Inflation and string cosmology

Июль 28, 2022

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Inflation and string cosmology

Содержание

2. Contents: From the Big Bang theory to Inflationary Cosmology Eternal inflation and string theory landscape
3. Two major cosmological discoveries: The new-born universe experienced rapid acceleration (inflation) A new (slow) stage of
4. Closed, open or flat universe Closed universe. Parallel lines intersect Open universe. Parallel lines diverge Flat
5. Big Bang Theory acceleration closed flat open If vacuum has positive energy density (dark energy), the
6. Inflationary Universe Inflation is an extremely rapid acceleration in the universe soon after its creation.
7. Inflation Starobinsky, 1980 – modified gravity, R + R2 a complicated but almost working model Guth,
8. What was before the Big Bang? Why is our universe so homogeneous (better than 1 part
9. Where did the energy come from? Some basic facts: 1) Energy of matter in the universe
10. Energy of matter in the Big Bang theory According to the Big Bang theory, the total
11. solves many problems of the old Big Bang theory, and explains how the whole universe could
12. Inflation as a theory of a harmonic oscillator Eternal Inflation
13. Einstein equation: Klein-Gordon equation: Equations of motion: Compare with equation for the harmonic oscillator with friction:
14. Logic of Inflation: Large φ large H large friction field φ moves very slowly, so that
15. Inflation makes the universe flat, homogeneous and isotropic In this simple model the universe typically grows
16. Quantum fluctuations produced during inflation φ x Small quantum fluctuations of all physical fields exist everywhere.
17. φ x When expansion of the universe continues, new quantum fluctuations become stretched, stop oscillating, and
18. φ x This process continues, and eventually the universe becomes populated by inhomogeneous scalar field. Its
19. WMAP5 + Acbar + Boomerang + CBI
20. Observations
21. WMAP and the temperature of the sky
22. This is a photographic image of quantum fluctuations blown up to the size of the universe
23. On a much, much larger scale… Inflationary multiverse
24. Predictions of Inflation: 1) The universe should be homogeneous, isotropic and flat, Ω = 1 +
25. Big Bang Earth Astronomers use our universe as a “time machine”. By looking at the stars
26. Big Bang Earth The light from distant galaxies travel to us for billions of years, so
27. Big Bang Earth Looking even further, we can detect photons emitted 400000 years after the Big
28. Big Bang Earth Inflationary theory tells us that this cosmic fire was created not at the
29. Big Bang Inflation If we look there very carefully, we will see small perturbations of space,
30. From the Universe to the Multiverse In realistic theories of elementary particles there are many scalar
31. Genetic code of the Universe There may be one fundamental law of physics, like a single
32. In string theory, genetic code is written in the properties of compactification of extra dimensions Up
33. String Theory Landscape Perhaps 10100 - 101000 different minima in string theory
34. Kandinsky Universe
35. Landscape of eternal inflation
36. Self-reproducing Inflationary Universe Big Bang ? We live here
37. "It is said that there is no such thing as a free lunch. But the universe
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Contents:
From the Big Bang theory to Inflationary Cosmology
Eternal inflation and

string theory landscape

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Two major cosmological discoveries:
The new-born universe experienced rapid acceleration

(inflation)
A new (slow) stage of acceleration started 5 billion years ago (dark energy)

How did it start, and how it is going to end?

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Closed, open or flat universe
Closed universe. Parallel lines intersect
Open universe.

Parallel lines diverge

Flat universe. Parallel lines remain parallel, but the distance between them grow with time

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Big Bang Theory
acceleration
closed
flat
open
If vacuum has positive energy density (dark energy),

the universe may accelerate, as it is shown on the upper curve. Such universe may not collapse even if it is closed.

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Inflationary Universe
Inflation is an extremely rapid acceleration in the universe

soon after its creation.

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Inflation
Starobinsky, 1980 – modified gravity, R + R2 a complicated

but almost working model

Guth, 1981 - old inflation (inflation in a false vacuum)

1983 - chaotic inflation

1991 - hybrid inflation

A.L., 1982 - new inflation

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What was before the Big Bang?
Why is our universe so homogeneous

(better than 1 part in 10000) ?
Why is it isotropic (the same in all directions)?
Why all of its parts started expanding simultaneously?
Why is it flat? Why parallel lines do not intersect? Why it contains so many particles?

Inflation was invented in an attempt to answer almost metaphysical questions:

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Where did the energy come from?
Some basic facts:
1) Energy

of matter in the universe IS NOT CONSERVED: dE = -p dV
Volume V of an expanding universe grows, so its energy decreases if pressure p is positive.
2) Total energy of matter and of gravity (related to the shape and the volume of the universe) is conserved, but this conservation is somewhat unusual:

The sum of the energy of matter and of the gravitational energy is equal to zero

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Energy of matter in the Big Bang theory
According to the Big

Bang theory, the total mass of matter soon after the Big Bang was greater than 1080 ton

Before the Big Bang there was NOTHING, and then suddenly we got A HUGE AMOUNT OF ENERGY
Where did it come from?

To create our universe we would need more than 1080 tons of high tech explosive compressed to a size of 1cm, and exploded simultaneously, with accuracy 10-43 s.

Mass = Energy: E = mc2

Who could do it?…

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solves many problems of the old Big Bang theory, and explains

how the whole universe could be created from less than a milligram of matter

Inflationary theory

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Inflation as a theory of a harmonic oscillator
Eternal Inflation

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Einstein equation:
Klein-Gordon equation:
Equations of motion:
Compare with equation for the harmonic oscillator

with friction:

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Logic of Inflation:
Large φ
large H
large friction
field φ moves

very slowly, so that its potential energy for a long time remains nearly constant

This is the stage of inflation

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Inflation makes the universe flat, homogeneous and isotropic
In this simple model

the universe typically grows 101000000000000 times during inflation.
Now we can see just a tiny part of the universe of size ct = 1010 light yrs. That is why the universe looks homogeneous, isotropic, and flat.

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Quantum fluctuations produced during inflation
φ
x
Small quantum fluctuations of all physical

fields exist everywhere. They are similar to waves, which appear and then rapidly oscillate, move and disappear. Inflation stretched them, together with stretching the universe. When the wavelength of the fluctuations becomes sufficiently large, they stop moving and oscillating, and do not disappear. They look like frozen waves.

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φ
x
When expansion of the universe continues, new quantum fluctuations become stretched,

stop oscillating, and freeze on top of the previously frozen fluctuations.

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φ
x
This process continues, and eventually the universe becomes populated by inhomogeneous

scalar field. Its energy takes different values in different parts of the universe. These inhomogeneities are responsible for the formation of galaxies.

Sometimes these fluctuations are so large that they can increase the value of the scalar field in some parts of the universe. Then inflation in these parts of the universe occurs again and again. In other words, the process of inflation becomes eternal.
We will illustrate it now by computer simulation of this process.

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WMAP5 + Acbar + Boomerang + CBI

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Observations

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WMAP and the temperature of the sky

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This is a photographic image of quantum fluctuations blown up to

the size of the universe

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On a much, much larger scale…
Inflationary multiverse

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Predictions of Inflation:
1) The universe should be homogeneous, isotropic and flat,

Ω = 1 + O(10-4) [Ω=ρ/ρ0]
Observations: the universe is homogeneous, isotropic and flat, Ω = 1 + O(10-2)
Inflationary perturbations should be gaussian and adiabatic, with flat spectrum, ns = 1+ O(10-1)
Observations: perturbations are gaussian and adiabatic, with flat spectrum, ns = 1 + O(10-2)

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Big Bang
Earth
Astronomers use our universe as a “time machine”. By looking

at the stars close to us, we see them as they were several hundreds years ago.

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Big Bang
Earth
The light from distant galaxies travel to us for billions

of years, so we see them in the form they had billions of years ago.

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Big Bang
Earth
Looking even further, we can detect photons emitted 400000 years

after the Big Bang. But 30 years ago everyone believed that there is nothing beyond the cosmic fire created in the Big Bang at the time t = 0.

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Big Bang
Earth
Inflationary theory tells us that this cosmic fire was created

not at the time t = 0, but after inflation. If we look beyond the circle of fire surrounding us, we will see enormously large empty space filled only by a scalar field.

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Big Bang
Inflation
If we look there very carefully, we will see small

perturbations of space, which are responsible for galaxy formation. And if we look even further, we will see how new parts of inflationary universe are created by quantum fluctuations.

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From the Universe to the Multiverse
In realistic theories of elementary particles

there are many scalar fields, and their potential energy has many different minima. Each minimum corresponds to different masses of particles and different laws of their interactions.

Quantum fluctuations during eternal inflation can bring the scalar fields to different minima in different exponentially large parts of the universe. The universe becomes divided into many exponentially large parts with different laws of physics operating in each of them. (In our computer simulations we will show them by using different colors.)

SU(5)

SU(3)xSU(2)xU(1)

SU(4)xU(1)

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Genetic code of the Universe
There may be one fundamental law

of physics, like a single genetic code for the whole Universe. However, this law may have different realizations. For example, water can be liquid, solid or gas. In elementary particle physics, the effective laws of physics depend on the values of the scalar fields.

Quantum fluctuations during inflation can take the scalar fields from one minimum of their potential energy to another, altering its genetic code. Once it happens in a small part of the universe, inflation makes this part exponentially big.

This is the cosmological mutation mechanism

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In string theory, genetic code is written in the properties of

compactification of extra dimensions

Up to 10500 different combinations

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String Theory Landscape
Perhaps 10100 - 101000 different minima in

string theory

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Kandinsky Universe

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Landscape of eternal inflation

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Self-reproducing Inflationary Universe
Big Bang ?
We live here

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"It is said that there is no such thing as

a free lunch. But the universe is the ultimate free lunch".
Alan Guth

Now we know that the universe is not just a free lunch: It is an eternal feast were ALL possible types of dishes are served.

Inflation and string cosmology

Содержание

Contents:From the Big Bang theory to Inflationary CosmologyEternal inflation and

Two major cosmological discoveries: The new-born universe experienced rapid acceleration

Closed, open or flat universeClosed universe. Parallel lines intersectOpen universe.

Big Bang TheoryaccelerationclosedflatopenIf vacuum has positive energy density (dark energy),

Inflationary UniverseInflation is an extremely rapid acceleration in the universe

InflationStarobinsky, 1980 – modified gravity, R + R2 a complicated

What was before the Big Bang?Why is our universe so homogeneous

Where did the energy come from?Some basic facts: 1) Energy

Energy of matter in the Big Bang theoryAccording to the Big

solves many problems of the old Big Bang theory, and explains

Inflation as a theory of a harmonic oscillatorEternal Inflation

Einstein equation:Klein-Gordon equation:Equations of motion:Compare with equation for the harmonic oscillator

Logic of Inflation:Large φ large H large frictionfield φ moves

Inflation makes the universe flat, homogeneous and isotropicIn this simple model

Quantum fluctuations produced during inflationφxSmall quantum fluctuations of all physical

φxWhen expansion of the universe continues, new quantum fluctuations become stretched,

φxThis process continues, and eventually the universe becomes populated by inhomogeneous