Volovik G.E. «Comment to the CPT-symmetic Universe: Two possible extensions» Письма в ЖЭТФ, 109, № 10, с. 705-706 (2019)

In L. Boyle, K. Finn, N. Turok, Phys. Rev. Lett., 121 (2018), 251301; L. Boyle, K. Finn, N. Turok, arXiv: 1803.08930 the antispacetime Universe was suggested as the analytic continuation of our Universe across the Big Bang singularity in conformal time. We consider two different scenarios of analytic continuation. In one of them the analytic continuation is extended to the temperature of the system. This extension suggests that if such analytic continuation is valid, then it is possible that the initial stage of the evolution of the Universe on our side of the Big Bang was characterized by the negative temperature. In the second scenario, the analytic continuation is considered in the proper time. In this scenario the Big Bang represents the bifurcation point at which the Z2 symmetry between the spacetime and antispacetime is spontaneously broken. The extension of the Universe beyond the Big Bang using the analytic continuation across the singularity has been considered for the radiation-dominated epoch. In this analytic continuation, at which the scale factor a(τ) changes sign at τ=0, the gravitational tetrads also change sign giving rise to what is called the antispacetime. This means that the Universe on the other side of the Big Bang is the mirror image of the Universe on our side of the Big Bang. Different types of the antispacetime obtained by the space reversal P and time reversal T operations were considered ealier, including those where the determinant of the tetrads e changes sign. Later the consideration has been extended to thermal states, where possible analytic continuation of the temperature across the transition from spacetime to antispacetime has been considered [G. E. Volovik, Pis’ma v ZhETF, 109 (2019), 10, arXiv: 1806.06554]. Here we discuss two scenarios of analytic contunuation across the Big Bang.