Cosmological Models

John O’Byrne School of Physics University of Sydney

Using diagrams and pp slides from Seeds Foundations of Astronomy and the Supernova Cosmology Project http://www-supernova.lbl.gov

Observation: Isotropy: On the largest scales, the local universe looks the same in any direction that one observes. Either: We occupy a special place in the universe (violating the Location Principle) or: On the largest scales, the universe has the same physical properties everywhere (Homogeneity)

We adopt the latter as a fundamental assumption. This is the basis of Modern Cosmology The Cosmological Principle

To this we usually add Universality: The laws of physics are the same everywhere in the universe.

1 The Anthropic Principle

Notes that the universe is fine-tuned to our existence Fine-tuning …. •Strength of gravity •Smoothness of the Big Bang •Masses of sub-atomic particles •Strength of the strong nuclear force •Magnitude of the Cosmological Constant

Controversial - Is it just an easy way out of difficult questions?

Explanations? •Chance •Theory of Everything •The Multiverse

Cosmology and General Relativity

The basis of any theory of cosmology is General Relativity. The equations of General Relativity permit a variety of different solutions - i.e. a variety of different structures and different “histories” of the universe

Expanding, contracting and static universes, plus many combinations of these possibilities.

2 Observation: Hubble’s Law

Distant galaxies are receding from us with a speed proportional to distance - defined by the Hubble Constant

Redshift

What we actually observe is Redshift (z)

1+ z = observed emitted …caused by the expansion of space

R 1+ z = when observed Rwhen emitted where R is a scale factor

3 The Expanding Universe On large scales, galaxies are moving apart, with velocity proportional to distance. It’s not galaxies moving through space. Space is expanding, carrying the galaxies along!

The galaxies themselves are not expanding!

Redshift

Redshift (z) is a Cosmological redshift and NOT a Doppler redshift It is NOT a velocity of galaxies through space and is NOT governed by Special Relativity

Interpretation as a Doppler shift would make us a special centre of expansion and violate the location principle

Conversion of observed redshift (except small values) to velocities or distances requires a particular model of the universe to be assumed

4 The Necessity of a Big Bang

If galaxies are moving away from each other with a speed proportional to distance, there must have been a beginning, when everything was concentrated:

The Big Bang!

?

Evidence for a Big Bang

1. The expansion of the universe 2. The cosmic microwave background 3. The abundance of the light elements

5 Looking Back Towards the Early Universe

The more distant the objects we observe, the further back into the past of the universe we are looking.

The Cosmic Background Radiation

The radiation from the very early phase of the universe is detectable today as the Cosmic Microwave Background

Blackbody radiation with a temperature of T = 2.73 K

6 Abundance of Light Elements

Helium

Model Universes Current rate of expansion - given by the “Maximum” Hubble constant age of the H universe: 0

~ 1/H0 Size scale of the Universe

Time

H ~ 72 km/s/Mpc (±10%)

7 Traditional Model Universes

< c => universe will expand forever

> c => Universe will collapse back = c Size scale of the Universe

Time

If the density of matter/energy equaled the critical density, then (in traditional models) the universe would be on the border between collapse and expanding forever Also, the geometry of the universe would be flat! Meaning?

Shape and Geometry of the Universe Take a 2-dimensional analogy:

How can a 2-D creature investigate the geometry of the sphere?

Measure curvature of its space!

k = 0 (zero curvature)

k = +1 k = -1 (positive curvature) (negative curvature)

8 Cosmological Parameters

H - Hubble parameter (in km/s/Mpc) k - spatial curvature

R(t) - scale size R(t) 1 a(t) = = R 1 z a(t) - scale factor now +

pressurei wi - equation of state wi = = 0 (matter) densityi =1/3(radiation)

densityi i - density parameter i = densitycritical d(t) - deceleration parameter (q>0 for deceleration)

Confused? Various parameters are related.

Problems with the simple Big Bang

1) The flatness problem: The universe seems to be nearly flat. Why so close? Even a tiny deviation from perfect flatness at the time of the big bang should have been amplified to a huge deviation today. Extreme fine tuning required! 2) The isotropy of the cosmic background: If information can only travel through the universe at the speed of light, then structure in the cosmic background should not be correlated over large angular scales! Contradiction to almost perfect isotropy of the cosmic background!

9 Inflation • Inflation: period of sudden expansion during the very early evolution of the universe

• Perhaps triggered by the sudden energy release from the decoupling of the strong and electroweak forces

New favoured Model

Hubble Constant Ho 72 km/s/Mpc ± 10%

Cosmological density parameter o 1.02 ± 0.02

Baryon density parameter b 0.044 ± 0.004

Matter density parameter m 0.27 ± 0.04

Dark-energy density parameter 0.73 ± 0.04 Time since the Big Bang 13.7 ± 0.2 billion years Age of universe at Decoupling 379 ± 8 thousand years Redshift of the microwave background 1089 ± 1

Inflationary period at age ~ 10-35 s

10 New favoured Model

NEW favourite m = 0.3 = 0.7

Old favourite m = 1.0 = 0.0 Size scale of the Universe

Time

Measuring the Deceleration of the Universe

By observing type Ia supernovae, astronomers can measure the Hubble relation at large distances i.e. the Distance/redshift relation

It was expected that this would measure the deceleration of the universe, but …

11 The Accelerating Universe

Other evidence: Fluctuations in the Cosmic Microwave Background

Angular size of the CMB fluctuations allows us to probe the geometry of space-time! CMB fluctuations have a characteristic size of 1 degree.

12 Analysis of the Cosmic Background Fluctuations

Analyze frequency of occurrence of fluctuations on a particular angular scale

Universe has a flat geometry consistent with the new favourite model

Other evidence:Large Scale Structure

A large survey of distant galaxies shows the largest structures in the universe: Filaments and walls of galaxy superclusters, and voids of largely empty space.

- structure originating in the Cosmic Microwave Background

13 Other evidence:Large Scale Structure

The structure (technically the power spectrum) of both • the CMB, and • the distribution of galaxies

suggest that m (the density of matter) ~ 0.27

The Accelerating Universe

14 Dark Matter

• Combined mass of all “visible” matter (i.e. emitting any kind of radiation) in the universe adds up to much less than the critical density.

• Galaxy rotation curves and Gravitational lensing shows that some clusters contain 10 times as much mass as is directly visible.

• There must be DARK matter

The Nature of Dark Matter Can dark matter be composed of normal matter? • If so, then its mass would mostly come from protons and neutrons (“baryons”) • The density of baryons right after the big bang leaves a unique imprint in the abundances of deuterium and lithium.

• Density of baryonic matter is only ~ 4 % of critical density. • Most dark matter must be non-baryonic!

15 “Dark Energy”

• “negative pressure” in spacetime has a repulsive effect to explain the acceleration - has been called “dark energy” • any dark energy contributes to the energy density of the vacuum has the same effect as Einstein’s “Cosmological Constant”, (upper-case lambda)

• is a free parameter in Einstein’s fundamental equation of general relativity; previously believed to be 0

• Energy corresponding to seems to account for the missing mass/energy needed to produce a flat space-time.

Problems Many of the ‘old’ problems seemed ‘solved’ leaving just minor things like • what is dark matter? and • what is dark energy?

Quantum field theory predicts energy density of the vacuum up to 10120 greater than is observed

Why is so close to zero? - the cosmological constant problem

Why are and m so close now - a special epoch?

16 Modelling dark energy Matter and radiation have constant equations of

state (wm = 0 and wr = 1/3)

Cosmological constant has w = 1 Other options: Dark energy with constant w: e.g. strings w = -1/3, domain walls w = -2/3 Quintessence: generic name for dark energy with time-varying w - e.g. supergravity, superstring, branes,… Interaction: dark energy interacts with matter or energy - e.g. unifying dark energy and dark matter Modifications to GR: modifying the basic equations

Modelling dark energy Most dark energy models can be described with a constant or varying equation of state e.g. constant w w < -1/3 universe accelerates - now required w > -1/3 universe decelerates w < -1 density od dark energy increases with expansion - the ‘big rip’

17 Modelling dark energy

One case: As a function of time (t) 6 and redshift (z) 5 4 For dark energy models a(t) 3 with a constant equation 2 of state 1 0 Source: Luke Barnes 2005 Honours Thesis

q(t)

X(t)

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