My question concerns "timescape cosmology" and measurements of dark energy based on CMB radiation.
The background to the question is
Lawrence H. Dam, Asta Heinesen, David L. Wiltshire, "Apparent cosmic acceleration from Type Ia supernovae", Monthly Notices of the Royal Astronomical Society, Volume 472, Issue 1, 21 November 2017, Pages 835–851, https://doi.org/10.1093/mnras/stx1858
These authors investigate the following idea. The standard way to approach cosmology, to date, has been to make the approximation that the universe is homogenous on a large scale. Having made this approximation, one gets a lot of interesting insight, including measurements of Hubble parameter and density parameters etc. One finds that the expansion is accelerating, for example, so the dark energy or cosmological constant is non-zero and positive. But, say, Dam, Heinesen and Wiltshire, the universe isn't quite homogeneous in fact, so let's see what impact this may have on our models of the cosmic expansion. After taking this into account, they assert, one can match the observations on supernovas without requiring acceleration (or only having a little acceleration).
Here are two quotations from the abstract
"Using the largest available supernova data set, the JLA catalogue, we find that the timescape model fits the luminosity distance-redshift data with a likelihood that is statistically indistinguishable from the standard spatially flat $\Lambda$ cold dark matter cosmology by Bayesian comparison."
"Irrespective of which model ultimately fits better, we argue that as a competitive model with a non-FLRW expansion history, the timescape model may prove a useful diagnostic tool for disentangling selection effects and astrophysical systematics from the underlying expansion history."
For another paper related to this, see https://arxiv.org/pdf/1306.3208.pdf.
The general idea seems to be being called "timescape cosmology"
My question is three-fold.
It is obvious that one can get increased precision, in principle, by adopting a more realistic model of the cosmos than the completely homogeneous model. Is this "timescape cosmology" succeeding in doing that?
Here is the main part of my question. Measurements from Planck mission report the dark energy parameter $\Omega_\Lambda$ with great confidence. They get $0.683$ and quote a precision around 1 percent. But the paper quoted above seems to suggest that $\Omega_\Lambda$ may be much lower or even zero. Can these two results be reconciled, or is one or both of them severely wrong? In particular:
does the error-bar quoted by the Planck mission include the influence of uncertainty about what is the right equation for evolution of a not-quite-homogeneous universe?