Type Ia supernovae (SNIe) are generally accepted to act as standardisable candles, and their use in cosmology led to the first confirmation of the as yet unexplained accelerated cosmic expansion. Many of the theoretical models to explain the cosmic acceleration assume modifications to Einsteinian General Relativity which accelerate the expansion, but the question of whether such modifications also affect the ability of SNIe to be standardisable candles has rarely been addressed. This paper is an attempt to answer this question. For this we adopt a semi-analytical model to calculate SNIe light curves in non-standard gravity. We use this model to show that the average rescaled intrinsic peak luminosity -- a quantity that is assumed to be constant with redshift in standard analyses of Type Ia supernova (SNIa) cosmology data -- depends on the strength of gravity in the supernova's local environment because the latter determines the Chandrasekhar mass -- the mass of the SNIa's white dwarf progenitor right before the explosion. This means that SNIe are no longer standardisable candles in scenarios where the strength of gravity evolves over time, and therefore the cosmology implied by the existing SNIa data will be different when analysed in the context of such models. As an example, we show that the observational SNIa cosmology data can be fitted with both a model where $(��_{\rm M}, ��_��)=(0.62, 0.38)$ and Newton's constant $G$ varies as $G(z)=G_0(1+z)^{-1/4}$ and the standard model where $(��_{\rm M}, ��_��)=(0.3, 0.7)$ and $G$ is constant, when the Universe is assumed to be flat.

25 pages, 8 figures, updated to match published version