## ASTR 207 – Ch. 26: Cosmology

Cosmology

The study of the structure and evolution of the entire universe.

Sloan Great Wall

The largest known structure in the universe, stretches 300 mpc. There is nothing larger than this.

Pencil Beam Survey

A narrow field of view, only a few small patches in the sky, that studies extremely faint, hence far away, galaxies. Clusters and walls show up as ‘spikes’ in a graph.

Galaxy Survey

A redshift survey that explores the large-scale distribution of galaxies in space.

The Cosmological Principle

Homogenous – the universe is the same everywhere on scales greater than a few 100 mpc

Isotropic – the universe is the same in all directions.

Isotropic – the universe is the same in all directions.

Implications of the Cosmological Principle

– Implies that because the universe is the same everywhere, there is no edge to the universe (homogeny)

– Implies that there is no center, because that would mean that the universe would not be the same in all directions from any non-central point.

– Implies that there is no center, because that would mean that the universe would not be the same in all directions from any non-central point.

In what sense, and on what scale, is the universe homogeneous and isotropic?

On very large scales – more than 300 mpc – the distribution of galaxies seems to be roughly the same in all directions.

Olber’s paradox

A thought experiment suggesting that if the universe were homogenous, infinite, and unchanging, the entire night sky would be as bright as the surface of the sun.

Recession Velocity

Equal to Hubble’s Constant (70 km/s/mpc)x distance

Primeval Fireball

Hot, dense state at very early times, just after the Big Bang. According to Hubble’s Law, 14 billion years ago all the galaxies in the universe lay on top of each other. Then, the universe began to expand at a rapid rate, and its density and temperature fell rapidly as the volume increased.

The Big Bang

Event that cosmologists consider the beginning of the universe, in which all matter and radiation in the entire universe came into being.

The Expansion of the Universe

– Hubble’s law describes the expansion of the universe.

– The universe expands with space homogenously, it does not expand into the empty spaces between galaxies, for example. This does not mean, though, that the galaxies themselves expand.

– The universe expands with space homogenously, it does not expand into the empty spaces between galaxies, for example. This does not mean, though, that the galaxies themselves expand.

Cosmological Redshift

As a photon moves in space, its wavelength is influenced by the expansion of the universe. As the universe expands, photons of radiation are stretched in wavelength, giving rise to the cosmological redshift. Photons with a larger redshift are OLDER because the universe was SMALLER when they were emitted.

Why does Hubble’s law imply a Big Bang?

Because tracing the motion backwards in time, it implies that all galaxies, and in fact everything in the entire universe, were located at a single point at the same instant in the past.

Escape Speed

The speed necessary for one object to escape the gravitational pull of another. Anything that moves away from a gravitating body with more than escape speed will never return.

Two possibilities for the Universe

Either the universe will continue expanding (if it is low density) or the universe will stop expanding and collapse (if it is high density)

Critical density

9x 10 to the power of -27 kg/m3

The density corresponding to a universe in which gravity acting alone would be sufficient to halt the present expansion.

The density corresponding to a universe in which gravity acting alone would be sufficient to halt the present expansion.

Two Futures – High Density

HIGH DENSITY:

– If the cosmos emerged from the Big Bang with sufficiently high density, then it contains enough matter to halt its own expansion and the recession of galaxies will stop. Red shifts will turn to blue shifts as the universe begins collapsing inward and stars and planets and galaxies will collide with increasing frequency and violence as space diminishes. The entire universe will shrink towards a super dense, super hot singularity, much like the one from which it originated, the “big crunch”

– If the cosmos emerged from the Big Bang with sufficiently high density, then it contains enough matter to halt its own expansion and the recession of galaxies will stop. Red shifts will turn to blue shifts as the universe begins collapsing inward and stars and planets and galaxies will collide with increasing frequency and violence as space diminishes. The entire universe will shrink towards a super dense, super hot singularity, much like the one from which it originated, the “big crunch”

Two Futures – Low Density

Gravity of a low density universe will be too weak to half the present expansion. The universe will expand forever, the galaxies continually receding, their radiation steadily weakening with increasing distance.

In time, we will see no galaxies in the sky beyond the Local Group. Eventually, the Local Group will peter out as their fuel supply is consumed. A “cold death” will happen whereby all radiation, matter, and life are eventually destined to freeze. This would take about a trillion years to happen.

In time, we will see no galaxies in the sky beyond the Local Group. Eventually, the Local Group will peter out as their fuel supply is consumed. A “cold death” will happen whereby all radiation, matter, and life are eventually destined to freeze. This would take about a trillion years to happen.

What are the 2 basic properties for the future expansion of the universe?

The universe can expand forever, in which case we die a cold death in which all activity gradually fades away, or the expansion can stop and the universe will recollapse to a fiery Big Crunch.

Relativity

The presence of matter or energy causes a warping, or curvature of spacetime and the curved trajectories of free falling particles within warped spacetime are what Newton thought of as orbits under the influence of gravity. The amount of warping depends on the amount of matter present.

What actually contributes to the curvature of space?

Both matter and energy must be taken into account, with energy properly converted into matter units by division by the square of the speed of light.

(3×10 to the power of 8m/s)squared = 1.1×10 to the power of minus 17 kg

– Density of the universe then includes not only atoms and molecules, but also invisible dark matter and everything that carries energy.

(3×10 to the power of 8m/s)squared = 1.1×10 to the power of minus 17 kg

– Density of the universe then includes not only atoms and molecules, but also invisible dark matter and everything that carries energy.

Cosmic density parameter

The ratio of the universe’s actual density to the critical value.

Critical density – universe with density equal to critical density

Critical density of less than 1 – universe with low density

Critical density of more than 1 – universe with high density

Critical density – universe with density equal to critical density

Critical density of less than 1 – universe with low density

Critical density of more than 1 – universe with high density

Closed universe

Geometry that the universe as a whole would have if the density of matter is ABOVE the critical value at high density. A closed universe is finite in extent and has no edge, like the surface of a sphere. It has enough mass to stop the present expansion and will eventually collapse.

Positive Curvature

The surface of a sphere curves in the ‘same direction’ from any given point in a closed or high density universe.

Open Universe

Geometry that the universe would have if the density of matter were less than the critical value. In an open universe, there is not enough matter to halt expansion of the universe. The universe is infinite.

Negative Curvature

The surface of the universe curves like a saddle in a low density or open universe (infinite)

Critical Universe

Universe in which the density of matter is equal to the critical density. The universe in infinite in extent and has zero curvature. Expansion will continue forever but will approach an expansion speed of zero.

How is the curvature of space related to the density of the universe?

A low density universe has negative curvature, a critical density universe is spatially flat (Euclidean), and a high-density universe has positive curvature (and is finite in extent)

Density of the universe

It seems that, when averaged over the entire universe, even taking into account dark matter, the density of the universe isn’t much more than 30% critical density. Therefore, the universe is low density and will continue to expand forever.

Decelerating Universe

Because expansion rate is decreasing, objects at great distances, that is, objects that emitted their radiation long ago, should appear to be receding FASTER.

Accelerating Universe

Because expansion is increasing, far away objects recede less than Hubble’s law would predict.

Dark Energy

Generic name given to the unknown cosmic force field thought to be responsible for the observed acceleration of the Hubble expansion. The expansion of the universe is opposed by the attractive force of gravity and sped up by the repulsion due to dark energy. As the universe expands, the gravitational force weakens, whereas the force due to dark energy increases.

Cosmological Constant

Quantity originally introduced by Einstein into general relativity to make his equations describe a static universe. Now one of several candidates for the repulsive ‘dark energy’ force responsible for the observed cosmic acceleration.

Why do astronomers think the universe will expand forever?

There doesn’t seem to be enough matter to halt the collapse, and in addition, the observed cosmic acceleration suggests the existence of a large-scale repulsive force in the cosmos that also opposes recollapse.

Geometry of the Universe

As best we can tell, the universe on the largest scales is geometrically flat.

Two forces involved in the expansion of the universe.

GRAVITY tends to slow expansion while DARK MATTER tends to accelerate it.

Cosmic Age

Both the expansion and the age of the cosmos are governed by the competition between gravity and dark energy. According to current observations, dark energy seems destined to win. The age of a universe without dark energy is always less than 1/Hubbles Constant (70km/s/mpc) and DECREASES for larger values of present-day density.

–> The existence of a repulsive cosmological constant INCREASES the age of the cosmos.

The age of the universe appears to be 1/Hubble’s Constant (70 km/s/mpc)

– Our current best guess of the age of the universe is 14 billion years***

–> The existence of a repulsive cosmological constant INCREASES the age of the cosmos.

The age of the universe appears to be 1/Hubble’s Constant (70 km/s/mpc)

– Our current best guess of the age of the universe is 14 billion years***

Why have astronomers concluded that dark energy is the major constituent of the universe?

The observed acceleration of the universe implies that some nongravitational force must be at work. Dark energy is our current best theory of the cause of that force. In addition, galactic and cosmological observations indicate that the universe is spatially flat, and hence has critical density, but that the density of matter (mostly dark) cannot account for the cosmic acceleration is in good agreement with the required extra density (about 70% of critical value)

Cosmic microwave background

The almost perfectly isotropic radio signal that is the electromagnetic remnant of the Big Bang,

When was the cosmic microwave background formed?

At the time of the Big Bang. It is the electromagnetic remnant of the primeval fireball.

What evidence do we have that there is no structure in the universe on very large scales? How large is very large?

Based on galaxy surveys and pencil beam surveys, we know that the universe is both homogeneous and isotropic. 300 mpc is the larger scale, there is no known structure larger.

What is the cosmological principle?

The universe is homogeneous and isotropic, that is it is the same everywhere on large scales.

What is Olbers’s paradox? How is it resolved?

Olbers’s paradox is the obvious contradiction that the entire night sky should be extremely luminous due to the amount of stars in the sky, and the fact that the sky is actually dark at night. Olbers’ paradox is resolved in that, as Olbers assumed, the universe is not infinite and has evolved over time, contrary to his beliefs.

Explain how an accurate measure of Hubble’s constant can lead to an estimate of the age of the universe.

Age is inversely proportional to Hubble’s constant. Because Hubble’s Constant (70km/s/mpc) is indicative of the rate at which the universe is expanding, we simply have to divide by one.

We appear to be at the centre of the Hubble Flow. Why doesn’t this observation violate the cosmological principle?

Every other place in the universe also appears to be at the centre.

Why isn’t it correct to say that the expansion of the universe involves galaxies flying outward into empty space?

Because the only way we can have Hubble’s law hold and retain the cosmological principle is to realize that the Big Bang involved the entire universe, not just the matter and radiation within it, but the universe itself, which is expanding.

Where did the Big Bang occur?

The Big Bang did not happen at any particular location in space, because space itself was being compressed to a point at that instant – the Big Bang happened everywhere at once.

How does the cosmological redshift relate to the expansion of the universe?

It occurs as a photon’s wavelength is ‘stretched’ by cosmic expansion. The extent of the observed redshift is a direct measure of the expansion of the universe since the photon was emitted.

What properties of the universe determine whether it will or will not expand forever?

The DENSITY and MASS of the universe will determine this. If the universe is OVER critical density (9×10 to the power of -27kg/m3) then it will continue to expand until everything simply disappears and the Milky Way becomes cold and dark.

What will become the ultimate fate of the universe if it does not expand forever?

Expansion will stop, but gravity will continue and the universe will contract. Nearby galaxies will blueshift (move towards us) and the density and temperature of the universe will rise as it starts to collapse in on itself. Stars and galaxies will collide violently as the available space diminishes and the universe shrinks towards a super hot and super dense singularity much like the one from which we originated, ‘the big crunch’

Is there enough luminous matter to halt the current cosmic expansion?

No. Even with dark matter considered the universe is approximately only at 30% critical density.

Is there enough dark matter to halt the current cosmic expansion?

No. Even with dark matter considered the universe is approximately only at 30% critical density.

What do observations of distant supernovae tell us about the expansion of the universe?

They allow astronomers to measure changes in the rate of expansion of the universe. In a decelerating universe, supernovae would show a greater increase in redshift than predicted by Hubble’s law. In an accelerating universe (such that we’ve observed), there is more of a decrease in redshift than predicted by Hubble’s law.

What is the cosmological constant and what does it tell us about the universe?

It is one leading dark-energy candidate, an additional ‘vacuum energy’ force associated with empty space and effective only on very large scales. It tells us that the universe is constantly expanding as it has an overall repulsive effect.

Why are the measurements of globular cluster ages important to cosmology?

These ancient star clusters are thought to have formed at around the same time as our galaxy, so they date the time of galaxy formation.

What is the significance of the cosmic microwave background?

It is an isotropic blackbody radiation field that fills the entire universe. Its present temperature is 3K. The existence of the microwave background is direct evidence that the universe expanded from a hot, dense, state.

Why does the temperature of the microwave background fall as the universe expands?

This is a consequence of Earth’s motion through space. We are moving with respect to that frame of reference, so the radiation in front of us is blueshifted white behind us it is redshifted. In reality, the microwave background temperature is isotropic.

How can we measure Earth’s motion with respect to the universe?

The only thing we can ever hope to do in an expanding universe is to determine our velocity (speed and direction) with respect to ever larger collections of matter, and larger scales. The Earth moves at about 30 km/sec in an orbit centered on the Sun. The sun looks like a stationary object locally, but we know it is moving around the center of the galaxy with a speed of 220 km/sec. For many kinds of astronomical study, the center of the Milky Way is ‘at rest’ and stars and gas clouds circulate around it. For other studies, we have to consider the motion of our galaxy relative to the center of mass of our local cluster of galaxies, or the motion of our local cluster relative to more distant clusters. The speeds and directions of all these motions, at any given time, have to be vectorially added.

If observations made from the middle of a large city are isotropic then

There are tall buildings in every direction

The cosmological principle would be invalidated if we found that

The observed structure of the universe depends on the direction in which we look.

When we use Hubble’s law to estimate the age of the universe the answer we get

is the same for all galaxies

Olbers’s paradox is resolved by

the finite age of the universe

The galactic distances use to measure the acceleration of the universe are determine by observations of

exploding white dwarfs

The observed acceleration of the universe means that

the amount of dark energy exceeds the total mass-energy of matter in the universe.

On the basis of our current best estimate of the present mass density of the universe, astronomers think that

The universe is infinite in extent and will expand forever.

The age of the universe is estimated to be

greater than the age of the Milky Way

The cosmic background radiation is observed to come from

All directions equally

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