability of populated DS volumes is a simple consequence of the information loss problem for eternal DS spaces resulting from the finite and constant value of its temperature T-DS similar or equal to Lambda(-1/2) and entropy S = 3/(G Lambda). By contrast, for geometries with Lambda = 0, structures can condense and entropy production can continue without bounds at any epoch. The probability of finding observers in Lambda = 0 geometries is thus overwhelming higher than in DS spaces. As a result, anthropic reasoning does not explain the small but nonzero vacuum energy observed in our universe. We also address the case where observers are considered only at a specially chosen time-like the present epoch-but relax the allowed values of starting density fluctuations and hence the redshift of galaxy formation. In this latter case, the bounds on a Lambda can be millions of times larger than previous estimates-and the observed value. We thus conclude that anthropic reasoning has limited predictive power.
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