In Search of the Big In Search of the Big BangBang

The Hubble LawAccording to the Hubble Law, the space between the galaxies is constantly increasing, with VVelocity = H = H00 D D istance

This is not occurring locally: the density of material in the galaxy and the Local Group has long since caused gravity to reverse the Hubble expansion. But globally, the universe is expanding.

An Age to the Universe

The Hubble Law implies the universe began with a Big Bang, which started the galaxies flying apart. It also implies a finite age to the universe. This age depends on two things:

• The expansion rate of the universe. (“How fast are the galaxies flying apart?”)

• The density of the universe. (“How much is gravity slowing down the expansion?”)

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A Fate to the Universe

The Hubble Law also implies 3 possible fates for the universe: The universe will expand forever (an unbound or open

universe) Gravity will eventually reverse the expansion and cause

the universe to collapse into a “Big Crunch” (a bound or closed universe)

The universe is precisely balanced between open and closed (a marginally bound or flat universe)

The Shape of the UniverseAccording to Einstein, mass bends space. This means that the universe has a shape. This shape is related to the density of the universe.

Type Shape of Universe

Open Universe

Closed Universe

Flat Universe

The Age and Fate of the Universe

If there were no mass (i.e., no gravity) in the universe, the Hubble expansion would proceed at a constant speed. The age of the universe would then just be given by 1 / H0, and the universe would expand forever.

In a real universe with mass, gravity must have (over time) slowed the Hubble expansion. In the past, the galaxies must have been moving apart faster. The age must therefore be less than 1 / H0. For a “flat” universe, the age is 2/3 of 1/ H0.

The faster the universe is expanding (i.e., the larger the value of H0), the more matter there must be to “close” the universe.

H0 is therefore key to knowing the age and fate of the universe! And note: H0 = V / D, and velocities are easy to measure via the Doppler shift! All you is the distances to galaxies!

The Distances to GalaxiesIn general, galaxies are too far away to observe RR Lyrae or main sequence stars. You need a brighter standard candle!

Recall the Instability Strip. Pop II (low mass) objects aren’t the only type of star to wander through the strip after igniting helium. High mass (Pop I) stars can also enter the strip. These stars are called Cepheid variables.

The Cepheids of the Large Magellanic CloudCepheid variables can be 100 times brighter than RR Lyr stars, but they do not all have the same brightness. They are difficult to measure in the Milky Way due to dust, but many Cepheids exist in the Large Magellanic Cloud, our nearest (non-dwarf) galaxy.

The LMC is close enough so that we can identify its RR Lyrae stars. We therefore know its distance.

l = L / r2

The Cepheid Period-Luminosity RelationIn 1912, Henrietta Leavitt showed that LMC Cepheids had a range of brightness (some extremely luminous, some faint). But the brighter the Cepheid, the longer it took to pulsate. This Period-Luminosity relation makes Cepheids a standard candle.

The Distance Ladder

Trigonometric Parallax

Spectroscopic Parallax

RR Lyrae Stars

Cepheids

Cepheid DistancesUsing Cepheids as a standard candle, one can obtain the distances to galaxies as far away as 20 Mpc.

But this is still not far enough away. Peculiar velocities are still too important. We need a brighter standard candle!

The Tully-Fisher RelationAccording to Newton, the rotation speed of a galaxy depends on its mass, and the greater the mass, the brighter the galaxy.

If we can translate mass into absolute luminosity, we can have a standard candle that is as bright as a galaxy. And we can do this – by calibrating the relationship using galaxies whose distances are known from Cepheids.

Type Ia SupernovaeWhen an accreting 1.4 M white dwarf goes over the Chandrasekhar limit, it becomes a Type Ia supernova. SN Ia can be seen across the universe.

We can determine exactly how bright SN Ia are by measuring their brightness in galaxies with known Cepheid distances.

The Distance Ladder

Trigonometric Parallax

Spectroscopic Parallax

RR Lyrae Stars

Cepheids

T-F Relation SN Ia

Hubble Law

The Age of the Universe

Our current measurements give a value of the Hubble Constant of H0 = 72 8 km/s/Mpc. This implies an age for the universe of …

13 billion years, if we live in an empty universe 9 billion years, if we live in a flat universe

But the stars in globular clusters are at least 13 billion years old. Did we do something wrong … ?

Telescopes as Time Machine

Under the Big Bang hypothesis, the universe was very different in the past. Can we prove this? Yes!

Light travels at a finite speed: the light we see today started out long ago. The farther away the object, the further back in time we observe. (And remember, the greater the distance, the greater the redshift.)

With big telescopes or telescopes in space, we can look for high-redshift galaxies and look back in time.

Galaxies at High Redshift

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Some of these galaxies date from a time when the universe was only 10% of its present age!

Galaxies at High Redshift

In the deepest images, the high redshift galaxies appear bluer, and more irregular than galaxies in the nearby universe. Many high redshift galaxies are interacting.

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The Microwave Background

Suppose we were to look further back in time, to when the universe was only 100,000 years old. At that time …

The universe was very dense and under great pressure. According to the equation of state, high pressure means

high temperature. According to the blackbody law, high temperature means

light was produced. Since this was a long time ago, if we were to observe it,

the light would be redshifted into the microwave region of the spectrum.

Since the entire universe was glowing, this light should come from all over the sky.

The History of Light

The light from the Big Bang should now appear as emission from a blackbody at 3 degrees above absolute zero.

Prediction vs. Observation• 1948: 3 degree blackbody emission from the entire universe

predicted by George Gamow

• 1965: 3 degree blackbody emission found by Arno Penzias and Robert Wilson

• 1998: Blackbody spectrum measured by the COBE satellite

Prediction of Big Bang confirmed!

The All-Sky Microwave BackgroundBecause the Earth is moving through space, the microwave background should be redshifted in one part of the sky, and blueshifted in another part of the sky.

Blue is cooler (moving away); red is hotter (moving toward)

The All-Sky Microwave Background

When the Earth’s motion is removed, the distribution of microwaves on the sky becomes more uniform.

The All-Sky Microwave BackgroundWhen emission from cold gas in the Milky Way is removed, the remaining distribution becomes very (but not perfectly) smooth.

The fluctuations are only a few parts in 10,000!

The All-Sky Microwave BackgroundFrom the equation of state, slightly higher temperatures means slightly higher densities and pressures. The red areas are over-dense by a factor of 1.00004.

From these primordial density fluctuations come today’s galaxies and clusters.

The All-Sky Microwave Background

Over time, the very small density fluctuations of the early universe have been amplified many times by gravity. The galaxies and clusters we see today grew from the very small fluctuations in the microwave background.

The All-Sky Microwave BackgroundThe hot gas of the early universe cools and, with the aid of gravity, gets turned into galaxies and clusters of galaxies.

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Formation of StructureOver time, the very small density fluctuations of the early universe have been amplified many times by gravity.

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The Shape of the Universe

The microwave background fluctuations also allow us to determine the shape of the universe. (The method is complicated: it has to do with how far apart the positive (and negative) areas appear on the sky. Theory tells us how far they should be, and we can observe how far apart they are.)

We observe that the Universe is Flat!

The Deceleration of the UniverseThe age of the universe depends on both its expansion rate (the Hubble Constant) and its density. Determining density is hard, since most of the mass is invisible. But over time, gravity has slowed down the expansion rate. By looking into the past, we can see how the universe has decelerated.

Closed

Flat

Empty

Closed

Flat

Empty

HUBBLE DIAGRAM

Measuring the Deceleration

Type Ia supernovae can be used as standard candles to look across the universe and measure the deceleration via a Hubble Diagram. This was done in 1998. The answer is…

The universal expansion is not slowing down at all due to gravity. In fact, the expansion is speeding up!!!

The Accelerating Universe!!!

The universe is not slowing down at all. In fact, it’s speeding up!!! We live in an accelerating universe!

It’s as if there’s another force pushing the universe apart – a Cosmological Constant!!!

The Accelerating Universe!!!

Whatever this force is, we think that it is growing stronger as the universe evolves. The more empty space in the universe, the greater the acceleration – as if the vacuum of space has pressure!