Type Ia supernovae are vital to our understanding of the Universe due to their use in measuring cosmological distances and their significance in enriching the interstellar medium with heavy elements. They are understood to be the thermonuclear explosions of white dwarfs, but the exact mechanism(s) leading to these explosions remains unclear. The two competing models are the single degenerate scenario, wherein a white dwarf accretes material from a companion star and explodes when it reaches the Chandrasekhar limit, and the double degenerate scenario, wherein the explosion results from a merger of two white dwarfs. Here we report results which rule out hot, luminous progenitors consistent with the single degenerate scenario for four young Type Ia supernova remnants in the Large Magellanic Cloud. Using the integral field spectrograph WiFeS, we have searched these remnants for relic nebulae ionized by the progenitor, which would persist for up to $sim 10^5$ years after the explosion. We detected no such nebula around any of the remnants. By comparing our upper limits with photoionization simulations performed using Cloudy, we have placed stringent upper limits on the luminosities of the progenitors of these supernova remnants. Our results add to the growing evidence disfavouring the single degenerate scenario.
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