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Thestringtheorylandscapealsoprovidesaplayground
for eternal inﬂation. Eternal inﬂation is an very early
stage of inﬂation, during which the universe reproduces
itself, so that inﬂation becomes eternal to the future.
Eternal inﬂation, if indeed happened (for counter ar-
guments see, for example [9]), can populate the string
theory landscape, providing an explanation for the cos-
mological constant problem in our bubble universe by
anthropic arguments.
In this Letter, we shall focus on the multi-stream inﬂa-
tion scenario. Multi-stream inﬂation is proposed in [4].
And in [5], it is pointed out that the bifurcations can
lead to multiverse. Multi-stream inﬂation assumes that
during inﬂation there exist bifurcation(s) in the inﬂation
trajectory. For example, the bifurcations take place nat-
urally in a random potential, as illustrated in Fig. 1. We
brieﬂy review multi-stream inﬂation in Section II. The
details of some contents in Section II can be found in
[4]. We discuss some new implications of multi-stream
inﬂation for the inﬂationary multiverse in Section III.
∗wangyi@hep.physics.mcgill.ca
FIG. 1. In this ﬁgure, we use a tilted random potential to
mimic a inﬂationary potential in the string theory landscap e.
One can expect that in such a random potential, bifurcation
eﬀects happens generically, as illustrated in the trajecto ries
in the ﬁgure.
FIG. 2. One sample bifurcation in multi-stream inﬂation.
The inﬂation trajectory bifurcates into AandBwhen the
comoving scale k1exits the horizon, and recombines when
the comoving scale k2exits the horizon.
II. OBSERVABLE BIFURCATIONS
In this section, we discuss the possibility that the bi-
furcation of multi-stream inﬂation happens during the
observable stage of inﬂation. We review the production
of non-Gaussianities, features and asymmetries [4] in the2
FIG. 3. In multi-stream inﬂation, the universe breaks up
into patches with comoving scale k1. Each patch experienced
inﬂation either along trajectories AorB. 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 k1exits the
horizon, the inﬂation trajectory bifurcates into Aand
B. When comoving wave number k2exits the horizon,
the trajectories recombines into a single trajectory. The
universe breaks into of order k1/k0patches (where k0de-
notes the comoving scale of the current observable uni-
verse), each patch experienced inﬂation either along tra-
jectories AorB. The choice of the trajectories is made
by the isocurvature perturbation δχat scale k1. 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-
jectoryAand trajectory Bexperience 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, resultingin a correctionto the powerspectrum, and
potentially large non-Gaussianities. As shown in [6], the
amount of non-Gaussianity is of order
fNL∼P−1/2
ζ/parenleftbigg1
H∂3V
∂χ3/parenrightbigg/parenleftBigg˙θ
H/parenrightBigg3
, (1)
whereθdenotes the angle between the true inﬂation di-
rection and the ϕdirection.
As shown in Fig. 3, the universe is broken into patches
during multi-stream inﬂation. There arewall-likebound-
aries between these patches. During inﬂation, theseboundaries 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
scalek1and squeezed non-Gaussianity correlating scale

Thestringtheorylandscapealsoprovidesaplayground

for eternal inﬂation. Eternal inﬂation is an very early

stage of inﬂation, during which the universe reproduces

itself, so that inﬂation becomes eternal to the future.

Eternal inﬂation, if indeed happened (for counter ar-

guments see, for example [9]), can populate the string

theory landscape, providing an explanation for the cos-

mological constant problem in our bubble universe by

anthropic arguments.

In this Letter, we shall focus on the multi-stream inﬂa-

tion scenario. Multi-stream inﬂation is proposed in [4].

And in [5], it is pointed out that the bifurcations can

lead to multiverse. Multi-stream inﬂation assumes that

during inﬂation there exist bifurcation(s) in the inﬂation

trajectory. For example, the bifurcations take place nat-

urally in a random potential, as illustrated in Fig. 1. We

brieﬂy review multi-stream inﬂation in Section II. The

details of some contents in Section II can be found in

[4]. We discuss some new implications of multi-stream

inﬂation for the inﬂationary multiverse in Section III.

∗wangyi@hep.physics.mcgill.ca

FIG. 1. In this ﬁgure, we use a tilted random potential to

mimic a inﬂationary potential in the string theory landscap e.

One can expect that in such a random potential, bifurcation

eﬀects happens generically, as illustrated in the trajecto ries

in the ﬁgure.

FIG. 2. One sample bifurcation in multi-stream inﬂation.

The inﬂation trajectory bifurcates into AandBwhen the

comoving scale k1exits the horizon, and recombines when

the comoving scale k2exits the horizon.

II. OBSERVABLE BIFURCATIONS

In this section, we discuss the possibility that the bi-

furcation of multi-stream inﬂation happens during the

observable stage of inﬂation. We review the production

of non-Gaussianities, features and asymmetries [4] in the2

FIG. 3. In multi-stream inﬂation, the universe breaks up

into patches with comoving scale k1. Each patch experienced

inﬂation either along trajectories AorB. 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 k1exits the

horizon, the inﬂation trajectory bifurcates into Aand

B. When comoving wave number k2exits the horizon,

the trajectories recombines into a single trajectory. The

universe breaks into of order k1/k0patches (where k0de-

notes the comoving scale of the current observable uni-

verse), each patch experienced inﬂation either along tra-

jectories AorB. The choice of the trajectories is made

by the isocurvature perturbation δχat scale k1. 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-

jectoryAand trajectory Bexperience 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, resultingin a correctionto the powerspectrum, and

potentially large non-Gaussianities. As shown in [6], the

amount of non-Gaussianity is of order

fNL∼P−1/2

ζ/parenleftbigg1

H∂3V

∂χ3/parenrightbigg/parenleftBigg˙θ

H/parenrightBigg3

, (1)

whereθdenotes the angle between the true inﬂation di-

rection and the ϕdirection.

As shown in Fig. 3, the universe is broken into patches

during multi-stream inﬂation. There arewall-likebound-

aries between these patches. During inﬂation, theseboundaries 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

scalek1and squeezed non-Gaussianity correlating scale