# Is cosmology completely broken?

Thirty years ago, when I was taught cosmology as an undergraduate, it felt pretty much like a subject that was close to being fully described: indeed this was the era when Stephen Hawking could announce that we were close to a “theory of everything”.

In simplified form the cosmology was this: the universe (and there was just one) was created 13 billion years ago in a “Big Bang”, the echo of which we could see in the cosmic microwave background (the red shift of which allowed us to place an age of the universe itself). Since then the universe had been expanding and the key question was whether there was sufficient mass to halt this expansion (i.e. that gravitational attraction would overcome the impulse of the Bang) or would it expand for ever. Contemporary observations suggested that the universe’s mass was close to the critical value that separated these two outcomes and the big issue seemed to be getting better observations to determine this question. Beyond that, cosmology was not very open…

Core to the cosmology we were taught was a very simple yet extremely powerful idea: the cosmological principle. Namely, that at a sufficiently large scale and at the same point in time, the universe looks the same in every direction when seen from any point. In fact this idea was treated as close to axiomatic.

(Of course, without some form of cosmological principle then cosmology itself becomes pretty metaphysical – if our observations and experiments have no general validity they cannot tell us much about the universe.)

Three decades later, though, and cosmology is something of a mess. Our observations not only suggest that visible matter is a minority of all matter, but that matter (including the unseen and so far undetected “dark matter”) is a minority of the matter-energy (the two being equivalent as $E=mc^2$ famously tells us) and that a “dark energy” dominates and is actually accelerating the universe’s expansion.

Dark energy is little more than a term in a mathematical equation, something that reminds me all too much of phlogiston but it’s fair to say that most cosmologists are satisfied that it exists.

But not all of them.

As an excellent and highly accessible article in the New Scientist  makes clear, a number are arguing that the problem is that the cosmological principle, or at least our rigid application of it to our observations, is leading us astray. For if the universe was fundamentally lumpy and not smooth at a large scale then it could create the “illusion” of dark energy: put simply if some bits of the universe had less matter in them, then they would expand faster (or in general relativistic terms have greater negative curvature) as gravity would not hold them back – but if we did not factor for that in our interpretations of the observations we would instead assume it was a general effect that applied everywhere.

The advocates of standard cosmology do not deny that the curvature of the universe impacts the passage of the light we see when we observe it – but respond that the homogeneity of the universe at a large scale – i.e., the cosmological principle, means that the patches of negative curvature are cancelled out by the patches of positive curvature and the overall impact on our observations is neutral.

The impact of clumpyness/emptyness on our observations is called “backreaction” and key question for the black energy sceptics is whether it leaves traces in observations that we misinterpret as pointers to dark energy.

The debate, as so often in scientific research is quite brutal – if you say someone’s conclusion is “unphysical” it is pretty much like accusing them of being no good at their job…

The abstract of the paper Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?:

No. In a number of papers Green and Wald argue that the standard FLRW model approximates our Universe extremely well on all scales, except close to strong field astrophysical objects. In particular, they argue that the effect of inhomogeneities on average properties of the Universe (backreaction) is irrelevant. We show that this latter claim is not valid. Specifically, we demonstrate, referring to their recent review paper, that (i) their two-dimensional example used to illustrate the fitting problem differs from the actual problem in important respects, and it assumes what is to be proven; (ii) the proof of the trace-free property of backreaction is unphysical and the theorem about it fails to be a mathematically general statement; (iii) the scheme that underlies the trace-free theorem does not involve averaging and therefore does not capture crucial non-local effects; (iv) their arguments are to a large extent coordinate-dependent, and (v) many of their criticisms of backreaction frameworks do not apply to the published definitions of these frameworks. It is therefore incorrect to infer that Green and Wald have proven a general result that addresses the essential physical questions of backreaction in cosmology.