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Thermal non-Gaussianity in Near-Milne universe

The thermal non-Gaussianity in Near-Milne universe is investigated in this letter. Through classifying thermal fluctuations into two types, one characterized by a phase transition and the other without phase transition, we show that for fluctuations undergoing a phase transition, the non-Gaussianity depends linearly on $k$, but in non-phase transition case it is proportional to $k^{-3γ},γ>0$. Moreover, if the phase transition scenario is similar to that in holographic cosmology, we find that the non-Gaussianity $f_{NL}^{equil}$ can reach ${\cal O}(1)$ or larger than ${\cal O}(1)$ by fine tuning of the equation of state $ω_{C}$. Especially at the limit of $ω_{C}\to -5/3$, the non-Gaussianity can be very large. On the other hand, for non-phase transition case, the non-Gaussianity estimator $f_{NL}^{equil}$ is approximately $f_{NL}^{equil}\simeq 5/108$ when the energy is sub-extensive, especially when $γ\to 0^{+}$. However, when $γ\to 4$, large non-Gaussianity can be obtained.