Natalia Shuhmaher- Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics
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Early Stages of the Universe: Brane
Gas-Driven Bulk Dynamics
Natalia Shuhmaher (McGill)
Based on:
JHEP 0601, 074 (2006)
PRL 96, 161301 (2006)
by Robert Brandenberger, N.S.
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Outline
Overview
Outline of the Approach
Emerging Brane Inflation ModelsRemark on the horizon and entropy problems
Conclusions
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Overview
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
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Basic Idea
Toy Phenomenological model motivated by String Theory
In Use:
FRW Cosmology in extra dimensionsBranes (neglect charges and fluxes) ≡ topologicaldefects
Orbifold fixed planes
In our scenario:
Topology distinguishes 3 ’our’ dimensions
Difference in topology =⇒ difference in evolution
Starting point: A dense gas of branes
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Outline of the Approach
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
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Setup
Assumptions:
M = R × T 3 × T d/Z 2 (d - # of extra dimensions )
Total Energy = l−1
& ρi = l−
d−4
(e.g. l ∼ ls)
Orbifold fixed planes
Bulk matter
-p branes
l s
l s
Standard Initial Conditions:
Universe starts
Small
DenseUnique scale
An isotropic brane gas
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Overall Dynamics
Isotropicexpansion
Contraction of extra dimensions
Standard BigBang Cosmology
Timeline
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Phase of Expansion
Metric: ds2 = dt2 − a(t)2dx2 − b(t)2dy2
Isotropy: a(t) = b(t)
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Phase of Expansion
Metric: ds2 = dt2 − a(t)2dx2 − b(t)2dy2
Isotropy: a(t) = b(t)Expansion governed by
a
a+ (2 + d)(
a
a)2 =
8πG
3 + d − 1[ρ − P ]
Equation of state
P = wρ
Leads to
a(t) = b(t) ∼ tα ; α =2
(3 + d)(1 + w)
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p -Branes
3-brane: T µν = (ρ,−ρ,−ρ,−ρ, 0,...)
5-brane: T µν = (ρ,−ρ,−ρ,−ρ,−ρ,−ρ, 0,...)
Perfect fluid approximation for the brane gas
w =P
ρ= −
p
3 + d=⇒ α =
2
3 + d − p
Conclusion: The expansion phase is non-inflationaryfor codimension ≥ 3 branes
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From Expansion to Contraction
n s
pd
bl V
b
~
3
pbranes
V
pbranes
V t
tNatalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
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From Expansion to Contraction
n s
pd
bl V
b
~
3
pbranes
V
pbranes
V t
t
Brane potential dominates
when V = ρ
leading to contraction ofextra dimensions
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
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Emerging Brane Inflation Models
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Motivation II
Main Problem:Brane inflation doesn’t occur for generic initial conditions
one needs either
much weaker couplings than expected from string theory
large initial separation (r ≫ ls)
Conventional approaches: all extra dimensions are static=⇒ any starting point with r ≫ ls poses hierarchy problem
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
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Motivation II
Main Problem:Brane inflation doesn’t occur for generic initial conditions
one needs either
much weaker couplings than expected from string theory
large initial separation (r ≫ ls)
Conventional approaches: all extra dimensions are static=⇒ any starting point with r ≫ ls poses hierarchy problem
New approach: preceding expansion phase due to a gas of p-branes
leads to a large separation.
Advantage: Natural starting point
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
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Effective 4d view
Bulk Expansion Phase
V()
Inflation
V()
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
Eff ti Fi ld Th A h
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Effective Field Theory Approach
Canonically normalized scalar field ϕ:
ϕ = d(d + 2)
2m pl
log(b)
Effective 4d potential:
V eff (ϕ) = g2s ldsb(ϕ)−dV (b(ϕ))
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
E l
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Example
Consider inter-brane potential
V (lsb) = −µ1
(lsb)n, n < d + 3 − p =⇒ V eff (ϕ) ∝ −e−αϕ/mpl
Add brane tension/ account for zero cosmological constant
4d potential
V (ϕ) = Λ4+d−n
ld−n
s − Λ4+d−n
ld−n
s e
−α ϕ
mpl
Ifϕ ≫ m p/α ln(α2 + 1)
then a(t) is accelerating
N e-foldings require Allowing
lsΛ (α2N )−
d+3−p−n
(d+n)(d+4−n) Λ ∼ 0.1 l
−
1s
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
S
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Summary
Natural starting point
Radion serves as an inflaton
Emerging initial conditions for inflationUnique scale
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Remark on Horizon and Entropyproblems
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
Entropy Problem
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Entropy Problem
Assuming adiabatic expansionEntropy per co-moving volume which corresponds to H −1
0:
S U = #H
−3
0 T
3
0 = 10
90
≈ (1mm)3T 3 pl
Entropy problem = Hierarchy problem: ρ = m4
pl
corresponds to Universe of mm sizenot m−1
pl size
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
Entropy Problem
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Entropy Problem
Assuming adiabatic expansionEntropy per co-moving volume which corresponds to H −1
0:
S U = #H
−3
0 T
3
0 = 10
90
≈ (1mm)3T 3 pl
Entropy problem = Hierarchy problem: ρ = m4
pl
corresponds to Universe of mm sizenot m−1
pl size
Standard Solution:
Amplification of energy during early phaseNon-adiabatic phase transition converting energy to radiation
Unusual technic: Energy amplified in codimension ≥ 3 branes
=⇒ no accelerated expansion
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
Projected Energy Density Phase 1
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Projected Energy Density - Phase 1
Expansion
Extra dimensions
Extra dimensions
Orbifold fixed lane
p brane
pbranes
tPhase 1
3-branes
5-branes
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
Horizon Problem
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Horizon Problem
Standard Cosmology
forward light cone
t
trec
xt0
past light cone
Inflationt
x
trec
t0
tInf
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
Horizon Problem
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Horizon Problem
Standard Cosmology
forward light cone
t
trec
xt0
past light cone
Inflationt
x
trec
t0
tInf
Scenario without inflationt
tSC
x
trec
t0
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
Summary
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Summary
Horizon Problem: long period of dynamics in extradimensions
Entropy problem is addressed outside inflationary
scenarios
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
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Conclusions
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.
Conclusions
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Conclusions
Natural starting point for string inspired cosmology
New phase in the early Universe: bulk expansiongoverned by p-branes
Undressing hierarchies:
dynamical solution of initial conditions problem(inflationary)
entropy problem (non inflationary)
Possible solution of horizon problem in non-inflationarycontext
Natalia Shuhmaher Early Stages of the Universe: Brane Gas-Driven Bulk Dynamics – p.