I am not a physicist, but I do have a background in engineering (EE and computer science) and have followed physics and cosmology on a primarily conceptual basis for many years. I have looked at Stephen Weinberg's 1987 prediction for the approximate magnitude and sign of the vacuum energy $\rho_V$ and I cannot understand why this prediction is considered by some to be remarkable.

I've read his 2005 paper, "Living in the Multiverse", several times and have studied the topic fairly extensively. It still seems to me that Weinberg is acknowledging that is was a prediction based on anthropic reasoning, i.e., "this value for $\rho_V$ can't be too large and positive, because then galaxies and stars would not not form...should be less than the mass density of the universe at the time when galaxies first condense. Since this was in the past, when the mass density was larger than at present, the anthropic upper limit on the vacuum energy density is larger than the present mass density, but not many orders of magnitude greater" (quoting Weinberg in the cited paper).

As I understand it, he then went on to estimate the probability distribution in a hypothetical multiverse of such a value of $\rho_V$ and guessed that if we found ourselves with an actual value more improbable than about 12% probability that this suggested abandoning anthropic reasoning. He was actually reasoning at that time about the ratio of the energy density $\rho_V$ to critical density denoted $\Omega_{\Lambda}$ since he had no good idea at the time what were the early fractional density fluctuations (which WMAP data eventually provided him). He concluded that if $\Omega_{\Lambda}$ turned out to be much less than 0.6 it would be too improbable a value (and subsequent observations of type Ia supernovae showed that the expansion of the universe was accelerating with estimated $\Omega_{\Lambda}$ around 0.7)

While this demonstrates Weinberg's brilliance (undisputed) and amazing understanding of physics at very fundamental levels, why is it nonetheless not a prediction of the usual Goldilocks kind, i.e., there are many possible universes and we naturally find ourselves in one whose parameters permit us to exist (this seems a tautology to me)? The 15.6% probability he gives after refining his estimate with the WMAP data and some other modifications seems relatively low in any case, keeping in mind that it is a probability on a hypothetical distribution of possible multiverse/string theory vacua solutions. This doesn't seem to be a falsifiable prediction like, e.g., Lee Smolin's prediction that no neutron star should be discovered with a mass greater than 2 solar masses. I acknowledge that I am not very familiar with Smolin's underlying proposal of cosmological natural selection where the landscape (seemingly a synonym for multiverse, i.e., the whole range of possible string theory or other basic parameter distributing theory solutions) is dominated by universes with parameters that drive the production of black holes to a local peak in the landscape (to quote wikipedia), but at least it seems not to be based on anthropic reasoning.

  • $\begingroup$ It was basically just a measurement. He had some data (universe is old and quite big with structure etc) and inferred the CC in GR from that data. No need to even say the word anthropic $\endgroup$
    – innisfree
    Mar 19, 2016 at 21:07
  • $\begingroup$ Yep, any mention of the word anthropic is a tautology, except that it's not a sophisticated one. Whether the energy density makes any sense to begin with, is physically questionable. Assuming that it does make sense, one can estimate it based on the existing universe, which as innisfree correctly says, is no different from any other measurement. The problem with these estimates is that they are model dependent and the ultimate model is not even known. $\endgroup$
    – CuriousOne
    Mar 20, 2016 at 1:47
  • $\begingroup$ @CuriousOne whenever you measure any parameter, it's model dependent and no one knows the ultimate (whatever that means) model. The cc is no different from e.g. mass of electron or $\alpha_s$ in that regard $\endgroup$
    – innisfree
    Mar 20, 2016 at 12:40
  • $\begingroup$ @innisfree: That's true, but the universe is a fundamentally different system than e.g. a solid state system. I have multiple versions of the latter and I can often vary several experimental parameters like doping density or the composition etc.. That allows us to see functional dependencies of a measurement and that can be compared to model predictions. The universe has its parameters dialed in and we can't run multiple experiments. That makes it much harder to distinguish between different models. I agree, it doesn't impact the scientific method directly, but it does make execution harder. $\endgroup$
    – CuriousOne
    Mar 20, 2016 at 19:26
  • $\begingroup$ Thanks for the expert comments (I'm grateful for the generosity). You've got me studying the means of estimating the energy density. I've gotten a handle on the WMAP background temp black body and estimated photon proton counts (but I need more coffee), so I understand better your comments re model dependence (e.g., where the density lies depends on your model, dark matter/energy/neutrinos, etc.). The Weinberg prediction was simply a measurement based on model assumptions. $\endgroup$ Mar 20, 2016 at 19:35


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