FIG. 3. In multi-stream inflation, the universe breaks up into patches with comoving scale k$_{1}$ . Each patch experienced inflation either along trajectories A or B . These different patches can be responsible for the asymmetries in the CMB. CMB, and investigate some other possible observational effects. To be explicit, we focus on one single bifurcation, as illustrated in Fig. 2. We denote the initial (before bifur- cation) inflationary direction by ϕ , and the initial isocur- vature direction by χ . For simplicity, we let χ = 0 before bifurcation. When comoving wave number k 1 exits the horizon, the inflation trajectory bifurcates into A and B . When comoving wave number k 2 exits the horizon, the trajectories recombines into a single trajectory. The universe breaks into of order k 1 /k 0 patches (where k 0 de- notes the comoving scale of the current observable uni- verse), each patch experienced inflation either along tra- jectories A or B . The choice of the trajectories is made by the isocurvature perturbation δχ at scale k 1 . This picture is illustrated in Fig. 3. We shall classify the bifurcation into three cases: Symmetric bifurcation . If the bifurcation is symmetric, in other words, V ( ϕ, χ ) = V ( ϕ, − χ ), then there are two potentially observable effects, namely, quasi-single field inflation, and a effect from a domain-wall-like objects, which we call domain fences. As discussed in [4], the discussion of the bifurcation effect becomes simpler when the isocurvature direction has mass of order the Hubble parameter. In this case, except for the bifurcation and recombination points, tra- jectory A and trajectory B experience quasi-single field inflation respectively. As there are turnings of these tra- jectories, the analysis in [6] can be applied here. The perturbations, especially non-Gaussianities in the isocur- vature directions are projected onto the curvature direc- tion, resulting in a correction to the power spectrum, and potentially large non-Gaussianities. As shown in [6], the amount of non-Gaussianity is of order f$_{NL}$ ∼ P − 1 / 2 ζ ( 1 H ∂ $^{3}$V ∂χ 3 )( ˙ θ H ) 3 , (1) where θ denotes the angle between the true inflation di- rection and the ϕ direction. As shown in Fig. 3, the universe is broken into patches during multi-stream inflation. There are wall-like bound- aries between these patches. During inflation, these 2 boundaries are initially domain walls. However, after the recombination of the trajectories, the tensions of these domain walls vanish. We call these objects domain fences. As is well known, domain wall causes disasters in cosmology because of its tension. However, without tension, domain fence does not necessarily cause such disasters. It is interesting to investigate whether there are observational sequences of these domain fences. Nearly symmetric bifurcation If the bifurcation is nearly symmetric, in other words, V ( ϕ, χ ) ≃ V ( ϕ, − χ ), but not equal exactly, which can be achieved by a spon- taneous breaking and restoring of an approximate sym- metry, then besides the quasi-single field effect and the domain fence effect, there will be four more potentially observable effects in multi-stream inflation, namely, the features and asymmetries in CMB, non-Gaussianity at scale k 1 and squeezed non-Gaussianity correlating scale k 1 and scale k with k 1 < k < k 2 . The CMB power asymmetries are produced because, as in Fig. 3, patches coming from trajectory A or B can have different power spectra P A ζ and P B ζ , which are de- termined by their local potentials. If the scale k 1 is near to the scale of the observational universe k 0 , then multi- stream inflation provides an explanation of the hemi- spherical asymmetry problem [10]. The features in the CMB (here feature denotes extra large perturbation at a single scale k 1 ) are produced as a result of the e-folding number difference δN between two trajectories. From the δN formalism, the curvature perturbation in the uniform density slice at scale k 1 has an additional contribution δζ$_{k}$$_{1}$ ∼ δN ≡ | N$_{A}$ − N$_{B}$ | . (2) These features in the CMB are potentially observable in the future precise CMB measurements. As the addi- tional fluctuation δζ$_{k}$$_{1}$ does not obey Gaussian distribu- tion, there will be non-Gaussianity at scale k 1 . Finally, there are also correlations between scale k 1 and scale k with k 1 < k < k 2 . This is because the ad- ditional fluctuation δζ$_{k}$$_{1}$ and the asymmetry at scale k are both controlled by the isocurvature perturbation at scale k 1 . Thus the fluctuations at these two scales are correlated. As estimated in [4], this correlation results in a non-Gaussianity of order f$_{NL}$ ∼ δζ$_{k}$$_{1}$ ζ$_{k}$$_{1}$ P A ζ − P B ζ P A ζ P − 1 / 2 ζ . (3) Non-symmetric bifurcation If the bifurcation is not symmetric at all, especially with large e-folding number differences (of order O (1) or greater) along different tra- jectories, the anisotropy in the CMB and the large scale structure becomes too large at scale k 1 . However, in this case, regions with smaller e-folding number will have exponentially small volume compared with regions with larger e-folding number. Thus the anisotropy can behave in the form of great voids. We shall address this issue in more detail in [11]. Trajectories with e-folding number