Do supernovae indicate an accelerating universe?

In the late 1990's, observations of two directionally-skewed samples of, in total, 93 Type Ia supernovae were analysed in the framework of the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology. Assuming these to be 'standard(isable) candles' it was inferred that the Hubble expansion rate is accelerating as if driven by a positive Cosmological Constant. in Einstein's theory of gravity. This is still the only direct evidence for the 'dark energy' that is the dominant component of today's standard.CDM cosmological model. Other data such as baryon acoustic oscillations (BAO) in the large-scale distribution of galaxies, temperature fluctuations in the cosmic microwave background (CMB), measurement of stellar ages, the rate of growth of structure, etc are all 'concordant' with this model but do not provide independent evidence for accelerated expansion. The recent discussions about whether the inferred acceleration is real rests on analysis of a larger sample of 740 SNe Ia which shows that these are not quite standard candles, and more importantly highlights the 'corrections' that are applied to analyse the data in the FLRW framework. The latter holds in the reference frame in which the CMB is isotropic, whereas observations are carried out in our heliocentric frame in which the CMB has a large dipole anisotropy. This is assumed to be of kinematic origin i.e. due to our non-Hubble motion driven by local inhomogeneity in the matter distribution which has grown under gravity from primordial density perturbations traced by the CMB fluctuations. The Lambda CDM model predicts how this peculiar velocity should fall off as the averaging scale is raised and the universe becomes sensibly homogeneous. However observations of the local 'bulk flow' are inconsistent with this expectation and convergence to the CMB frame is not seen. Moreover, the kinematic interpretation implies a corresponding dipole in the sky distribution of high redshift quasars, which is rejected by observations at 4.9 sigma. Hence the peculiar velocity corrections employed in supernova cosmology are inconsistent and discontinuous within the data. The acceleration of the Hubble expansion rate is in fact anisotropic at 3.9 sigma and aligned with the bulk flow. Thus dark energy could be an artefact of analysing data assuming that we are idealised observers in an FLRW universe, when in fact the real universe is inhomogeneous and anisotropic out to distances large enough to impact on cosmological analyses.