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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Was There A Big Bang?Challenges of Early Universe Cosmology
Robert BrandenbergerMcGill University
February 22, 2012
1 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Outline
1 IntroductionMotivationReview of Inflationary CosmologyProblems of Inflationary CosmologyMessage
2 String Gas CosmologyPrinciplesFeatures of String Gas Cosmology
3 String Gas Cosmology and Structure FormationAnalysisSignatures in CMB anisotropy maps
4 Conclusions
2 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Plan
1 IntroductionMotivationReview of Inflationary CosmologyProblems of Inflationary CosmologyMessage
2 String Gas CosmologyPrinciplesFeatures of String Gas Cosmology
3 String Gas Cosmology and Structure FormationAnalysisSignatures in CMB anisotropy maps
4 Conclusions
3 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Goals of Early Universe Cosmology
Understand origin and early evolution of the universe.Explain observed large-scale structure.Make predictions for future observations.
4 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Goals of Early Universe Cosmology
Understand origin and early evolution of the universe.Explain observed large-scale structure.Make predictions for future observations.
4 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Goals of Early Universe Cosmology
Understand origin and early evolution of the universe.Explain observed large-scale structure.Make predictions for future observations.
4 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Large-Scale Structure
From: talk by O. Lahav
5 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Anisotropies in the Cosmic MicrowaveBackground (CMB)
Credit: NASA/WMAP Science Team6 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Quantification of the CMB data
Credit: NASA/WMAP Science Team
7 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Framework
Space-time described by Einstein’s theory of GeneralRelativity.Space-time dynamical (no longer absolute like inNewtonian theory)Matter curves space-timeMatter: Cold matter + radiation
8 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Framework
Space-time described by Einstein’s theory of GeneralRelativity.Space-time dynamical (no longer absolute like inNewtonian theory)Matter curves space-timeMatter: Cold matter + radiation
8 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Framework
Space-time described by Einstein’s theory of GeneralRelativity.Space-time dynamical (no longer absolute like inNewtonian theory)Matter curves space-timeMatter: Cold matter + radiation
8 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Framework
Space-time described by Einstein’s theory of GeneralRelativity.Space-time dynamical (no longer absolute like inNewtonian theory)Matter curves space-timeMatter: Cold matter + radiation
8 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Standard Big Bang Cosmology
Standard Big Bang Cosmology (SBB): the old paradigm ofcosmology ( 1960).The SBB is based on:
Cosmological principle: universe homogeneous andisotropic on large scales.Einstein equations governing dynamics of space-time.Classical matter as source in the Einstein equations(cold matter + radiation)
9 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Standard Big Bang Cosmology (ctd.)
Universe begins as a homogeneous and very hotfireballInitially radiation dominates: hot plasmaSpace expands and matter coolsAfter about 30,000 years cold matter starts to dominate.After about 300,000 years atoms (hydrogen) forms anduniverse becomes transparent to lightNow the age of the universe is about 13 billion years.
10 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Standard Big Bang Cosmology (ctd.)
Universe begins as a homogeneous and very hotfireballInitially radiation dominates: hot plasmaSpace expands and matter coolsAfter about 30,000 years cold matter starts to dominate.After about 300,000 years atoms (hydrogen) forms anduniverse becomes transparent to lightNow the age of the universe is about 13 billion years.
10 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Standard Big Bang Cosmology (ctd.)
Universe begins as a homogeneous and very hotfireballInitially radiation dominates: hot plasmaSpace expands and matter coolsAfter about 30,000 years cold matter starts to dominate.After about 300,000 years atoms (hydrogen) forms anduniverse becomes transparent to lightNow the age of the universe is about 13 billion years.
10 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Standard Big Bang Cosmology (ctd.)
Universe begins as a homogeneous and very hotfireballInitially radiation dominates: hot plasmaSpace expands and matter coolsAfter about 30,000 years cold matter starts to dominate.After about 300,000 years atoms (hydrogen) forms anduniverse becomes transparent to lightNow the age of the universe is about 13 billion years.
10 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Standard Big Bang Cosmology (ctd.)
Universe begins as a homogeneous and very hotfireballInitially radiation dominates: hot plasmaSpace expands and matter coolsAfter about 30,000 years cold matter starts to dominate.After about 300,000 years atoms (hydrogen) forms anduniverse becomes transparent to lightNow the age of the universe is about 13 billion years.
10 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Standard Big Bang Cosmology (ctd.)
Universe begins as a homogeneous and very hotfireballInitially radiation dominates: hot plasmaSpace expands and matter coolsAfter about 30,000 years cold matter starts to dominate.After about 300,000 years atoms (hydrogen) forms anduniverse becomes transparent to lightNow the age of the universe is about 13 billion years.
10 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Standard Big Bang Cosmology (ctd.)
Universe begins as a homogeneous and very hotfireballInitially radiation dominates: hot plasmaSpace expands and matter coolsAfter about 30,000 years cold matter starts to dominate.After about 300,000 years atoms (hydrogen) forms anduniverse becomes transparent to lightNow the age of the universe is about 13 billion years.
10 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Successes of the SBB Model
Key success: Existence and black body nature of the CMB.
11 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Conceptual Problems of the SBB Model
No explanation for the homogeneity, spatial flatness andlarge size and entropy of the universe.Horizon problem of the SBB:
t
x
t 0
t rec
0
l p
l f
(t)
(t)
12 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Conceptual Problems of the SBB Model II
No explanation of the observed inhomogeneities in thedistribution of matter and anisotropies in the CosmicMicrowave Background possible!
13 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Current Paradigm for Early UniverseCosmology
The Inflationary Universe Scenario is the current paradigmof early universe cosmology (1980).Successes:
Solves horizon problemSolves flatness problemSolves size/entropy problemProvides a causal mechanism of generating primordialcosmological perturbations (Chibisov & Mukhanov,1981).
14 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Current Paradigm for Early UniverseCosmology
The Inflationary Universe Scenario is the current paradigmof early universe cosmology (1980).Successes:
Solves horizon problemSolves flatness problemSolves size/entropy problemProvides a causal mechanism of generating primordialcosmological perturbations (Chibisov & Mukhanov,1981).
14 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Current Paradigm for Early UniverseCosmology
The Inflationary Universe Scenario is the current paradigmof early universe cosmology (1980).Successes:
Solves horizon problemSolves flatness problemSolves size/entropy problemProvides a causal mechanism of generating primordialcosmological perturbations (Chibisov & Mukhanov,1981).
14 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Credit: NASA/WMAP Science Team15 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Credit: NASA/WMAP Science Team
16 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Challenges for the Current Paradigm
In spite of the phenomenological successes, theinflationary scenario suffers from several conceptualproblems.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?
17 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Challenges for the Current Paradigm
In spite of the phenomenological successes, theinflationary scenario suffers from several conceptualproblems.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?
17 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Challenges for the Current Paradigm
In spite of the phenomenological successes, theinflationary scenario suffers from several conceptualproblems.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?
17 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Challenges for the Current Paradigm
In spite of the phenomenological successes, theinflationary scenario suffers from several conceptualproblems.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?
17 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Review of Inflationary Cosmology
Context:General RelativityScalar Field Matter
Inflation:phase with exponential expansion of spacerequires matter with negative pressurerequires a slowly rolling scalar field ϕ
18 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Review of Inflationary Cosmology
Context:General RelativityScalar Field Matter
Inflation:phase with exponential expansion of spacerequires matter with negative pressurerequires a slowly rolling scalar field ϕ
18 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Review of Inflationary Cosmology
Context:General RelativityScalar Field Matter
Inflation:phase with exponential expansion of spacerequires matter with negative pressurerequires a slowly rolling scalar field ϕ
18 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Review of Inflationary Cosmology
Context:General RelativityScalar Field Matter
Inflation:phase with exponential expansion of spacerequires matter with negative pressurerequires a slowly rolling scalar field ϕ
18 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Time line of inflationary cosmology:
ti : inflation beginstR: inflation ends, reheating
19 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Review of Inflationary Cosmology II
Space-time sketch of inflationary cosmology:
Note:H = a
acurve labelled by k : wavelength of a fluctuation
20 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
inflation renders the universe large, homogeneous andspatially flatclassical matter redshifts→ matter vacuum remainsquantum vacuum fluctuations: seeds for the observedstructure [Chibisov & Mukhanov, 1981]
21 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Conceptual Problems of InflationaryCosmology
What is the scalar field?Why does it have the special conditions to obtaininflation?Trans-Planckian problemSingularity problemApplicability of General Relativity
22 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Conceptual Problems of InflationaryCosmology
What is the scalar field?Why does it have the special conditions to obtaininflation?Trans-Planckian problemSingularity problemApplicability of General Relativity
22 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Conceptual Problems of InflationaryCosmology
What is the scalar field?Why does it have the special conditions to obtaininflation?Trans-Planckian problemSingularity problemApplicability of General Relativity
22 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
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 slightly more thanthe minimal length it must have, then the wavelength issmaller than the Planck length at the beginning ofinflation→ new physics MUST enter into the calculation of thefluctuations.
23 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
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 slightly more thanthe minimal length it must have, then the wavelength issmaller than the Planck length at the beginning ofinflation→ new physics MUST enter into the calculation of thefluctuations.
23 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
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 slightly more thanthe minimal length it must have, then the wavelength issmaller than the Planck length at the beginning ofinflation→ new physics MUST enter into the calculation of thefluctuations.
23 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
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 slightly more thanthe minimal length it must have, then the wavelength issmaller than the Planck length at the beginning ofinflation→ new physics MUST enter into the calculation of thefluctuations.
23 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Singularity Problem
Standard cosmology: Penrose-Hawking theorems→initial singularity→ incompleteness of the theory.Inflationary cosmology: In scalar field-driveninflationary models the initial singularity persists [Bordeand Vilenkin]→ incompleteness of the theory.
24 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Singularity Problem
Standard cosmology: Penrose-Hawking theorems→initial singularity→ incompleteness of the theory.Inflationary cosmology: In scalar field-driveninflationary models the initial singularity persists [Bordeand Vilenkin]→ incompleteness of the theory.
24 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Singularity Problem
Standard cosmology: Penrose-Hawking theorems→initial singularity→ incompleteness of the theory.Inflationary cosmology: In scalar field-driveninflationary models the initial singularity persists [Bordeand Vilenkin]→ incompleteness of the theory.
24 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Applicability of GR
Einstein’s theory breaks down at extremely highdensities.In models of inflation, the energy scale of at whichinflation takes place is close to the limiting scale for thevalidity of Einstein’s theory.We cannot trust the predictions made using GR.
25 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Applicability of GR
Einstein’s theory breaks down at extremely highdensities.In models of inflation, the energy scale of at whichinflation takes place is close to the limiting scale for thevalidity of Einstein’s theory.We cannot trust the predictions made using GR.
25 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Applicability of GR
Einstein’s theory breaks down at extremely highdensities.In models of inflation, the energy scale of at whichinflation takes place is close to the limiting scale for thevalidity of Einstein’s theory.We cannot trust the predictions made using GR.
25 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Zones of Ignorance
26 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Message I
Current realizations of inflation have serious conceptualproblems.We need a new paradigm of very early universecosmology based on new fundamental physics.Hypothesis: New paradigm based on SuperstringTheory.The new paradigm of early universe cosmology maynot involve inflation.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].
27 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Message I
Current realizations of inflation have serious conceptualproblems.We need a new paradigm of very early universecosmology based on new fundamental physics.Hypothesis: New paradigm based on SuperstringTheory.The new paradigm of early universe cosmology maynot involve inflation.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].
27 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Message I
Current realizations of inflation have serious conceptualproblems.We need a new paradigm of very early universecosmology based on new fundamental physics.Hypothesis: New paradigm based on SuperstringTheory.The new paradigm of early universe cosmology maynot involve inflation.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].
27 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Message I
Current realizations of inflation have serious conceptualproblems.We need a new paradigm of very early universecosmology based on new fundamental physics.Hypothesis: New paradigm based on SuperstringTheory.The new paradigm of early universe cosmology maynot involve inflation.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].
27 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Message II
String Gas Cosmology makes testable predictions forcosmological observations
Blue tilt in the spectrum of gravitational waves [R.B., A.Nayeri, S. Patil and C. Vafa, 2006]Line discontinuities in CMB anisotropy maps [N. Kaiserand A. Stebbins, 1984]Line discontinuities can be detected using the CANNYedge detection algorithm [S. Amsel, J. Berger and R.B.,2007, R. Danos and R.B., 2008, 2009]
28 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Message II
String Gas Cosmology makes testable predictions forcosmological observations
Blue tilt in the spectrum of gravitational waves [R.B., A.Nayeri, S. Patil and C. Vafa, 2006]Line discontinuities in CMB anisotropy maps [N. Kaiserand A. Stebbins, 1984]Line discontinuities can be detected using the CANNYedge detection algorithm [S. Amsel, J. Berger and R.B.,2007, R. Danos and R.B., 2008, 2009]
28 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Message II
String Gas Cosmology makes testable predictions forcosmological observations
Blue tilt in the spectrum of gravitational waves [R.B., A.Nayeri, S. Patil and C. Vafa, 2006]Line discontinuities in CMB anisotropy maps [N. Kaiserand A. Stebbins, 1984]Line discontinuities can be detected using the CANNYedge detection algorithm [S. Amsel, J. Berger and R.B.,2007, R. Danos and R.B., 2008, 2009]
28 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Plan
1 IntroductionMotivationReview of Inflationary CosmologyProblems of Inflationary CosmologyMessage
2 String Gas CosmologyPrinciplesFeatures of String Gas Cosmology
3 String Gas Cosmology and Structure FormationAnalysisSignatures in CMB anisotropy maps
4 Conclusions
29 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
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
30 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
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
30 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
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
30 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
T-Duality
T-Duality
Momentum modes: En = n/RWinding modes: Em = mRDuality: R → 1/R (n,m)→ (m,n)
Mass spectrum of string states unchanged
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Adiabatic ConsiderationsR.B. and C. Vafa, Nucl. Phys. B316:391 (1989)
Temperature-size relation in string gas cosmology
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Singularity Problem in Standard andInflationary Cosmology
Temperature-size relation in standard cosmology
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Dynamics
Assume some action gives us R(t)
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Dynamics II
We will thus consider the following background dynamics forthe scale factor a(t):
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
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.
Note: this argument assumes constant dilaton [R. Danos, A.Frey and A. Mazumdar]
36 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
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.
Note: this argument assumes constant dilaton [R. Danos, A.Frey and A. Mazumdar]
36 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
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.
Note: this argument assumes constant dilaton [R. Danos, A.Frey and A. Mazumdar]
36 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
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.
Note: this argument assumes constant dilaton [R. Danos, A.Frey and A. Mazumdar]
36 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Plan
1 IntroductionMotivationReview of Inflationary CosmologyProblems of Inflationary CosmologyMessage
2 String Gas CosmologyPrinciplesFeatures of String Gas Cosmology
3 String Gas Cosmology and Structure FormationAnalysisSignatures in CMB anisotropy maps
4 Conclusions
37 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Structure formation in inflationary cosmology
N.B. Perturbations originate as quantum vacuumfluctuations.
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Background for string gas cosmology
39 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
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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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Power spectrum of cosmological fluctuations
Key features:
scale-invariant like for inflationslight red tilt like for inflation
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Spectrum of Gravitational Waves
Key features:
scale-invariant (like for inflation)slight blue tilt (unlike for inflation)
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Network of cosmic superstrings
Remnant of the Hagedorn phase: network of cosmicsuperstringsThis string network will be present at all times and willachieve a scaling solution like cosmic strings formingduring a phase transition.Scaling Solution: The network of strings looksstatistically the same at all times when scaled to theHubble radius.
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Kaiser-Stebbins Effect
Space perpendicular to a string is conical with deficit angle
α = 8πGµ , (1)
Photons passing by the string undergo a relative Dopplershift
δTT
= 8πγ(v)vGµ , (2)
→ network of line discontinuities in CMB anisotropy maps.N.B. characteristic scale: one degree in the sky, but to seethat there is a sharp temperature jump one needs goodangular resolution .
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
45 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Gaussian map due to thermal superstringfluctuations
10’0 x 100 map of the sky at 1.5’ resolution (South PoleTelescope specifications)
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Cosmic superstring contribution
100 x 100 map of the sky at 1.5’ resolution
47 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
This signal is superimposed on the Gaussian map. Therelative power of the string signature depends on Gµ and isbound to contribute less than 10% of the power.
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Temperature map Gaussian + cosmicsuperstrings
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
CANNY edge detection algorithm
Challenge: pick out the string signature from theGaussian "noise" which has a much larger amplitudeNew technique: use CANNY edge detection algorithm[Canny, 1986]Idea: find edges across which the gradient is in thecorrect range to correspond to a Kaiser-Stebbins signalfrom a stringStep 1: generate "Gaussian" and "Gaussian plusstrings" CMB anisotropy maps: size and angularresolution of the maps are free parameters, flat skyapproximation, cosmic string toy model in which a fixednumber of straight string segments is laid down atrandom in each Hubble volume in each Hubble timestep between trec and t0.
50 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
CANNY algorithm II
Step 2: run the CANNY algorithm on the temperaturemaps to produce edge maps.Step 3: Generate histogram of edge lengthsStep 4: Use Fisher combined probability test to checkfor difference compared to a Gaussian distribution.
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Results
For South Pole Telescope (SPT) specification: limitGµ < 2× 10−8 can be set [R. Danos and R.B., 2008]Anticipated SPT instrumental noise only insignficantlyeffects the limits [A. Stewart and R.B., 2008]
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Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Results
For South Pole Telescope (SPT) specification: limitGµ < 2× 10−8 can be set [R. Danos and R.B., 2008]Anticipated SPT instrumental noise only insignficantlyeffects the limits [A. Stewart and R.B., 2008]
52 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Plan
1 IntroductionMotivationReview of Inflationary CosmologyProblems of Inflationary CosmologyMessage
2 String Gas CosmologyPrinciplesFeatures of String Gas Cosmology
3 String Gas Cosmology and Structure FormationAnalysisSignatures in CMB anisotropy maps
4 Conclusions
53 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Conclusions I
Cosmology is a vibrant field with lots of observationaldataParadigms of early universe cosmology have beendevelopedParadigm 1: Standard Big Bang ModelParadigm 2: Inflationary Universe scenario - currentparadigmParadigm 2 has conceptual problems→ motivates thesearch for an improved paradigm.Superstring theory may provide a new paradigm.Superstring cosmology may resolve the Big Bangsingularity.It is possible to observationally probe string cosmology.
54 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Conclusions I
Cosmology is a vibrant field with lots of observationaldataParadigms of early universe cosmology have beendevelopedParadigm 1: Standard Big Bang ModelParadigm 2: Inflationary Universe scenario - currentparadigmParadigm 2 has conceptual problems→ motivates thesearch for an improved paradigm.Superstring theory may provide a new paradigm.Superstring cosmology may resolve the Big Bangsingularity.It is possible to observationally probe string cosmology.
54 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Conclusions I
Cosmology is a vibrant field with lots of observationaldataParadigms of early universe cosmology have beendevelopedParadigm 1: Standard Big Bang ModelParadigm 2: Inflationary Universe scenario - currentparadigmParadigm 2 has conceptual problems→ motivates thesearch for an improved paradigm.Superstring theory may provide a new paradigm.Superstring cosmology may resolve the Big Bangsingularity.It is possible to observationally probe string cosmology.
54 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Conclusions I
Cosmology is a vibrant field with lots of observationaldataParadigms of early universe cosmology have beendevelopedParadigm 1: Standard Big Bang ModelParadigm 2: Inflationary Universe scenario - currentparadigmParadigm 2 has conceptual problems→ motivates thesearch for an improved paradigm.Superstring theory may provide a new paradigm.Superstring cosmology may resolve the Big Bangsingularity.It is possible to observationally probe string cosmology.
54 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Conclusions I
Cosmology is a vibrant field with lots of observationaldataParadigms of early universe cosmology have beendevelopedParadigm 1: Standard Big Bang ModelParadigm 2: Inflationary Universe scenario - currentparadigmParadigm 2 has conceptual problems→ motivates thesearch for an improved paradigm.Superstring theory may provide a new paradigm.Superstring cosmology may resolve the Big Bangsingularity.It is possible to observationally probe string cosmology.
54 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Conclusions I
Cosmology is a vibrant field with lots of observationaldataParadigms of early universe cosmology have beendevelopedParadigm 1: Standard Big Bang ModelParadigm 2: Inflationary Universe scenario - currentparadigmParadigm 2 has conceptual problems→ motivates thesearch for an improved paradigm.Superstring theory may provide a new paradigm.Superstring cosmology may resolve the Big Bangsingularity.It is possible to observationally probe string cosmology.
54 / 56
Early Universe
R. Branden-berger
IntroductionMotivation
Inflation
Problems
Message
String gasPrinciples
Features
StructureAnalysis
Signatures in CMBanisotropy maps
Conclusions
Conclusions II
SGC leaves behind a network of cosmic superstringsThese cosmic superstrings give rise to linediscontinuities in CMB anisotropy maps which can beprobed using a CANNY edge detection algorithm.Undergraduates participate in this cutting edgeresearch!
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