An emergence of cosmic space has been suggested by Padmanabhan [Emergence and expansion of cosmic space as due to the quest for holographic equipartition, arXiv:hep-th/1206.4916] where he proposed that the expansion of the universe originates from a difference between the number of degrees of freedom on a holographic surface and the one in the emerged bulk. Now, a natural question that arises is how this proposal would explain the production of fermions and an emergence of the Pauli exclusion principle during the evolution of the universe? We try to address this issue in a system of [Formula: see text]-branes. In this model, there is a high symmetry and the system is composed of [Formula: see text]-branes to which only scalar fields are attached that represent scalar modes of the graviton. Then, when [Formula: see text]-branes join each other and hence form [Formula: see text]-branes, this symmetry is broken and gauge fields are formed. Therefore, these [Formula: see text]-branes interact with the anti-[Formula: see text]-branes and the force between them leads to a break of a symmetry such as the lower and upper parts of these branes are not the same. In these conditions, gauge fields which are localized on [Formula: see text]-branes and scalars which are attached to them symmetrically, decay to fermions with upper and lower spins which attach to the upper and lower parts of the [Formula: see text]-branes anti-symmetrically. The curvature produced by the coupling of identical spins has the opposite sign of the curvature produced by non-identical spins which lead to an attractive force between anti-parallel spins and a repelling force between parallel spins and hence an emergence of the Pauli exclusion principle. By approaching [Formula: see text]-branes to each other, the difference between curvatures of parallel spins and curvatures of anti-parallel spins increases, which leads to an inequality between the number of degrees of freedom on the surface and the one in the emerged bulk and hence lead to an occurrence of the cosmic expansion. By approaching [Formula: see text]-branes to each other, the square of the energy of the system becomes negative and hence tachyonic states arise. To remove these states, [Formula: see text]-branes compactify, the sign of gravity changes and anti-gravity emerges which leads to the branes moving away from each other. By joining [Formula: see text]-branes, [Formula: see text]-branes are produced which are similar to an initial system that oscillates between compacting and opening branches. Our universe is placed on one of these [Formula: see text]-branes and by changing the difference between the amount of couplings between identical and non-identical spins, it contracts or expands.
Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
