‘It’s possible that what we’re lacking is a proper understanding of vacuum energy,’ Lila suggested. ‘You know the naïve version: if you look at the free light field, and assume the right kind of relationship between the mass of a photon and the dimensions of the cosmos, each mode of the field that wraps around the cosmos a whole number of times is like a simple oscillator. Wave mechanics tells us that an oscillator like that can’t have an energy of zero: the lowest energy level has some non-zero value. So even if the cosmos were empty, the vacuum would have as much energy as you’d get by adding up the lowest levels of all the possible modes of the light field.’

‘Plus the same kind of contributions from all the modes of the luxagen field,’ Agata added.

‘Yes. Which are actually negative, if you take the mathematics seriously.’ Lila buzzed softly. ‘When I was developing the gravitational theory, I was never sure if I should claim that this kind of energy would need to be included as a source of curvature – and then go on to insist that the very mild curvature that empty space seems to possess is proof that the two kinds of vacuum energy more or less cancel each other out.’

‘Hmm.’ Agata wasn’t sure whether Lila was mocking this idea or trying to resurrect it, so it seemed wiser not to offer an opinion of her own.

‘The thing is, though,’ Lila continued, ‘the naïve version is just that. We don’t know if the cosmos really has the right dimensions to allow any free modes of either field, and we don’t know how to calculate the vacuum energy under more realistic assumptions: taking account of the interaction between luxagens and photons, and taking account of the curvature of four-space.’

Agata said, ‘But if the vacuum energy is a source of curvature, and the curvature itself can influence the vacuum energy . . .’

‘Then it’s much less clear what combinations of the two are actually possible,’ Lila replied. ‘That’s what I’m hoping would shed some light on the gradient problem.’

‘Ah.’ Agata finally caught a glimmer of that illumination. ‘If we take account of the way the geometry of the cosmos determines what kind of waves can exist – which governs the vacuum energy, which contributes to the curvature – we might end up showing that a uniform cosmos would be self-contradictory.’

‘It’s conceivable,’ Lila said cautiously. ‘Of course, that wouldn’t help much if a tiny wrinkle in the curvature was enough to make things work out. What we’d need is for there to be no solutions without a significant entropy gradient.’

Agata understood the proposal now – and it was terrifying. To make any progress they would need to combine field theory, wave mechanics and cosmology in a manner that no one had ever achieved before.