I’m also skeptical that the luminosity of a SN Ia if G were different would scale as G^-3 (or M_ch^2).
Ni-56 production is not a simple rate-limited process; SNe Ia undergo a deflagration that (in most cases) transitions to a detonation. They burn about half their mass to Ni-56 (depending on when the detonation occurs). Even if Ni-56 production were a simple process, the radius (and thus the density) of the white dwarf also changes with G.
Answer: Simple analysis of Chandrasekhar mass was presented in the appendix to the article:
So the author took into consideration changes in the Radius. The reviewer seems to be wrong when stating that the density changes. That is not supported by the equations above. This is an important result (albeit trivial). It means that pressure and temperature profiles remains the same and are independent upon G, making Nucleosynthesis G-independent.
The Chain reaction is given by:
White Dwarfs are mostly Carbon and Oxygen. During detonation, a temperatures and pressure shockwave acts as a nuclear chemistry cauldron. Increased temperature, collisional rates modulates the reaction rates of the intermediate reactions (expediting them). The approximation of this chain reaction as a simple second-order reaction is clearly supported by this argument.
The observation of Type 1A Supernova explosions measure Peak Absolute Luminosity (it could measure integrated luminosity instead). The reason for measuring peak absolute luminosity is that variable ejecta make photon diffusion very variable. The peak absolute luminosity is related to both rate of Niand the duration of the coasting burn process.
Arnett, W. D. 1982, ApJ, 253, 785
Arnett indicated that the luminosity depends upon the rate dN/dt. In reality it should be [N-56](t=0), that is the maximum concentration of Ni just before ejecta makes light diffusion difficult. The maximum concentration of N is dN/dt * RampingTime. Ramping time is the time it takes for the explosion to travel from the core to the surface of the White Dwarf. Since he considered in his article that all RampingtTmes to be the same for all Supernovas, that aspect becomes irrelevant (just a multiplicative constant).
One can consider that the RampingTime has been normalized by WLR and thus Radius are normalized. In that case, we are left with the influence of dN/dt=k[C]. Since the radius are normalized, the concentration of Carbon falls by G.
If one uses your argument the Radius are not identical and depend upon G then the RampingTime will decrease accordingly, yielding the same effect.