THE BIG BANG A Model of the Beginning and Future of the Universe

Newton’s Universe It is infinite – there can’t be anything outside of it It is uniform – Every direction has the same amount of stars and galaxies It is static – Although planets orbit the sun, everything in the universe generally stays in the same place. Olber- if this is true, then why is the sky dark at night ?

R Olber’s Paradox -1 Consider a (spherical) shell of stars that are uniformly distributed on the spheres edge All the stars a radius R from the Earth have a total brightness B with respect to Earth

Olber’s Paradox -2 Consider a 2 nd shell of stars with twice the radius of the first. This shell would have 4x’s the surface area (SA = 4  r 2 ) so it can hold 4x’s as many stars as the first shell 2R

Olber’s Paradox -3 Since there are 4x’s as many stars, they would give off 4x’s as much light as the first shell. But since light intensity is inversely proportional to the square of the distance (L  1/d 2 ), each star that is 2R from Earth appears ¼ as bright as the stars a distance R from Earth. But 4x’s as many stars each at ¼ the apparent brightness would have the same total brightness- B as the stars at a distance R

Olber’s Paradox -4 According to this reasoning, the sky should never be dark because the amount of light received by Earth is constant. Therefore….  Newton was wrong about the universe being uniform. Could he have been wrong about the universe being infinite and static as well?

The Big Bang: What was it? 1.The creation of space and time 2.All the matter and energy in the universe was crushed together into one point. 3.Space began to expand, and everything in it expanded with space (the universe is NOT expanding into a vacuum. Space is itself expanding)

The Expansion Every galaxy is moving away from every other galaxy (Regardless of the point of reference) Balloon Analogy: As space expands, all galaxies are further from every other galaxy The rate of expansion has accelerated from its initial rate (more on this later.)

Details of the Big Bang The universe underwent a short period ( – sec) of huge expansion (inflationary epoch) As the universe expanded, it cooled. When it was cool enough, quarks and leptons,then hadrons, then finally atoms and molecules formed. At about 10 9 years, the universe is 75% H and 25% He More matter than antimatter is formed From 10 9 years until present, stars, galaxies, and galactic clusters form (due to gravity)

Evidence for the Big Bang Model-1 1. The red shift in the spectra received from stars in distant galaxies. Light wave from stationary star Light wave from receding star (exaggerated to illustrate point) shorter  higher f longer  less f

Explanation: Space is expanding away from us, which shows a redshift in stellar spectra. This is known as cosmological redshift.

2. Cosmic Background Radiation (CBR) Discovered by Robert Wilson and Arno Penzias Electromagnetic radiation in the microwave range This radiation had the same intensity from every direction in space. It agreed with the predictions of the afterglow of the big bang (a universe temp ~3K) Using Wein’s law (temp of a blackbody emitter): = 2.9 x / T T = 2.9 x / 1.1 x m T = 2.76 K Intensity Peak  mm) Evidence for the Big Bang Model-2

Evidence for the Big Bang Model-3 3. Hubble’s Law The recessional velocity of a galaxy is proportional to its distance from Earth or v = HD V = recessional velocity D = Distance of galaxy from Earth H = Hubble’s “constant” Distance / Mpc Recessional velocity / km s -1 Slope = H The current value of H o is 72 km/sec Mpc (or 22 km/sec MLY)

Evidence for the Big Bang Model-4 Hubble’s Law (cont.) The distances to galaxies are determined by using Cepheids in those galaxies The recessional velocities are determined by using the redshift of the absorption spectra (or redshift factor z) of Hydrogen in the galaxies. The equation is… = wavelength  = change in wavelength v = recessional velocity c = speed of light (3 x 10 8 ms -1 ) v c =  Limitations: Distance measurements less accurate for farther galaxies For nearby galaxies, recessional velocities difficult to distinguish from other galactic motions (orbital) z =

Evidence for the Big Bang Model-5 Example of recessional velocity: A characteristic absorption line often seen in stars is due to ionized Helium. It occurs at nm. If an astrophysicist measures this wavelength at 499.3, what is the recessional velocity of this galaxy? v c =  nm – nm nm = v 3 x 10 8 ms -1 = v v =1.97 x 10 7 ms -1 z = or 6.55 x 10 -2

Cosmic Scale Factor (R) -1 A measure of how big the universe is relative to today (a size and time relationship) The redshift factor (Z) indicates the degree of expansion or the scale of the universe. Since the wavelength we measure ( m ) is different than what the star emitted ( o ), we can write this relationship: Since R α λ, we can than write R= measured scale R o = scale at time of emission

Cosmic Scale Factor (R) -2 Example: If the redshift factor for a galactic spectra is 2, how much has the universe expanded since the radiation was given off? R = 3 The universe has expanded by a factor of 3 since the emission of radiation. Since T α 1/λ, and λ α R, as the Universe expands, T will be inversely proportional to R (T α 1/R)

Age of the Universe -1 *Determining the Age of the Universe Since V = H o D and V = D / T, then H o D = D / T, therefore H o = 1 / T OR T = 1 / H o The age of the universe is the inverse of Hubble’s constant *Assumes a constant rate of expansion

Age of the Universe -2 Example calculations of the age of the universe: Since T = 1 / H o = 1 / 15.3 = s MLY km -1 = 5.30 x sec = 1.68 x yrs or 16.8 billion years #1 How old is the universe if H o = 18 km s -1 MLY -1 ? sec MLY km x 1 km 10 3 m x 10 6 LY 1 MLY x 9.46 x m 1 LY 5.30 x sec x 1 hr 3600 s x 1 day 24 hrs x 1 yr 365days

Age of the Universe - 3 Example calculations of the age of the universe: Since T = 1 / H o = 1 / 48 = s Mpc km -1 = 4.63 x sec = 1.47 x yrs or 14.7 billion years #2 How old is the universe if H o = 65 km s -1 Mpc -1 ? sec Mpc km x 1 km 10 3 m x 10 6 pc 1 Mpc x 9.46 x10 15 m 1 LY 4.63 x sec x 1 hr 3600 s x 1 day 24 hrs x 1 yr 365days x 3.26 LY 1 pc

The Cosmological Principle 1. The universe is homogeneous. There is no preferred position in the universe to observe from (we aren’t at the center of the universe.) 2. The universe is isotropic. Although you see differences in our galaxy, you see no difference in the structure of the universe as you look in different directions.

Critical Density The mass of a galaxy is determined as follows: The # of stars are and their sizes are estimated The orbital speeds of stars and galaxies are used to determine the mass. F c = mv 2 /r ; F g = Gm 1 m 2 /r 2 ; since F c = F g then mv 2 /r = Gm 1 m 2 /r 2, so v 2 = Gm/r The theoretical value of the density needed for a flat universe is 5 x kg/m 3 (30 proton masses / m 3 ) Based on our calculations, we can only see 10% of the matter that must exist in the universe. The rest that we can’t see is referred to as dark matter

The Future of the Universe Gravitational attraction has slowed the expansion Three possible fates of the universe: 1.OPEN- gravity is unable to stop the expansion (the density of matter is too low). The universe expands forever 2.CLOSED- gravity is able to stop the expansion and then collapse the universe because the density is high (Big Crunch). 3.FLAT- gravity slows the expansion, but it takes an infinite time to come to rest. This occurs if the universe was just the right density (Known as the critical density)

The Future of the Universe Time now Size of observable universe closed flat open

Derivation of Critical Density-1 From Newton: KE = ½ mv 2 and PE = -GMm/R The Total Energy (E T )of an expanding sphere is equal to PE + KE = ½ mv 2 – GMm/R When the universe ceases to expand, E T = 0, so ½ mv 2 = GMm/R  The volume (V) of a sphere = 4/3  R 3  Density (  ) = M/V, so M=  V ½ v 2 = GM/R

Derivation of Critical Density-2  Substituting: Rearranging: ½ v 2 = G  V/R ½ v 2 = G  4/3  R 3 )/R ½ v 2 = G  4/3  R 2  c  3v 2 /8  GR 2 Since v= H o d, and d = R, v = H o R  c  3H o 2 /8  G  c  3(H o R) 2 /8  GR 2

Rotation Curves -1 To determine the rotational speed of a galaxy, astronomers focus on individual stars within the galaxy Stars at different distances will have different orbital speeds (due to different gravitational forces.)

Rotation Curves -2 Rotational Velocity Derivation Fc = Fg so mv 2 / r = GMm/ r 2 v 2 = GM/ r v =√GM/r Since (V) of a sphere = 4/3  R 3 Density (  ) = M/V, so M=  V Therefore M=  4/3  R 2

Rotation Curves -3 This indicates that there is a lot more mass within a galaxy that we can see. An explanation for this is….. Newton’s Law of Gravitation predicts that the rotational velocity of a star would decrease with distance from the galactic center. But observations showed the following:

Dark Matter Massive Astronomical Compact Halo Objects (MACHOS) – brown dwarves (low mass ‘failed stars’), Black dwarves, high mass planets, Black Holes. Neutrinos –uncharged particles with practically no mass Particles we don’t know about. The search has been on for Weakly Interacting Massive Particles (WIMPs) Our theories of gravity may not be correct Cloud everything the dark matter does! Matter which doesn’t emit/reflect light. Possible Sources:

Accelerating Expansion Improvements in technology have allowed astronomers to view more distant objects Remember that Type 1A supernovae can be used as standard candles (objects of known luminosity) When we observe these supernovae in very distant galaxies they have much greater z values This indicates that the furthest parts of the universe are expanding at an accelerating rate This seems to be counterintuitive- we would expect that the rate of expansion would be decreasing due to gravitational attraction.

Dark Energy -1 An explanation for the observed accelerating expansion of the universe for nearby galaxies. This acceleration seems to have begun about 5 billion years ago. Einstein had inserted a cosmological constant in his equations for General Relativity to balance gravitational attraction. This was done to keep the universe at a constant size He abandoned this constant when data showed the universe was expanding. The Cosmological Constant is now being reconsidered.

Dark Energy -2 closed flat open Accelerating due to dark energy

Fluctuations in the CMB These fluctuations of temperature (0.001K) show fluctuations in density. These density differences allow the formation of galaxies.

Unanswered Questions Why more matter than antimatter? What caused the initial expansion of the universe? *was gravity initially a repulsive force? Where did all of the energy/matter come from? Where did the laws of physics come from? Why are they what they are?

Cosmological Argument Everything that has a beginning (or comes to be) has a cause The universe has a beginning Therefore the universe has a cause

“One who claims to be a skeptic of one set of beliefs is actually a true believer in another set of beliefs.” Philllip E. Johnson

“Men stumble over truth from time to time, but most pick themselves up and hurry off as if nothing happened.” Winston Churchill

“People almost invariably arrive at their beliefs not on the basis of proof but on the basis of what they find attractive.” Blaise Pascal

“Science without religion is lame; religion without science is blind.” Albert Einstein