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Fri, 22 Jan 2016

Dark energy: onus of proof reversed

The simplest explanation for "dark energy" is that it measures recent evolution of average negative curvature. We think that it mainly represents the recent formation of cosmic voids on scales of tens of megaparsecs; these voids dominate scalar averaged quantities. In other words, the onus of proof has been reversed, in a quantified way: dark energy as something beyond classical general relativity should be disfavoured by Occam's Razor unless a relativistic inhomogeneous cosmological model is used. This seems so far to have largely gone under the radar...

Observationally, there's no disputing the existence of dark energy in the restricted sense of providing a good observational fit to several of the main cosmological observational datasets, modulo a rather unrealistic assumption of the model used in the fitting procedure. The assumption is that the class of possible spacetimes, i.e., solutions of the Einstein equation of general relativity, is the FLRW (Friedmann-Lemaître-Robertson-Walker) family. The FLRW models require that after choosing a way to split up space and time (a foliation), the spatial slice (i.e., a 3-dimensional space) is homogeneous—the density is the same everywhere, so galaxies and voids cannot exist. In fact, cosmologists usually make a hack, modelling galaxies and voids by patching Newtonian gravity into an Einstein "background"—since using the Einstein equation is more tricky. This hack bypasses the basic problem without solving it.

Since in reality, galaxies, clusters of galaxies, the cosmic web and voids and supervoids exist beyond any reasonable doubt, the FLRW family should be expected to go wrong at recent epochs and at small (less than a few gigaparsecs) scales. And the small-scale, recent epoch is the only epoch at which a non-zero cosmological constant (or dark energy parameter ΩΛ) can (at present) be observationally distinguished from a zero cosmological constant. So it happens that just where and when we can expect things to go wrong with FLRW, ΩΛ suddenly appears, provided that we assume FLRW in our interpretation of the data despite expecting FLRW to be wrong! What is it that goes wrong? The picture above shows voids on the scales of a few tens of megaparsecs from the 2dFGRS. From a relativistic space point of view, expansion rates are different in different regions. This also happens in the hack of adding Newtonian galaxy and void formation to Einsteinian expansion, but in that case the expansion is forced to be rigid, by assumption, preventing the Einstein equation from being applied correctly. Even when we interpret the observations from a rigid comoving space point of view, the numbers show that the ratio of the "peculiar velocities" of galaxies coming out of voids to the sizes of the voids is big: several hundred km/s divided by something like 10 Mpc, giving a few times 10 km/s/Mpc. This void peculiar expansion rate is not much smaller than the Hubble constant, which is about 70 km/s/Mpc. At an order of magnitude level, the expansion rate is definitely inhomogeneous. This is why interpreting the observations in terms of homogeneous expansion gives a big error.

In other words, unless we use a relativistic cosmological model that takes inhomogeneous curvature and virialisation into account, we cannot claim that the "detected" ΩΛ is anything other than a structure formation parameter of a fit through cosmological data using an oversimplified fitting function. The second picture at the right shows that going from right (early times) to left (today), the amount of inhomogeneity (the virialisation fraction) grows from almost nothing to a big fraction of the total mass density today. Alternatively, if we ignore the growth in inhomogeneity, then we get ΩΛ, interpreted from the data assuming homogeneity, growing from almost nothing to a big fraction (70%) of the total density today. If we ignore inhomogeneity, then miraculously dark energy appears instead!

Several relativistic structure formation cosmological models are available, though still in their infancy. However, what has been a little distracting from working on these is that some observational cosmologists thought that there existed a mathematical theorem—the Green and Wald formalism—showing that dark energy could not be a "fitting function" description of curvature and kinematical backreaction, the general-relativistic effects of treating both structure formation and expansion of the Universe together. This is why my colleagues and I had to publish a clarification showing the main flaws in this reasoning. In particular, the Green and Wald formalism is not applicable to the main relativistic structure formation cosmological models that have been proposed in the research literature over the past five years or so. Green and Wald's formalism remains an interesting contribution to the field of relativistic cosmology, but it does not "save" dark energy from being anything more exotic than spatially averaged, evolving negative curvature. After a few tweets [1] [2], a blog entry, and a reblog we can get back to work. :)

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Wed, 20 Jan 2016

About this blog

When I had to choose a topic for my Honours year thesis (like a Masters year) the problem was that as a young person whose curiosity had survived the education system, I was interested in everything. Which is just what I responded to Dayal Wickramasinghe, one of the lecturers in the Maths Department who knew me well and who I could hope would give me wise advice, when he asked me what I found interesting. "Boud," he said, "I think you're a cosmologist".

It was a self-fulfilling prediction. My research career started with my Honours year with Dayal learning the basics of the standard late '80s version of the hot big bang model and trying to save that standard model during my doctorate at the Mount Stromlo and Siding Spring Observatories, using observations of faint galaxy populations and introducing N-body simulation merger history trees of dark matter galaxy haloes. I had an itinerant postdoctoral life doing cosmology research in Paris, Sussex, Tokyo, Warsaw, Pune and Meudon, focussing especially on developing and applying observational methods for measuring the topology of the Universe, which wasn't astropolitically correct in 1995, but was exciting: it's a fundamental geometrical property (in Euler's sense) of the Universe that we live in. And I accepted a faculty position at the Radioastronomy Department of the Toruń Centre for Astronomy in the Faculty of Physics, Astronomy and Informatics at the Nicolaus Copernicus University, where I now do cosmology research and teaching.

I have always believed in open, rational, structured communication, and it seems to me that blogs occupy a useful niche in the cybersphere linking scientists' work and thinking with the wider community and, in turn, with itself.

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