What Was Before the Big Bang? Framework Space-Time Cosmology of the Very Early Universe Std

Home , Initial singularity

Early Universe

R. Branden- berger

Cosmology What was before the Big Bang? Framework Space-Time Cosmology of the Very Early Universe Std. Cosmology

Inﬂation

String gas Robert Brandenberger Conclusions McGill University

February 21, 2013

1 / 68 Outline

Early Universe

R. Branden- berger 1 What is Cosmology? Cosmology Framework 2 Space-Time Framework Std. Cosmology Space-Time Inﬂation Standard Big Bang Cosmology String gas

Conclusions 3 Inﬂationary Cosmology

4 String Cosmology

5 Conclusions

2 / 68 Plan

Early Universe

R. Branden- berger 1 What is Cosmology? Cosmology Framework 2 Space-Time Framework Std. Cosmology Space-Time Inﬂation Standard Big Bang Cosmology String gas

Conclusions 3 Inﬂationary Cosmology

4 String Cosmology

5 Conclusions

3 / 68 Goals of Early Universe Cosmology

Early Universe

R. Branden- berger

Cosmology

Framework 1. Understand origin and early evolution of the universe. Space-Time Std. Cosmology What is the “Big Bang"? Inﬂation Was there a “Big Bang"? String gas

Conclusions What was before the “Big Bang"?

2. Explain observed large-scale structure.

4 / 68 Goals of Early Universe Cosmology

Early Universe

R. Branden- berger

Cosmology

Framework 1. Understand origin and early evolution of the universe. Space-Time Std. Cosmology What is the “Big Bang"? Inﬂation Was there a “Big Bang"? String gas

Conclusions What was before the “Big Bang"?

2. Explain observed large-scale structure.

4 / 68 Goals of Early Universe Cosmology

Early Universe

R. Branden- berger

Cosmology

Framework 1. Understand origin and early evolution of the universe. Space-Time Std. Cosmology What is the “Big Bang"? Inﬂation Was there a “Big Bang"? String gas

Conclusions What was before the “Big Bang"?

2. Explain observed large-scale structure.

4 / 68 Goals of Early Universe Cosmology

Early Universe

R. Branden- berger

Cosmology

Framework 1. Understand origin and early evolution of the universe. Space-Time Std. Cosmology What is the “Big Bang"? Inﬂation Was there a “Big Bang"? String gas

Conclusions What was before the “Big Bang"?

2. Explain observed large-scale structure.

4 / 68 Goals of Early Universe Cosmology

Early Universe

R. Branden- berger

Cosmology

Framework 1. Understand origin and early evolution of the universe. Space-Time Std. Cosmology What is the “Big Bang"? Inﬂation Was there a “Big Bang"? String gas

Conclusions What was before the “Big Bang"?

2. Explain observed large-scale structure.

4 / 68 Optical Telescopes: Gemini Telescope

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

5 / 68 Galaxies: Building Blocks of the Cosmology

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

6 / 68 Large-Scale Structure

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

From: talk by O. Lahav

7 / 68 Microwave Telescopes on the Earth: ACT Telescope

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

8 / 68 Microwave Telescopes on the Earth: SPT Telescope

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

9 / 68 Microwave Telescopes in Space: WMAP Telescope

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

10 / 68 Isotropic CMB Background

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

11 / 68 Anisotropies in the Cosmic Microwave Background (CMB)

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

Credit: NASA/WMAP Science Team 12 / 68 Quantiﬁcation of the CMB data

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

Credit: NASA/WMAP Science Team

13 / 68 Goals of Early Universe Cosmology

Early Universe

R. Branden- berger 1. Understand origin and early evolution of the universe.

Cosmology What is the “Big Bang"? Framework Space-Time Was there a “Big Bang"? Std. Cosmology What was before the “Big Bang"? Inﬂation

String gas Conclusions 2. Explain observed large-scale structure. Patterns in the distribution of galaxies on large scales. Anisotropies in CMB maps.

3. Make predictions for future observations.

14 / 68 Goals of Early Universe Cosmology

Early Universe

R. Branden- berger 1. Understand origin and early evolution of the universe.

Cosmology What is the “Big Bang"? Framework Space-Time Was there a “Big Bang"? Std. Cosmology What was before the “Big Bang"? Inﬂation

String gas Conclusions 2. Explain observed large-scale structure. Patterns in the distribution of galaxies on large scales. Anisotropies in CMB maps.

3. Make predictions for future observations.

14 / 68 Plan

Early Universe

R. Branden- berger 1 What is Cosmology? Cosmology Framework 2 Space-Time Framework Std. Cosmology Space-Time Inﬂation Standard Big Bang Cosmology String gas

Conclusions 3 Inﬂationary Cosmology

4 String Cosmology

5 Conclusions

15 / 68 Framework

Early Universe R. Branden- The Universe is: berger Space-time Cosmology Framework Matter which lives in space-time. Space-Time Std. Cosmology To describe the Universe: Inﬂation String gas Space-time described by Einstein’s theory of General Conclusions Relativity. Matter as described by Physics. More speciﬁcally: matter described on large scale by classical physics, on small scales by quantum mechanics and on even smaller scales by superstring theory?

16 / 68 Framework

16 / 68 Space-Time as Described by General Relativity

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology Space-time dynamical (no longer absolute like in Inﬂation Newtonian theory) String gas Conclusions Matter curves space-time.

17 / 68 Space-Time as Described by General Relativity

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology Space-time dynamical (no longer absolute like in Inﬂation Newtonian theory) String gas Conclusions Matter curves space-time.

17 / 68 Mass curves Space-Time

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

18 / 68 Space-Time as Described by General Relativity

Early Universe

R. Branden- berger

Cosmology Space-time dynamical (no longer absolute like in

Framework Newtonian theory) Space-Time Std. Cosmology Matter curves space-time: Space-time is dynamical. Inﬂation Note: Newton’s gravitational force is a consequence of String gas the curvature of space. Conclusions Einstein Equivalence Principle determines the motion of matter in curved space-time. Space with a homogeneous distribution of matter cannot be static - it must expand (or contract).

19 / 68 Space-Time as Described by General Relativity

Early Universe

R. Branden- berger

Cosmology Space-time dynamical (no longer absolute like in

19 / 68 Space-Time as Described by General Relativity

Early Universe

R. Branden- berger

Cosmology Space-time dynamical (no longer absolute like in

19 / 68 Space-Time as Described by General Relativity

Early Universe

R. Branden- berger

Cosmology Space-time dynamical (no longer absolute like in

19 / 68 The Expanding Universe

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

20 / 68 Evidence for the Expansion of Space

Early Universe The Hubble diagram for type Ia supernovae. R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

Kirshner R P PNAS 2004;101:8-13

Early Universe

R. Branden- berger Standard Big Bang Cosmology (SBB): the old paradigm of cosmology (ca. 1960). Cosmology

Framework Space-Time The SBB is based on: Std. Cosmology Inﬂation Cosmological principle: universe homogeneous and String gas isotropic on large scales. Conclusions General Relativity governing dynamics of space-time. Classical matter as source in the Einstein equations. Classical matter: cold (pressure-less) matter (describing the galaxies) + radiation(describing the CMB).

22 / 68 Standard Big Bang Cosmology

Early Universe

R. Branden- berger Standard Big Bang Cosmology (SBB): the old paradigm of cosmology (ca. 1960). Cosmology

22 / 68 Standard Big Bang Cosmology

Early Universe

R. Branden- berger Standard Big Bang Cosmology (SBB): the old paradigm of cosmology (ca. 1960). Cosmology

22 / 68 Standard Big Bang Cosmology

Early Universe

R. Branden- berger Standard Big Bang Cosmology (SBB): the old paradigm of cosmology (ca. 1960). Cosmology

22 / 68 Standard Big Bang Cosmology

Early Universe

R. Branden- berger Standard Big Bang Cosmology (SBB): the old paradigm of cosmology (ca. 1960). Cosmology

22 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger The universe is expanding now. Cosmology In the past it was hotter and more dense. Framework Space-Time Thus, it was expanding faster in the past. Std. Cosmology

Inflation At a finite time in the past the temperature was infinite.

String gas A ﬁnite box of space had zero size at that time. Conclusions This is the Big Bang!

What is the Big Bang? What was before the Big Bang?

To be taken seriously a theory must have made successful observational predictions.

23 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger The universe is expanding now. Cosmology In the past it was hotter and more dense. Framework Space-Time Thus, it was expanding faster in the past. Std. Cosmology

Inflation At a finite time in the past the temperature was infinite.

String gas A ﬁnite box of space had zero size at that time. Conclusions This is the Big Bang!

What is the Big Bang? What was before the Big Bang?

To be taken seriously a theory must have made successful observational predictions.

23 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger The universe is expanding now. Cosmology In the past it was hotter and more dense. Framework Space-Time Thus, it was expanding faster in the past. Std. Cosmology

Inflation At a finite time in the past the temperature was infinite.

String gas A ﬁnite box of space had zero size at that time. Conclusions This is the Big Bang!

What is the Big Bang? What was before the Big Bang?

To be taken seriously a theory must have made successful observational predictions.

23 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger The universe is expanding now. Cosmology In the past it was hotter and more dense. Framework Space-Time Thus, it was expanding faster in the past. Std. Cosmology

Inflation At a finite time in the past the temperature was infinite .

String gas A ﬁnite box of space had zero size at that time. Conclusions This is the Big Bang!

What is the Big Bang? What was before the Big Bang?

To be taken seriously a theory must have made successful observational predictions.

23 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger The universe is expanding now. Cosmology In the past it was hotter and more dense. Framework Space-Time Thus, it was expanding faster in the past. Std. Cosmology

Inflation At a finite time in the past the temperature was infinite .

String gas A ﬁnite box of space had zero size at that time. Conclusions This is the Big Bang!

What is the Big Bang? What was before the Big Bang?

To be taken seriously a theory must have made successful observational predictions.

23 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger The universe is expanding now. Cosmology In the past it was hotter and more dense. Framework Space-Time Thus, it was expanding faster in the past. Std. Cosmology

Inflation At a finite time in the past the temperature was infinite .

String gas A ﬁnite box of space had zero size at that time. Conclusions This is the Big Bang!

What is the Big Bang? What was before the Big Bang?

To be taken seriously a theory must have made successful observational predictions.

23 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger The universe is expanding now. Cosmology In the past it was hotter and more dense. Framework Space-Time Thus, it was expanding faster in the past. Std. Cosmology

Inflation At a finite time in the past the temperature was infinite .

String gas A ﬁnite box of space had zero size at that time. Conclusions This is the Big Bang!

What is the Big Bang? What was before the Big Bang?

To be taken seriously a theory must have made successful observational predictions.

23 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger The universe is expanding now. Cosmology In the past it was hotter and more dense. Framework Space-Time Thus, it was expanding faster in the past. Std. Cosmology

Inflation At a finite time in the past the temperature was infinite .

String gas A ﬁnite box of space had zero size at that time. Conclusions This is the Big Bang!

What is the Big Bang? What was before the Big Bang?

To be taken seriously a theory must have made successful observational predictions.

23 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger The universe is expanding now. Cosmology In the past it was hotter and more dense. Framework Space-Time Thus, it was expanding faster in the past. Std. Cosmology

Inflation At a finite time in the past the temperature was infinite .

String gas A ﬁnite box of space had zero size at that time. Conclusions This is the Big Bang!

What is the Big Bang? What was before the Big Bang?

To be taken seriously a theory must have made successful observational predictions.

23 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger Universe begins as a homogeneous and very hot

Cosmology ﬁreball. Framework Initially radiation dominates: hot plasma. Space-Time Std. Cosmology Space expands and matter cools. Inﬂation

String gas After about 30,000 years cold matter starts to dominate. Conclusions After about 300,000 years atoms (hydrogen) forms and universe becomes transparent to light Now the age of the universe is about 13 billion years.

Prediction: Existence and black body nature of the Cosmic Microwave Background.

24 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger Universe begins as a homogeneous and very hot

Cosmology ﬁreball. Framework Initially radiation dominates: hot plasma. Space-Time Std. Cosmology Space expands and matter cools. Inﬂation

Prediction: Existence and black body nature of the Cosmic Microwave Background.

24 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger Universe begins as a homogeneous and very hot

Cosmology ﬁreball. Framework Initially radiation dominates: hot plasma. Space-Time Std. Cosmology Space expands and matter cools. Inﬂation

Prediction: Existence and black body nature of the Cosmic Microwave Background.

24 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger Universe begins as a homogeneous and very hot

Cosmology ﬁreball. Framework Initially radiation dominates: hot plasma. Space-Time Std. Cosmology Space expands and matter cools. Inﬂation

Prediction: Existence and black body nature of the Cosmic Microwave Background.

24 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger Universe begins as a homogeneous and very hot

Cosmology ﬁreball. Framework Initially radiation dominates: hot plasma. Space-Time Std. Cosmology Space expands and matter cools. Inﬂation

Prediction: Existence and black body nature of the Cosmic Microwave Background.

24 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger Universe begins as a homogeneous and very hot

Cosmology ﬁreball. Framework Initially radiation dominates: hot plasma. Space-Time Std. Cosmology Space expands and matter cools. Inﬂation

Prediction: Existence and black body nature of the Cosmic Microwave Background.

24 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger Universe begins as a homogeneous and very hot

Cosmology ﬁreball. Framework Initially radiation dominates: hot plasma. Space-Time Std. Cosmology Space expands and matter cools. Inﬂation

Prediction: Existence and black body nature of the Cosmic Microwave Background.

24 / 68 Standard Big Bang Cosmology (ctd.)

Early Universe

R. Branden- berger Universe begins as a homogeneous and very hot

Cosmology ﬁreball. Framework Initially radiation dominates: hot plasma. Space-Time Std. Cosmology Space expands and matter cools. Inﬂation

Prediction: Existence and black body nature of the Cosmic Microwave Background.

24 / 68 Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

Credit: NASA/WMAP Science Team

25 / 68 Spectrometer

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

26 / 68 Successes of the SBB Model

Early Universe Key success: Existence and black body nature of the CMB. R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

27 / 68 Unanswered Questions

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology Inﬂation What is the Big Bang? String gas What was before the Big Bang? Conclusions

28 / 68 Conceptual Problems of the SBB Model

Early Universe No explanation for the homogeneity, spatial ﬂatness and R. Branden- berger large size and entropy of the universe.

Cosmology Horizon problem of the SBB:

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

t 0

l (t) p

t rec

l f (t) 0 x

29 / 68 Conceptual Problems of the SBB Model II

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology No explanation of the observed inhomogeneities in the Inﬂation distribution of matter and anisotropies in the Cosmic String gas

Conclusions Microwave Background possible!

30 / 68 What to do?

Early Universe

R. Branden- berger With a little help from a friend , the particle physicist:

Cosmology At very high temperatures close to the Big Bang Framework classical physics breaks down - and quantum Space-Time Std. Cosmology mechanics and particle physics give the right Inflation description of matter. String gas → Standard Big Bang theory breaks down. Conclusions In the very early universe matter is a plasma of elementary particles. All described in terms of quantum fields. Quantum field (scalar fields) can lead to a different expansion rate of space namely inflationary expansion.

31 / 68 What to do?

Early Universe

R. Branden- berger With a little help from a friend , the particle physicist:

31 / 68 What to do?

Early Universe

R. Branden- berger With a little help from a friend , the particle physicist:

31 / 68 What to do?

Early Universe

R. Branden- berger With a little help from a friend , the particle physicist:

31 / 68 What to do?

Early Universe

R. Branden- berger With a little help from a friend , the particle physicist:

31 / 68 What to do?

Early Universe

R. Branden- berger With a little help from a friend , the particle physicist:

31 / 68 What to do?

Early Universe

R. Branden- berger With a little help from a friend , the particle physicist:

31 / 68 What to do?

Early Universe

R. Branden- berger With a little help from a friend , the particle physicist:

31 / 68 What to do?

Early Universe

R. Branden- berger With a little help from a friend , the particle physicist:

31 / 68 Plan

Early Universe

R. Branden- berger 1 What is Cosmology? Cosmology Framework 2 Space-Time Framework Std. Cosmology Space-Time Inﬂation Standard Big Bang Cosmology String gas

Conclusions 3 Inﬂationary Cosmology

4 String Cosmology

5 Conclusions

32 / 68 Time line of inﬂationary cosmology

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

ti : inﬂation begins

tR: inﬂation ends, reheating

33 / 68 Successes of Inﬂationary Cosmology

Early Universe

R. Branden- berger The Inﬂationary Universe Scenario is the current paradigm

Cosmology of early universe cosmology (1980). Framework Space-Time Std. Cosmology Successes: Inﬂation

String gas Solves horizon problem Conclusions Solves ﬂatness problem Solves size/entropy problem Provides a causal mechanism of generating primordial cosmological perturbations (Chibisov & Mukhanov, 1981).

34 / 68 Successes of Inﬂationary Cosmology

Early Universe

R. Branden- berger The Inﬂationary Universe Scenario is the current paradigm

Cosmology of early universe cosmology (1980). Framework Space-Time Std. Cosmology Successes: Inﬂation

34 / 68 Successes of Inﬂationary Cosmology

Early Universe

R. Branden- berger The Inﬂationary Universe Scenario is the current paradigm

Cosmology of early universe cosmology (1980). Framework Space-Time Std. Cosmology Successes: Inﬂation

34 / 68 Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

Credit: NASA/WMAP Science Team

35 / 68 Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

Credit: NASA/WMAP Science Team

36 / 68 Review of Inﬂationary Cosmology

Early Universe

R. Branden- berger

Cosmology Context: Framework Space-Time General Relativity Std. Cosmology

Inflation Scalar Field Matter String gas Inflation: Conclusions phase with exponential expansion of space requires matter with negative pressure requires a slowly rolling scalar field ϕ

37 / 68 Review of Inﬂationary Cosmology

Early Universe

R. Branden- berger

Cosmology Context: Framework Space-Time General Relativity Std. Cosmology

Inflation Scalar Field Matter String gas Inflation: Conclusions phase with exponential expansion of space requires matter with negative pressure requires a slowly rolling scalar field ϕ

37 / 68 Review of Inﬂationary Cosmology

Early Universe

R. Branden- berger

Cosmology Context: Framework Space-Time General Relativity Std. Cosmology

Inflation Scalar Field Matter String gas Inflation: Conclusions phase with exponential expansion of space requires matter with negative pressure requires a slowly rolling scalar field ϕ

37 / 68 Review of Inﬂationary Cosmology

Early Universe

R. Branden- berger

Cosmology Context: Framework Space-Time General Relativity Std. Cosmology

Inflation Scalar Field Matter String gas Inflation: Conclusions phase with exponential expansion of space requires matter with negative pressure requires a slowly rolling scalar field ϕ

37 / 68 Review of Inﬂationary Cosmology II

Early Universe Space-time sketch of inﬂationary cosmology: R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

Note: a˙ H = a curve labelled by k: wavelength of a ﬂuctuation 38 / 68 Successes of Inﬂation

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time inflation renders the universe large, homogeneous and Std. Cosmology spatially flat Inflation String gas classical matter redshifts → matter vacuum remains Conclusions quantum vacuum fluctuations: seeds for the observed structure [Chibisov & Mukhanov, 1981]

39 / 68 Status of the Big Bang in Inﬂationary Cosmology

Early Universe

R. Branden- berger The inﬂationary phase had a beginning. Cosmology

Framework There was a Big Bang before the period of inﬂation. Space-Time Std. Cosmology Inﬂation Unanswered questions: String gas Conclusions What is the Big Bang? What was before the Big Bang?

Note: quantum ﬁeld theory is not applicable very close to the singularity.

40 / 68 Status of the Big Bang in Inﬂationary Cosmology

Early Universe

R. Branden- berger The inﬂationary phase had a beginning. Cosmology

Framework There was a Big Bang before the period of inﬂation. Space-Time Std. Cosmology Inﬂation Unanswered questions: String gas Conclusions What is the Big Bang? What was before the Big Bang?

Note: quantum ﬁeld theory is not applicable very close to the singularity.

40 / 68 Status of the Big Bang in Inﬂationary Cosmology

Early Universe

R. Branden- berger The inﬂationary phase had a beginning. Cosmology

Framework There was a Big Bang before the period of inﬂation. Space-Time Std. Cosmology Inﬂation Unanswered questions: String gas Conclusions What is the Big Bang? What was before the Big Bang?

Note: quantum ﬁeld theory is not applicable very close to the singularity.

40 / 68 Challenges for the Current Paradigm

Early Universe

R. Branden- berger In spite of the phenomenological successes, the

Cosmology inﬂationary scenario suffers from several conceptual Framework problems. Space-Time Std. Cosmology In light of these problems we need to look for input from Inﬂation new fundamental physics to construct a new theory String gas which will overcome these problems. Conclusions Question: Can Superstring theory lead to a new and improved paradigm? Question: Can this new paradigm be tested in cosmological observations? Question: Was there a Big Bang ?

41 / 68 Challenges for the Current Paradigm

Early Universe

R. Branden- berger In spite of the phenomenological successes, the

41 / 68 Challenges for the Current Paradigm

Early Universe

R. Branden- berger In spite of the phenomenological successes, the

41 / 68 Challenges for the Current Paradigm

Early Universe

R. Branden- berger In spite of the phenomenological successes, the

41 / 68 Challenges for the Current Paradigm

Early Universe

R. Branden- berger In spite of the phenomenological successes, the

41 / 68 Conceptual Problems of Inﬂationary Cosmology

Early Universe

R. Branden- berger

Cosmology Framework What is the scalar field? Space-Time Std. Cosmology Why does it have the special conditions to obtain Inflation inflation? String gas

Conclusions Trans-Planckian problem Singularity problem Applicability of General Relativity

42 / 68 Trans-Planckian Problem

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

Success of inflation: At early times scales are inside the Hubble radius → causal generation mechanism is possible. Problem: If time period of inflation is slightly more than the minimal length it must have, then the wavelength is smaller than the Planck length at the beginning of inflation 43 / 68 → new physics MUST enter into the calculation of the fluctuations. Singularity Problem

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Standard cosmology: Penrose-Hawking theorems → Std. Cosmology

Inflation initial singularity → incompleteness of the theory. String gas Inflationary cosmology: In scalar field-driven Conclusions inflationary models the initial singularity persists [Borde and Vilenkin] → incompleteness of the theory.

44 / 68 Singularity Problem

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Standard cosmology: Penrose-Hawking theorems → Std. Cosmology

44 / 68 Singularity Problem

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Standard cosmology: Penrose-Hawking theorems → Std. Cosmology

44 / 68 Applicability of GR

Early Universe

R. Branden- berger

Cosmology Framework Einstein’s theory breaks down at extremely high Space-Time Std. Cosmology densities. Inflation In models of inflation, the energy scale of at which String gas inflation takes place is close to the limiting scale for the Conclusions validity of Einstein’s theory. We cannot trust the predictions made using GR.

45 / 68 Applicability of GR

Early Universe

R. Branden- berger

45 / 68 Applicability of GR

Early Universe

R. Branden- berger

45 / 68 Zones of Ignorance

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

46 / 68 Message I

Early Universe

R. Branden- berger The current cosmological paradigm has serious Cosmology conceptual problems. Framework Space-Time We need a new paradigm of very early universe Std. Cosmology

Inﬂation cosmology. String gas With a little help from a friend - the string theorist! Conclusions New cosmological model motivated by superstring theory: 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].

47 / 68 Message I

Early Universe

R. Branden- berger The current cosmological paradigm has serious Cosmology conceptual problems. Framework Space-Time We need a new paradigm of very early universe Std. Cosmology

47 / 68 Message I

Early Universe

R. Branden- berger The current cosmological paradigm has serious Cosmology conceptual problems. Framework Space-Time We need a new paradigm of very early universe Std. Cosmology

47 / 68 Message I

Early Universe

R. Branden- berger The current cosmological paradigm has serious Cosmology conceptual problems. Framework Space-Time We need a new paradigm of very early universe Std. Cosmology

47 / 68 Message I

Early Universe

R. Branden- berger The current cosmological paradigm has serious Cosmology conceptual problems. Framework Space-Time We need a new paradigm of very early universe Std. Cosmology

47 / 68 Message II

Early Universe

R. Branden- berger String Gas Cosmology makes testable predictions for Cosmology cosmological observations Framework Space-Time Std. Cosmology Blue tilt in the spectrum of gravitational waves [R.B., A. Inﬂation Nayeri, S. Patil and C. Vafa, 2006] String gas Line discontinuities in CMB anisotropy maps [N. Kaiser Conclusions and A. Stebbins, 1984] Line discontinuities can be detected using the CANNY edge detection algorithm [S. Amsel, J. Berger and R.B., 2007, R. Danos and R.B., 2008, 2009]

48 / 68 Message II

Early Universe

48 / 68 Message II

Early Universe

48 / 68 Plan

Early Universe

R. Branden- berger 1 What is Cosmology? Cosmology Framework 2 Space-Time Framework Std. Cosmology Space-Time Inﬂation Standard Big Bang Cosmology String gas

Conclusions 3 Inﬂationary Cosmology

4 String Cosmology

5 Conclusions

49 / 68 What is String Theory?

Early Universe

R. Branden- berger String theory is a quantum theory of all forces of nature Cosmology including gravity. Framework Space-Time String theory uniﬁes all forces of nature. Std. Cosmology

Inﬂation Basic objects: elementary strings. Compared to String gas elementary point particles. Conclusions String theory is mathematically consistent only in 10 space-time dimensions. Thus, string theory predicts extra spatial dimensions.

Note: string theory is “in development".

50 / 68 What is String Theory?

Early Universe

R. Branden- berger String theory is a quantum theory of all forces of nature Cosmology including gravity. Framework Space-Time String theory uniﬁes all forces of nature. Std. Cosmology

Note: string theory is “in development".

50 / 68 What is String Theory?

Early Universe

R. Branden- berger String theory is a quantum theory of all forces of nature Cosmology including gravity. Framework Space-Time String theory uniﬁes all forces of nature. Std. Cosmology

Note: string theory is “in development".

50 / 68 What is String Theory?

Early Universe

R. Branden- berger String theory is a quantum theory of all forces of nature Cosmology including gravity. Framework Space-Time String theory uniﬁes all forces of nature. Std. Cosmology

Note: string theory is “in development".

50 / 68 What is String Theory?

Early Universe

R. Branden- berger String theory is a quantum theory of all forces of nature Cosmology including gravity. Framework Space-Time String theory uniﬁes all forces of nature. Std. Cosmology

Note: string theory is “in development".

50 / 68 What is String Theory?

Early Universe

R. Branden- berger String theory is a quantum theory of all forces of nature Cosmology including gravity. Framework Space-Time String theory uniﬁes all forces of nature. Std. Cosmology

Note: string theory is “in development".

50 / 68 What is String Theory?

Early Universe

R. Branden- berger String theory is a quantum theory of all forces of nature Cosmology including gravity. Framework Space-Time String theory uniﬁes all forces of nature. Std. Cosmology

Note: string theory is “in development".

50 / 68 Principles R.B. and C. Vafa, Nucl. Phys. B316:391 (1989)

Early Universe R. Branden- Idea: make use of the new symmetries and new degrees of berger freedom which string theory provides to construct a new Cosmology theory of the very early universe. Framework Assumption: Matter is a gas of fundamental strings Space-Time Std. Cosmology Assumption: Space is compact, e.g. a torus. Inﬂation Key points: String gas Conclusions New degrees of freedom: string oscillatory modes. Leads to a maximal temperature for a gas of strings, the Hagedorn temperature. New degrees of freedom: string winding modes. Leads to a new symmetry: physics at large R is equivalent to physics at small R.

51 / 68 Principles R.B. and C. Vafa, Nucl. Phys. B316:391 (1989)

51 / 68 “Large" is Equivalent to “Small" in String Theory

Early Universe

R. Branden- berger

Cosmology Framework T-Duality Space-Time Std. Cosmology Momentum modes: En = n/R Inﬂation String gas Winding modes: Em = mR Conclusions Duality: R → 1/R (n, m) → (m, n) Mass spectrum of string states unchanged

52 / 68 Temperature in String Cosmology R.B. and C. Vafa, Nucl. Phys. B316:391 (1989)

Early Universe

R. Branden- Temperature of a box of strings in thermal equilibrium. berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

53 / 68 Temperature in Standard and Inﬂationary Cosmology

Early Universe

R. Branden- berger

Cosmology Temperature of a box of particles in thermal equilibrium. Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

54 / 68 Dynamics

Early Universe

R. Branden- berger Assume some dynamical principle gives us R(t) Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

55 / 68 String Gas Cosmology R.B. and C. Vafa, Nucl. Phys. B316:391 (1989)

Early Universe

R. Branden- berger We will thus consider the following background dynamics for Cosmology the scale factor a(t): Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

56 / 68 Dimensionality of Space in SGC

Early Universe

R. Branden- berger Begin with all 9 spatial dimensions small, initial temperature close to T → winding modes about all Cosmology H spatial sections are excited. Framework Space-Time Std. Cosmology Expansion of any one spatial dimension requires the Inﬂation annihilation of the winding modes in that dimension. String gas

Conclusions

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

57 / 68 Dimensionality of Space in SGC

Early Universe

Conclusions

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

57 / 68 Dimensionality of Space in SGC

Early Universe

Conclusions

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

57 / 68 Structure formation in inﬂationary cosmology

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

N.B. Perturbations originate as quantum vacuum ﬂuctuations.

58 / 68 Background for string gas cosmology

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

59 / 68 Structure formation in string gas cosmology A. Nayeri, R.B. and C. Vafa, Phys. Rev. Lett. 97:021302 (2006)

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

N.B. Perturbations originate as thermal string gas ﬂuctuations. 60 / 68 Power spectrum of cosmological ﬂuctuations

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology Key features: Inflation scale-invariant like for inflation String gas Conclusions slight red tilt like for inflation

61 / 68 Anisotropies in the Cosmic Microwave Background (CMB)

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

Credit: NASA/WMAP Science Team 62 / 68 Quantiﬁcation of the CMB data

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology

Inﬂation

String gas

Conclusions

Credit: NASA/WMAP Science Team

63 / 68 Spectrum of Gravitational Waves

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time Std. Cosmology Key features: Inflation scale-invariant (like for inflation) String gas Conclusions slight blue tilt (unlike for inflation)

64 / 68 Status of the “Big Bang" in String Gas Cosmology

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time The universe was very, very hot and dense 13 billion Std. Cosmology years ago. Inﬂation

String gas In this sense there was a hot “primordial" ﬁreball. Conclusions But: there was no Big Bang Singularity. There was no beginning of time.

65 / 68 Status of the “Big Bang" in String Gas Cosmology

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time The universe was very, very hot and dense 13 billion Std. Cosmology years ago. Inﬂation

String gas In this sense there was a hot “primordial" ﬁreball. Conclusions But: there was no Big Bang Singularity. There was no beginning of time.

65 / 68 Status of the “Big Bang" in String Gas Cosmology

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time The universe was very, very hot and dense 13 billion Std. Cosmology years ago. Inﬂation

String gas In this sense there was a hot “primordial" ﬁreball. Conclusions But: there was no Big Bang Singularity. There was no beginning of time.

65 / 68 Status of the “Big Bang" in String Gas Cosmology

Early Universe

R. Branden- berger

Cosmology

Framework Space-Time The universe was very, very hot and dense 13 billion Std. Cosmology years ago. Inﬂation

String gas In this sense there was a hot “primordial" ﬁreball. Conclusions But: there was no Big Bang Singularity. There was no beginning of time.

65 / 68 Plan

Early Universe

R. Branden- berger 1 What is Cosmology? Cosmology Framework 2 Space-Time Framework Std. Cosmology Space-Time Inﬂation Standard Big Bang Cosmology String gas

Conclusions 3 Inﬂationary Cosmology

4 String Cosmology

5 Conclusions

66 / 68 Conclusions

Early Universe Cosmology is a vibrant ﬁeld with lots of observational R. Branden- berger data. Paradigms of early universe cosmology have been Cosmology developed. Framework Space-Time Paradigm 1: Standard Big Bang Model. Std. Cosmology

Inﬂation Paradigm 2: Inﬂationary Universe scenario - current

String gas paradigm. Conclusions In both Paradigms 1 and 2 there was a Big Bang singularity. Paradigm 2 has conceptual problems → motivates the search for an improved paradigm. Superstring theory may provide a new paradigm. Superstring cosmology may resolve the Big Bang singularity. It is possible to observationally probe string cosmology.

67 / 68 Conclusions

Inﬂation Paradigm 2: Inﬂationary Universe scenario - current

67 / 68 Conclusions

Inﬂation Paradigm 2: Inﬂationary Universe scenario - current

67 / 68 Conclusions

Inﬂation Paradigm 2: Inﬂationary Universe scenario - current

67 / 68 Conclusions

Inﬂation Paradigm 2: Inﬂationary Universe scenario - current

67 / 68 Conclusions

Inﬂation Paradigm 2: Inﬂationary Universe scenario - current

67 / 68 Conclusions

Inﬂation Paradigm 2: Inﬂationary Universe scenario - current

67 / 68 Conclusions

Inﬂation Paradigm 2: Inﬂationary Universe scenario - current

67 / 68 Conclusions

Inﬂation Paradigm 2: Inﬂationary Universe scenario - current

67 / 68 Status of the “Big Bang"

Early Universe We know that going back in time 13 billion years there R. Branden- berger was a very hot early phase, a primordial ﬁreball.

Cosmology If this is what you mean by “Big Bang": then there WAS

Framework a “Big Bang". Space-Time Std. Cosmology We do not know if there was a “Big Bang singularity", a Inﬂation beginning of time. String gas Our current paradigms of early universe cosmology Conclusions predict a beginning of time. But only if we extrapolate the models beyond where they can be used. Superstring theory may lead to a cosmology without a beginning of time. If this is true then there may not have been a “Big Bang" (singularity).

68 / 68