Cosmological Models

John O’Byrne School of University of Sydney

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

Observation: : On the largest scales, the local 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 ()

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

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

1 The

Notes that the universe is fine-tuned to our existence Fine-tuning …. •Strength of •Smoothness of the of sub-atomic particles •Strength of the strong nuclear •Magnitude of the

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

Explanations? •Chance • of Everything •The

Cosmology and

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 , plus many combinations of these possibilities.

2 : Hubble’s Law

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


What we actually observe is (z)

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

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

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

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 background 3. The abundance of the 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

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

Blackbody radiation with a of T = 2.73 K

6 Abundance of Light Elements


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

~ 1/H0 scale of the Universe


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


If the of / 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 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) - (q>0 for deceleration)

Confused? Various parameters are related.

Problems with the simple Big Bang

1) The : 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 , 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: of sudden expansion during the very early of the universe

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

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- parameter  0.73 ± 0.04 Time since the Big Bang 13.7 ± 0.2 billion 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


Measuring the Deceleration of the Universe

By observing type Ia supernovae, 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 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 , 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


• Combined 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 as much mass as is directly visible.

• There must be DARK matter

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

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

15 “

• “negative ” in has a repulsive effect to explain the - has been called “dark energy” • any dark energy contributes to the energy density of the 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 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 : generic name for dark energy with time-varying w - e.g. , superstring, ,… 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 ‘

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