Fractional Brane State in the Early Universe

TL;DR

This work extends black-hole microstate ideas to early-Universe cosmology by positing a maximal-entropy fractional brane state on T^{10} that yields an anisotropic equation of state p_i = w_i ρ. The authors derive entropy scalings for 2-, 3-, and 4-charge configurations, propose an entropy-maximization framework for the early Universe, and compute the resulting stress-energy, leading to analytic Einstein-equation solutions. They formulate a general set of cosmological equations with brane-induced pressures, cast them into a closed three-variable system, and solve via a Kasner-type ansatz and a tau-variable integration, obtaining Kasner-like late-time behavior for broad parameter ranges. The results suggest nonlocal quantum-gravity effects and high-entropy dominance by fractional branes could significantly alter early cosmological evolution, with potential implications for inflation, dark components, and horizon-scale correlations.

Abstract

In the early Universe matter was crushed to high densities, in a manner similar to that encountered in gravitational collapse to black holes. String theory suggests that the large entropy of black holes can be understood in terms of fractional branes and antibranes. We assume a similar physics for the matter in the early Universe, taking a toroidal compactification and letting branes wrap around the cycles of the torus. We find an equation of state p_i=w_i rho, for which the dynamics can be solved analytically. For black holes, fractionation can lead to non-local quantum gravity effects across length scales of order the horizon radius; similar effects in the early Universe might change our understanding of Cosmology in basic ways.

Figures (7)

• Figure 1: (a) Radiation filled Universe (b) All matter in black holes (c) Fuzzball picture suggests that interior of horizon is a very quantum domain (d) Quantum fuzz filling the entire Universe.
• Figure 2: (a) A string can wind several times around a compact cycle and carry vibrations (b) In the 'brane gas' model branes can wrap cycles and carry vibrations.
• Figure 3: Different kinds of branes 'fractionate' each other, giving a large entropy.
• Figure 4: (a) Downward facing parabola for $K_1+K_2<0$ (b) Upward facing parabola for $K_1+K_2>0$. In each case a physical choice of parameters leads to motion along the bold line segment.
• Figure 5: Plots of $\hat{\cal{P}}, -\hat{\tilde{\cal{Q}}}$ and a selection of $a_i$ for $w_i=\{ .9, -.9, -.9, -.9, -.9, -.1, -.1, -.1, -.1, -.1\}$, a set that gives $K_1+K_2<0$ and illustrates case (a) behavior. We have taken $\gamma_i(2)=a_i(2)=1$ for all $i$. We see that $\hat{\cal{P}}$ asymptotes to a constant.