Topological acceleration
https://cosmo.torun.pl/blog/scalar_averaging
Quest to understand the Universeenhttp://blogs.law.harvard.edu/tech/rssblosxom/2.1.2Dark energy: onus of proof reversedFri, 22 Jan 2016 00:00:00 +0100
https://cosmo.torun.pl/blog/2016/01/22#onus_proof
/scalar_averaginghttps://cosmo.torun.pl/blog/scalar_averaging/onus_proof
<p>
<a href="http://cosmo.torun.pl/~boud/blog_img/voids_negcurv.jpg"><img src="http://cosmo.torun.pl/~boud/blog_img/voids_negcurv.jpg"
style="float:left; width:400px; margin:10px"/></a>
The simplest explanation for "dark energy" is that it
<a href="http://arXiv.org/abs/0707.2153">measures recent evolution of average negative curvature</a>.
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 <strong>unless</strong> a
relativistic inhomogeneous cosmological model is used.
This seems
so far to have largely gone under the radar...</p>
<p>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-LemaĆ®tre-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.</p>
<p>
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 Ω<sub>Λ</sub>) 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, Ω<sub>Λ</sub> suddenly appears,
<em>provided that we assume FLRW in our interpretation of the data
despite expecting FLRW to be wrong!</em>
What is it that goes wrong? The picture above shows voids on the
scales of a few tens of megaparsecs from the
<a href="http://2dfgrs.net/">2dFGRS</a>. 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 <em>peculiar expansion rate</em>
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. <strong><em>This is why
interpreting the observations in terms of homogeneous expansion
gives a big error.</em></strong></p>
<p>
<a href="http://cosmo.torun.pl/~boud/blog_img/DE.jpg"><img src="http://cosmo.torun.pl/~boud/blog_img/DE.jpg"
style="float:right; width:400px; margin:10px"/></a>
In other words, <em>unless</em> we use a relativistic cosmological model that takes inhomogeneous
curvature and
<a href="http://arXiv.org/abs/1303.4444">virialisation into account</a>,
we cannot claim that the "detected" Ω<sub>Λ</sub>
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 <span style="color:green"><strong>in</strong>homogeneity (the virialisation
fraction)</span> 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
<span style="color:red">Ω<sub>Λ</sub>, <em>interpreted</em> from the data assuming homogeneity,</span>
growing from almost
nothing to a big fraction (70%) of the total density today. If we ignore inhomogeneity, then
miraculously dark energy appears instead!
</p>
<p>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 <a href="http://arXiv.org/abs/1505.07800">publish</a>
a <a href="http://cqgplus.com/2016/01/20/the-universe-is-inhomogeneous-does-it-matter">clarification</a>
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 <a href="https://twitter.com/seanmcarroll/status/604325262197567490">tweets [1]</a>
<a href="https://twitter.com/SyksyRasanen/status/690595794601271296">[2]</a>,
a <a href="http://trenchesofdiscovery.blogspot.fi/2015/07/cosmological-backreaction.html">blog
entry,</a> and
a <a href="https://telescoper.wordpress.com/2016/01/20/the-universe-is-inhomogeneous-does-it-matter/">reblog</a>
we can get back to work. :)</p>