Do supernovae indicate an accelerating universe?

In the late 1990s, observations of 93 Type Ia supernovae were analysed in the framework of the FLRW cosmology assuming these to be `standard(isable) candles. It was thus inferred that the Hubble expansion rate is accelerating as if driven by a positive Cosmological Constant $Lambda$. This is still the only direct evidence for the `dark energy that is the dominant component of the standard $Lambda$CDM cosmological model. Other data such as BAO, CMB anisotropies, stellar ages, the rate of structure growth, etc are all `concordant with this model but do not provide independent evidence for accelerated expansion. Analysis of a larger sample of 740 SNe Ia shows that these are not quite standard candles, and highlights the corrections 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 made 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. 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$sigma$. The acceleration of the Hubble expansion rate is also anisotropic at 3.9$sigma$ and aligned with the bulk flow. Thus dark energy may 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.