Non-detection of <SUP>6</SUP>Li in Spite plateau stars with ESPRESSO

The detection of Li-6 in Spite plateau stars contradicts the standard big bang nucleosynthesis prediction, known as the second cosmological lithium problem. We measure the isotopic ratio Li-6/Li-7 in three Spite plateau stars: HD 84937, HD 140283, and LP 815-43. We use 3D non-local thermodynamic equilibrium radiative transfer and for the first time apply this to high-resolution, high signal-to-noise ratio data from the ultra-stable ESPRESSO/Very Large Telescope spectrograph. These are among the best spectra ever taken of any metal-poor stars. As the measurement of Li-6/Li-7 is degenerate with other physical stellar parameters, we employ Markov chain Monte Carlo methods to find the probability distributions of measured parameters. As a test of systematics, we also use three different fitting methods. We do not detect Li-6 in any of the three stars, and find consistent results between our different methods. We estimate 2 sigma upper limits to Li-6/Li-7 of 0.7, 0.6, and 1.7 per cent, respectively, for HD 84937, HD 140283, and LP 815-43. Our results indicate that there is no second cosmological lithium problem, as there is no evidence of Li-6 in Spite plateau stars.