what recent papers have you seen that deal with this question? Here is one I found by Paolo Serra et al (2009) http://arxiv.org/abs/0908.3186 No Evidence for Dark Energy Dynamics from a Global Analysis of Cosmological Data Paolo Serra (UC Irvine), Asantha Cooray (UC Irvine), Daniel E. Holz (Los Alamos National Laboratory), Alessandro Melchiorri (University of Rome), Stefania Pandolfi (University of Rome), Devdeep Sarkar (UC Irvine, University of Michigan) Physical Review D Here is another by Tamara Davis et al (2007) http://inspirehep.net/record/742618 Scrutinizing Exotic Cosmological Models Using ESSENCE Supernova Data Combined with Other Cosmological Probes Astrophysical Journal One by Wood-Vasey et al (2007) http://inspirehep.net/record/741585?ln=en Observational Constraints on the Nature of the Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey Astrophysical Journal As time goes on the constraints on variation seem to tighten. I hear less and less about Lambda being a real "dark energy". I think we are getting closer to accepting it simply as another constant. A small constant amount of curvature. (Not even an energy.) but this is just my impression from what I read and how I hear people talk. I would like to have some more recent papers that support this point of view with objective evidence. Also if Lambda is simply a physical constant (a curvature) that appears naturally in the 1915 Einstein equation, along with the other physical constant Newton's G, then there seems to be no reason to relate it to the "vacuum energy" arising in conventional quantum field theory---the unrealistically high value of which is a problem for QFT, but not a concern of General Relativity. There is also the "WMAP7" report (7-year data from the WMAP mission) of Komatsu et al. Page 24 has some constraints on the equation of state w. In case Lambda is simply a constant, we would have w = -1. That is about what you get combining latest WMAP+BAO+SN data. The high-z supernova data is the most effective at constraining w. Here is the link. http://arxiv.org/abs/1001.4538 For example on page 24 in section 5.1 you see: "The high-z supernova data provide the most stringent limit on w. Using WMAP+BAO+SN, we find w = −0.980±0.053 (68% CL)..."