Chapter 28 Cosmology In the beginning…. And what we know about it, and how we know about it.

Way out there... For about 10 days the Hubble Space Telescope pointed at one spot in space. As far as we knew, nothing was there - at least nothing had been observed there before. Hubble Deep Field - the oldest galaxies –10 to 12 billion years old How old is the Universe? Is it infinitely old and infinitely large? How did it all begin? Or has the universe always been there?

Newton’s Universe Cosmology deals with the structure and the evolution of the universe as a whole. According to Newtonian cosmology, we live in a static, infinitely old and infinitely large universe with stars randomly scattered throughout the universe. In the early 1800s, the German astronomer Heinrich Olbers pointed out that something was wrong with this picture - Olbers’s Paradox.

Olbers’s Paradox If the Universe is infinite, why isn’t the sky bright at night? –We should be able to have a line of sight to galaxy or star in any direction we look, if the line of sight extends far enough. –But sky is dark, so there must be an end. End is due to expansion of Universe and resulting cosmic horizon - some of light from Universe has not reached us yet.

Expansion of the Universe Einstein’s relativity gave an entirely different picture of spacetime and gravity. His calculations showed that the universe must expand or contract, so he included a fudge factor into his equations - Cosmological Constant - so that his theory would support a static universe. Later, when it was established that the Universe is indeed expanding, he said that it was the biggest blunder in his life.

Expansion of the Universe While some disagree about how the universe came into existence, no one argues that the Universe is expanding. The first person to discover this was Edwin Hubble. He observed that all remote galaxies are moving away from us. Hubble’s Law - The further away something is from us, the faster it is receding from us. v = H 0 * d v = recession velocity, H = Hubble’s constant, d = distance

Conceptualizing the expansion of the Universe What does it actually mean to say that the universe is expanding? Think of small coins representing the galaxies glued on a balloon as it is blown up. As the balloon expands, the the amount of space between the coins gets larger and large. Similarly,as the universe expands, the amount of space between the widely separated galaxies increases.

Conceptualizing the expansion of the Universe The expanding balloon analogy.

Conceptualizing the expansion of the Universe Expansion occurs only in the space between galaxies and clusters of galaxies. Galaxies (or stars, or us) themselves do not expand, just like the coins do not expand. Think of a line of galaxies. The distance between each galaxy doubles in a certain time. There is no center, and all observers notice Hubble’s Law No matter which galaxy you call home you will see all other galaxies receding from you in accordance with the same Hubble Law

The expanding universe and the Hubble law The greater the original distance between the galaxies, the greater the amount that the distance has increased.

Creating space What is the universe expanding into? NOTE! The Universe is not expanding into pre-existing space - it “creates” space as it goes (!?), just as the surface of a balloon gets bigger as it is blown up. There is nothing “beyond” the universe, because there is no beyond. Asking what is beyond the universe is a meaningless question.

What we observe about the Universe: The Cosmological Principle Over very large distance scales the universe homogeneous –i.e. every region looks the same as every other region The universe is isotropic –The universe looks the same in every direction These two assumptions constitute the cosmological principle. –Gives precise meaning to the idea that we do not occupy a special location in space.

The Big Bang According to Hubble law the universe has been expanding for a very long time, and thus the matter in the past must have been closer together and denser than today. Therefore, a very long time ago all matter was compressed to single point (as energy). For some reason, point began to expand initiated by a colossal explosion known as the Big bang. As it expanded, it cooled, and developed into the Universe we see today.

The Hubble constant The Hubble constant H 0 tells how fast the Universe is expanding. v = H 0 *d H 0 seems to be around 65 (km/s)/Mpc, though scientists still debate this. The age of the universe(T 0 ) can be calculated from the equation T 0 = 1/H 0 ≈ 14 billion yrs. –age problem (limit to how large H 0 can be): if we use an H 0 that is too big then the universe gets younger but the oldest stars observed are older than Universe!

The Cosmic Horizon There is a limit to how deep in the Universe we can peer. We are at the center of the limits of our vision (a.k.a. the Cosmic Particle Horizon) –limit set by how old Universe is and speed of light: light from distant galaxies must have had time to reach us –our cosmic horizon is different from other galaxies - they are at their own center –This solves the Olbers’s Paradox. We do not receive light from galaxies beyond our horizon.

The cosmic horizon

The Cosmic Singularity At the moment of the Big Bang: –A state of infinite density filled the universe –A condition of infinite curvature existed, giving rise to a situation where space and time were jumbled. –Therefore, we cannot apply laws of physics to describe the moment of the Big bang. –This is very similar to the condition at the center of a black hole - i.e. at the black hole singularity –For this reason we refer to the black hole as the Cosmic Singularity.

Plank Time Due to the state of the universe during the BB, we cannot use laws of physics to describe this event. Nor can science answer what existed before the BB - these are fundamentally unknowable things. In fact, from the beginning of the BB until seconds after The BB, space & time was so jumbled-up that laws of Physics fails us –This time interval t P = sec. is referred to as the Plank time.

Amount of helium in the universe is more than expected if we believe that. –The universe originally contained only hydrogen. –all of the helium was produced inside stars Indicates that some helium was formed in early Universe before stars were formed. The presence of so much helium posed a major problem for astronomers. The answer to this dilemma was discovered during the 60s. Cosmic microwave background radiation (CMB)

It was once hot here... In 1960 Dicke & Peebles working on an idea put forward by Alpher & Hermann discovered that the abundance of helium can be accounted for if the early universe was hotter than the core of our Sun. In such a universe thermonuclear reactions occurred everywhere throughout the space, thus converting hydrogen to helium. Therefore, it was believed that the early universe must have been full of high-energy short-wavelength photons (radiation).

Cosmic microwave background radiation (CMB) This radiation is blackbody radiation and depends on the temperature, just like the radiation from the Sun. This radiation which fills all space is referred to as the Cosmic Microwave background radiation (CMB). It was discovered by Arno Penzias & Robert Wilson in the early 60s.

Cosmic microwave background radiation (CMB) “Cosmic:” no identifiable point source - comes from all directions - cosmic in origin “Microwave:” wavelengths (frequencies) in the microwave region of the electromagnetic spectrum “Background:” permeates all space “Radiation:” Electromagnetic radiation

The CMB Continuous spectrum from a source with temperature of 2.7 K Source seems to be space itself Source is really the hot early Universe itself, just before it cooled. We are seeing EM radiation as it reaches us for the first time from the farthest reaches of the Universe –as many light years away as the Universe is old

Why 2.7 K? Original temperature about Kelvin and density g/cm 3, but expansion has cooled it. Cooling occurs as space is stretched by expansion, and wavelengths get longer - redshift. The redshift caused by the expansion of the universe is called the cosmological redshift. The Big Bang happened EVERYWHERE in space - right here included!!

The discovery of the CMB radiation was the nail in the coffin for all the other competing cosmological theories of the time which avoided the big Bang scenario. –The Steady state Theory was the main challenger to the Big bang theory at the time. CMB radiation has no other explanation but the Big Bang. The CMB

Will the universe expand forever? What is the shape of the Universe? The density of the Universe Hard question to answer - requires knowing how much matter and radiation is in the Universe (equivalently: Energy density) Which plays a more important role in the Universe; Matter or energy? –Depends on when! At present the matter & radiation densities: –Radiation density  rad = 4.6 x kg/m 3 –Matter density  m = 2 to 4 x kg/m 3 ( 1 to 2 H atoms in 1 m 3 )

The density of the Universe Today, mater prevails over radiation in the Universe - matter-dominated Universe However, as you go back in time towards the BB, as the universe was more compressed, both densities were higher, but in addition photons were not so redshifted => higher energy. –Early universe was a radiation-dominated Universe –The transition from radiation dominated to matter dominated universe happened about 2500 yrs. after the BB

The Evolution of mass (energy) density of the Universe.

History of the Universe Very exciting in the beginning, very dull now. Hot early, cool later. Radiation dominated: At first, Universe very hot. Exotic forms of matter present, but were quickly destroyed. Mostly EM radiation like gamma rays present. Would see brightness everywhere. Matter dominated: (Like now) Universe dark, cooler. Matter forms and stays formed. Transition between two eras is where CMB came from

What shape is the Universe? Open Universe: Will expand forever. Negative curvature. Parallel lines always diverge. Closed Universe: Stops expanding and collapses again. Positive curvature. Parallel lines always converge. Flat Universe: exactly stops expanding but doesn’t collapse (really doesn’t exactly stop until infinite time). Zero curvature. Parallel lines remain parallel

What shape is the Universe? The curvature (Shape) of the universe depends on the combined matter + radiation density -  0 Critical Density  C : –If  0 =  C the universe is flat –If  0 >  C the universe is closed –If  0 <  C the universe is open Using H 0 = 70 km/s/Mpc we get –  C = 9.2 x kg/m 3 – 5.5 hydrogen atoms per cubic meter

What shape is the Universe? Astronomers prefer to use the Density parameter instead of density: –  0 =  0 /  C Therefore, the shape of the universe can be understood in terms of  0. Critical Density  C : –If  0 = 1 the universe is flat –If  0 > 1 the universe is closed –If  0 < 1 the universe is open

Flat space

Curved space

Measurements of open vs. closed universe These measurements are underway with a new generation of telescopes From current observations astrophysicists find that  0 = 1.0 with an uncertainty of 10%. This means that the universe is flat. The flatness of the universe presents a major dilemma.

Dark Energy The matter & Radiation density parameter  m/R lies between But  0 = 1.0 and if there is only matter & radiation in the Universe then  0 =  m/R !! The source of the missing density must be some form of energy that we cannot detect from its gravitational effects (like astronomers do with dark matter) nor does it emit any radiation. This mysterious energy is called Dark Energy

Dark Energy Therefore, the density parameter of the universe has two components:  0 =  m/R +  , where   is the dark energy density parameter. –   should be between 0.6 & 0.8 (since  m/R = 0.2 to 0.4 and  0 = 1.0). –That is dark energy accounts for 60% to 80% of the contents of the universe!! –It is believed that this dark energy to be a form of energy that provides an anti-gravity like effect that cause the universe to accelerate mare rapidly. –This concept goes back to Einstein and his cosmological constant.

Recent measurements: Is the expansion speeding up? Recently published measurements of velocity vs. distance using supernovae as distance indicators suggest that the rate of expansion is increasing. –Where is the energy driving this rate of increase coming from? Dark Energy?

Long ago galaxies receded more slowly than now

The Ultimate fate of the Universe How the universe is going to evolve depends on the matter+radiation density and the dark matter density of the universe. The rate of cosmological expansion is given in terms of the deceleration parameter q 0. –Unbounded universe: q 0 < 1/2. Expands for ever. –Bounded Universe: q 0 > 1/2. Gravity will eventually stop the expansion and then the universe will contract inward. At the end will contract to a point of infinte density in an event called the Big Crunch.

Key concepts Big Bang Cosmic horizon Hubble’s Law Definition and origin of the CMB The role of temperature during history of Universe Dark Energy The shape of the Universe, significance in terms of its future.