Testing String Theory with Cosmological Observations ...rhb/sample/Calgary2012c.pdf · Testing...

StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

String gasPrinciples

Features

StructurePerturbations

Analysis

Conclusions

Testing String Theory with CosmologicalObservations?

CAP-CRM Prize Lecture

Robert BrandenbergerMcGill University

June 15, 2012

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Thanks to:

Klaus Hepp (ETH Zürich)Konrad Osterwalder (ETH Zürich)Arthur Jaffe (Harvard)Jennie TraschenRaul Bott, Sidney Coleman (Harvard)Bill Press, Doug Eardley (Harvard)Neil Turok, Andy AlbrechtAnne-Christine Davis (DAMTP), Slava Mukhanov(LMU), Cumrun Vafa (Harvard), Xinmin Zhang (IHEPBeijing)

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Thanks to:

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Thanks to:

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Thanks to:

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Thanks to:

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Thanks to:

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Thanks to:

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Thanks to:

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Hume Feldman, Leandros Perivolaropoulos, JongKung, Jinwu Ye, Tomislav Prokopec, AndrewSornborger, Richhild Moessner, Mark Trodden, RaulAbramo, Matthew Parry, Martin Götz, StephonAlexander, Damien Easson, Antonio Guimaraes, ZeeyaMerali, Ghazal Geshnizjani, Scott Watson, ThorstenBattefeld.Subodh Patil, Natalia Shuhmaher, Patrick Martineau,Rebecca Danos, Nima Lashkari, Andrew Stewart,Francis Cyr-Racine, Jean Lachapelle, JohannaKarouby, Wei Xue, Laurence Perreault-LevasseurMy colleagues at McGill

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Hume Feldman, Leandros Perivolaropoulos, JongKung, Jinwu Ye, Tomislav Prokopec, AndrewSornborger, Richhild Moessner, Mark Trodden, RaulAbramo, Matthew Parry, Martin Götz, StephonAlexander, Damien Easson, Antonio Guimaraes, ZeeyaMerali, Ghazal Geshnizjani, Scott Watson, ThorstenBattefeld.Subodh Patil, Natalia Shuhmaher, Patrick Martineau,Rebecca Danos, Nima Lashkari, Andrew Stewart,Francis Cyr-Racine, Jean Lachapelle, JohannaKarouby, Wei Xue, Laurence Perreault-LevasseurMy colleagues at McGill

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Main Messages

There are alternatives to inflationary cosmology.String Theory leads to a new paradigm for earlyuniverse cosmology.String Theory can be tested with cosmologicalobservations.

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Outline

1 Inflation: Current Paradigm of Early Universe CosmologyMotivationReview of Inflationary CosmologyProblems of Inflationary CosmologyMessage

2 String Gas CosmologyPrinciplesFeatures of String Gas Cosmology

3 String Gas Cosmology and Structure FormationReview of the Theory of Cosmological PerturbationsAnalysis

4 Conclusions

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

4 Conclusions

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Current Paradigm for Early UniverseCosmology

The Inflationary Universe Scenario is the current paradigmof early universe cosmology.Successes:

Solves horizon problemSolves flatness problemSolves size/entropy problemProvides a causal mechanism of generating primordialcosmological perturbations (Chibisov & Mukhanov,1981).

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Current Paradigm for Early UniverseCosmology

The Inflationary Universe Scenario is the current paradigmof early universe cosmology.Successes:

Solves horizon problemSolves flatness problemSolves size/entropy problemProvides a causal mechanism of generating primordialcosmological perturbations (Chibisov & Mukhanov,1981).

7 / 40

StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Credit: NASA/WMAP Science Team8 / 40

StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Credit: NASA/WMAP Science Team

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Challenges for the Current Paradigm

In spite of the phenomenological successes, currentrealizations of the inflationary scenario suffer fromseveral conceptual problems.In light of these problems we need to look for input fromnew fundamental physics to construct a new theorywhich will overcome these problems.Question: Can Superstring theory lead to a new andimproved paradigm?Question: Can this new paradigm be tested incosmological observations?

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Review of Inflationary Cosmology

Context:General RelativityScalar Field Matter

Metric : ds2 = dt2 − a(t)2dx2 (1)

Inflation:phase with a(t) ∼ etH

requires matter with p ∼ −ρrequires a slowly rolling scalar field ϕ- in order to have a potential energy term- in order that the potential energy term dominatessufficiently long

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Time line of inflationary cosmology:

ti : inflation beginstR: inflation ends, reheating

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Review of Inflationary Cosmology II

Space-time sketch of inflationary cosmology:

Note:H = a

acurve labelled by k : wavelength of a fluctuation

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

inflation renders the universe large, homogeneous andspatially flatclassical matter redshifts→ matter vacuum remainsquantum vacuum fluctuations: seeds for the observedstructure [Chibisov & Mukhanov, 1981]sub-Hubble→ locally causal

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Conceptual Problems of InflationaryCosmology

Nature of the scalar field ϕ (the “inflaton")Conditions to obtain inflation (initial conditions, slow-rollconditions, graceful exit and reheating)Amplitude problemTrans-Planckian problemSingularity problemCosmological constant problemApplicability of General Relativity

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Trans-Planckian Problem

Success of inflation: At early times scales are insidethe Hubble radius→ causal generation mechanism ispossible.Problem: If time period of inflation is more than 70H−1,then λp(t) < lpl at the beginning of inflation→ new physics MUST enter into the calculation of thefluctuations.

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Cosmological Constant Problem

Quantum vacuum energy does not gravitate.Why should the almost constant V (ϕ) gravitate?

Λobs∼ 10120 (2)

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Applicability of GR

In all approaches to quantum gravity, the Einstein actionis only the leading term in a low curvature expansion.Correction terms may become dominant at much lowerenergies than the Planck scale.Correction terms will dominate the dynamics at highcurvatures.The energy scale of inflation models is typicallyη ∼ 1016GeV.→ η too close to mpl to trust predictions made usingGR.

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Zones of Ignorance

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Message

Current realizations of inflation have conceptualproblems.We need a new paradigm of very early universecosmology based on new fundamental physics.Hypothesis: New paradigm based on SuperstringTheory.New cosmological model motivated by superstringtheory: String Gas Cosmology (SGC) [R.B. and C.Vafa, 1989]New structure formation scenario emerges from SGC[A. Nayeri, R.B. and C. Vafa, 2006].Testable prediction for cosmological observations: Bluetilt in the spectrum of gravitational waves [R.B., A.Nayeri, S. Patil and C. Vafa, 2006]

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

4 Conclusions

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

PrinciplesR.B. and C. Vafa, Nucl. Phys. B316:391 (1989)

Idea: make use of the new symmetries and new degrees offreedom which string theory provides to construct a newtheory of the very early universe.Assumption: Matter is a gas of fundamental stringsAssumption: Space is compact, e.g. a torus.Key points:

New degrees of freedom: string oscillatory modesLeads to a maximal temperature for a gas of strings,the Hagedorn temperatureNew degrees of freedom: string winding modesLeads to a new symmetry: physics at large R isequivalent to physics at small R

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

T-Duality

Momentum modes: En = n/RWinding modes: Em = mRDuality: R → 1/R (n,m)→ (m,n)

Mass spectrum of string states unchangedSymmetry of vertex operatorsSymmetry at non-perturbative level→ existence ofD-branes

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Adiabatic ConsiderationsR.B. and C. Vafa, Nucl. Phys. B316:391 (1989)

Temperature-size relation in string gas cosmology

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Dynamics

Assume some action gives us R(t)

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Dynamics II

We will thus consider the following background dynamics forthe scale factor a(t):

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Dimensionality of Space in SGC

Begin with all 9 spatial dimensions small, initialtemperature close to TH → winding modes about allspatial sections are excited.Expansion of any one spatial dimension requires theannihilation of the winding modes in that dimension.

Decay only possible in three large spatial dimensions.→ dynamical explanation of why there are exactly threelarge spatial dimensions.

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Dimensionality of Space in SGC

Begin with all 9 spatial dimensions small, initialtemperature close to TH → winding modes about allspatial sections are excited.Expansion of any one spatial dimension requires theannihilation of the winding modes in that dimension.

Decay only possible in three large spatial dimensions.→ dynamical explanation of why there are exactly threelarge spatial dimensions.

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

4 Conclusions

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Theory of Cosmological Perturbations: Basics

Cosmological fluctuations connect early universe theorieswith observations

Fluctuations of matter→ large-scale structureFluctuations of metric→ CMB anisotropiesN.B.: Matter and metric fluctuations are coupled

Key facts:

1. Fluctuations are small today on large scales→ fluctuations were very small in the early universe→ can use linear perturbation theory2. Sub-Hubble scales: matter fluctuations dominateSuper-Hubble scales: metric fluctuations dominate

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Quantum Theory of Linearized FluctuationsV. Mukhanov, H. Feldman and R.B., Phys. Rep. 215:203 (1992)

Step 1: Metric and matter including fluctuations

ds2 = a2[(1 + 2Φ)dη2 − (1− 2Φ)dx2] (3)ϕ = ϕ0 + δϕ (4)

Note: Φ and δϕ related by Einstein constraint equationsStep 2: Expand the action for matter and gravity to secondorder about the cosmological background:

S(2) =12

∫d4x

((v ′)2 − v,iv ,i +

z ′′

zv2) (5)

v = a(δϕ+

z = aϕ′0H

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Step 3: Resulting equation of motion (Fourier space)

v ′′k + (k2 − z ′′

z)vk = 0 (8)

Features:

oscillations on sub-Hubble scalessqueezing on super-Hubble scales vk ∼ z

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Background for string gas cosmology

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Structure formation in string gas cosmologyA. Nayeri, R.B. and C. Vafa, Phys. Rev. Lett. 97:021302 (2006)

N.B. Perturbations originate as thermal string gasfluctuations.

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Method

Calculate matter correlation functions in the Hagedornphase (neglecting the metric fluctuations)For fixed k , convert the matter fluctuations to metricfluctuations at Hubble radius crossing t = ti(k)

Evolve the metric fluctuations for t > ti(k) using theusual theory of cosmological perturbations

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Extracting the Metric Fluctuations

Ansatz for the metric including cosmological perturbationsand gravitational waves:

ds2 = a2(η)((1 + 2Φ)dη2 − [(1− 2Φ)δij + hij ]dx idx j) . (9)

Inserting into the perturbed Einstein equations yields

〈|Φ(k)|2〉 = 16π2G2k−4〈δT 00(k)δT 0

0(k)〉 , (10)

〈|h(k)|2〉 = 16π2G2k−4〈δT ij(k)δT i

j(k)〉 . (11)

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Power Spectrum of Cosmological Perturbations

Key ingredient: For thermal fluctuations:

〈δρ2〉 =T 2

R6 CV . (12)

Key ingredient: For string thermodynamics in a compactspace

CV ≈ 2R2/`3s

T (1− T/TH). (13)

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Power Spectrum of Cosmological Perturbations

Key ingredient: For thermal fluctuations:

〈δρ2〉 =T 2

R6 CV . (12)

Key ingredient: For string thermodynamics in a compactspace

CV ≈ 2R2/`3s

T (1− T/TH). (13)

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Power spectrum of cosmological fluctuations

PΦ(k) = 8G2k−1 < |δρ(k)|2 > (14)= 8G2k2 < (δM)2 >R (15)= 8G2k−4 < (δρ)2 >R (16)

= 8G2 T`3s

11− T/TH

Key features:

scale-invariant like for inflationslight red tilt like for inflation

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Power spectrum of cosmological fluctuations

PΦ(k) = 8G2k−1 < |δρ(k)|2 > (14)= 8G2k2 < (δM)2 >R (15)= 8G2k−4 < (δρ)2 >R (16)

= 8G2 T`3s

11− T/TH

Key features:

scale-invariant like for inflationslight red tilt like for inflation

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Spectrum of Gravitational WavesR.B., A. Nayeri, S. Patil and C. Vafa, Phys. Rev. Lett. (2007)

Ph(k) = 16π2G2k−1 < |Tij(k)|2 > (18)

= 16π2G2k−4 < |Tij(R)|2 > (19)

∼ 16π2G2 T`3s

(1− T/TH) (20)

Key ingredient for string thermodynamics

< |Tij(R)|2 >∼ Tl3s R4

(1− T/TH) (21)

Key features:

scale-invariant (like for inflation)slight blue tilt (unlike for inflation)

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

Spectrum of Gravitational WavesR.B., A. Nayeri, S. Patil and C. Vafa, Phys. Rev. Lett. (2007)

Ph(k) = 16π2G2k−1 < |Tij(k)|2 > (18)

= 16π2G2k−4 < |Tij(R)|2 > (19)

∼ 16π2G2 T`3s

(1− T/TH) (20)

Key ingredient for string thermodynamics

< |Tij(R)|2 >∼ Tl3s R4

(1− T/TH) (21)

Key features:

scale-invariant (like for inflation)slight blue tilt (unlike for inflation)

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

4 Conclusions

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StringCosmology

R. Branden-berger

InflationMotivation

Inflation

Problems

Message

Features

Analysis

Conclusions

String Gas Cosmology: Model of cosmology of the veryearly universe based on new degrees of freedom andnew symmetries of superstring theory.SGC→ nonsingular cosmologySGC→ natural explanation of the number of largespatial dimensions.SGC→ new scenario of structure formationScale invariant spectrum of cosmological fluctuations(like in inflationary cosmology).Spectrum of gravitational waves has a small blue tilt(unlike in inflationary cosmology).

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Testing String Theory with Cosmological Observations ...rhb/sample/Calgary2012c.pdf · Testing...

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