Science 3210 001 : Introduction to Astronomy

Lecture 12 : Cosmology

Robert Fisher

Items

❑ Nathan Hearn guest lecture on dark matter today. Lunch in theloop (on me) with Nathan following the lecture at Frontera Frescofor anyone who wants to join us.

❑ Adler Planetarium field trip on May 4th - $16/person -- to becollected next week. Waiver forms (Bob -- pick these up from606!) to be signed!!

❑ Final projects due May 11th, along with a short (5-10 minute)presentation that day.

❑ Return midterms.

In the News This Week

❑ Water discovered on HD209458b !!!

❑ In memorium : Virginia Tech victims❑ Liviu Librescu (1930 - 2007)

Final Project

❑ Your final project is to construct a creative interpretation a scientifictheme we encountered during the class. You will present your work in afive minute presentation in front of the entire class on May 11.

❑ The project must have both a scientific component and a creative one.

❑ For instance, a Jackson Pollock-lookalike painting would fly, but ONLY ifyou said that it was your interpretation of the big bang cosmologicalmodel AND you could also demonstrate mastery of the basicastrophysics of the big bang while presenting your work.

❑ Be prepared to be grilled!

❑ Ideas :❑ Mount your camera on a tripod and shoot star trails.❑ Create a “harmony of the worlds” soundtrack for the Upsilon Andromeda

system.❑ Paint the night sky as viewed from an observer about to fall behind the

horizon of a black hole.❑ Write a short science fiction story about the discovery of intelligent life in the

universe.

Two Weeks Ago

❑ Michelson - Morley

❑ Special Relativity

❑ General Relativity

Last Week

❑ Black Holes, White Holes, Wormholes

❑ Galaxies❑ Distances in the universe❑ Types of galaxies

❑ Ellipticals❑ Spirals❑ Irregulars

Today

❑ Cosmology❑ Why is the night sky dark?❑ Newtonian Cosmology❑ Einstein, Hubble and the Expansion of the Universe❑ Cosmic Microwave Background

❑ Large-Scale Structure of the Universe❑ Clusters of Galaxies, Superclusters❑ Quasars

Cosmology -- The Study of the Structure of the Universe as a Whole

❑ Everyone has wondered about the “big” questions of cosmology❑ Did the universe have a beginning? If so, how did it begin?❑ Will the universe continue forever in time?❑ Is the universe infinite or finite?

❑ Every civilization has a “creation myth” which attempts to answerthese questions

❑ Modern science also seeks to answer these questions

❑ In the last fifty years, tentative answers to these questions havebegun to emerge, though they must still stand the rigors ofscience over time

Why is the Sky Dark at Night?

❑ The modern study of cosmology began with a seemingly trivial butactually deep paradox. Why is the sky dark at night?

❑ If the universe were infinite, and stars are uniformly distributedthroughout space, we should see an infinite amount of luminous matter.

❑ Not only would the night sky be bright, but it should be infinitely bright.

❑ The fact fact that the night sky is in fact dark points to an apparentparadox.

❑ The framing of the question is normally attributed to 19th centuryGerman astronomer Heinrich Olbers but was originally posed byJohannes Kepler some two hundred years previous.

Olbers Paradox is Like Viewing a Forest Full ofTrees… if the Forest Were Infinite!

Question

❑ What is wrong with Olbers’ argument?

Assumptions Underlying Olbers’ Paradox

❑ Like most paradoxes, the night sky paradox makes a number ofassumptions. Some of these are explicitly stated, others areimplicit.

❑ The universe is infinitely old and static (unchanging in time onaverage).

❑ The universe is infinitely large.

❑ Matter in the universe is uniformly distributed.

❑ Like many paradoxes, it is the unstated assumption (that theuniverse is infinitely old) which we now know to be incorrect, andinvalidates the argument.

Resolution to Olbers’ Paradox

❑ If we throw out the assumption that the universe is infinitely oldand static, then there is only a finite distance that light can travelin the age of the universe.

❑ Hence, only a finite amount of matter is visible in a universe witha finite age.

❑ The region of the universe visible to us is sometimes referred toas the cosmological horizon.

Speed of light x Age of Universe

Us

Physical Cosmology

❑ One of the most important ideaswhich developed in modernastrophysics is that the structureof the universe as a whole canbe understood using thefundamental principles ofphysics.

❑ On the very largest scales, muchlarger than individual galaxies,gravity is the only force which iseffective.

Large-Scale Structure

Physical Cosmology

❑ When modeled as a physical system, astrophysicists oftenreplace an amount of mass equivalent to an entire galaxy with asingle body, or particle.

❑ The entire assembly of particles is often referred to as an N-bodysystem, particularly when simulated on a computer.

Millenium Simulation (Springel et al)

Newtonian Cosmology

❑ The first serious attempt to formulate a fundamental scientificcosmological theory was due to Newton.

❑ Newton envisioned an infinite universe, on an absolute, fixedspace and time.

❑ Newton’s gravity provided the prescription of how bodies movedwithin this space.

❑ Each body in the universe is attracted by every other body underthe influence of gravity and gravity alone.

Cambridge, We Have a Problem… NewtonianCosmology is Totally Screwed Up

❑ Unfortunately, it turns out to be completely impossible toformulate a consistent cosmological theory using Newtonianphysics alone.

❑ In Newtonian cosmology, because gravity propagates infinitelyfast, if one clumps up matter in one place, the entire universeimmediately feels the gravitational pull of that clump, andcollapses in on it in a finite amount of time.

Cambridge, We Have a Problem… NewtonianCosmology is Totally Screwed Up

❑ Even if one seeded a bunch of clumps initially, these clumps would themselvescoalesce on about the same time.

❑ The lifespan of a Newtonian universe, based on the mean density of theintergalactic medium today, is about billion years.

❑ Clearly the Newtonian model cannot account for the age of the Earth, much lessdetailed observations of the cosmos (eg, the Newtonian universe is collapsing!)

❑ This model is fatally flawed, and it would take Einstein to fix that fatal flaw.

Einstein and Cosmology

❑ In 1915, Einstein had formulated his theory of General Relativity(GR), which describes how gravity can be accounted for by thecurvature of space and time under the influence of mass andenergy within it.

❑ It took until the end of WWI for Eddington to confirm GR using thebending of starlight during the 1917 solar eclipse.

❑ With the successes of GR in our own solar system, Einsteinturned to the same problem cosmological Newton had originallytackled -- what is the structure of the universe as a whole on verylarge scales?

Rare Photograph of Einstein Uncovered Recently

Einstein’s “Greatest Blunder”

❑ Einstein began with similar building blocks as Newton, assumingthat matter is smoothly distributed initially throughout space.

❑ There is a fundamental difference between Newton’s model andEinstein’s. In Einstein’s model, space and time themselves areevolving as the universe evolves.

❑ Einstein discovered that the matter within the universe wouldnaturally create an expansion of space in relativity theory.

❑ Taken at face value, Einstein’s original equations predict theexpansion of the universe!!

Cosmological Constant

❑ However, rather than accepting this description of an expandinguniverse (for which there was no direct evidence at the time),Einstein played with the equations to produce a static,unchanging universe similar in spirit to that originally proposed byNewton.

❑ To produce this outcome, Einstein needed to add an additionalterm to his equations of General Relativity -- the so-called“cosmological constant” term, which is only important on verylarge scales.

❑ The effect of the cosmological term is to counteract againstgravity and produce an effective repulsion.

Hubble and the Expansion of the Universe

❑ Working from Mt. WilsonObservatory near Pasadena,California, Edwin Hubble measuredthe distances to nearby galaxiesusing the Cepheid variable methodpioneered by Henrietta Leavitt wediscussed last week.

❑ In addition, Hubble also measuredthe spectra of these galaxies.

❑ Using the Doppler effect, he wasable to determine the speed withwhich they receded from us fromtheir spectra.

❑ Amazingly, he found that thespeed of recession was directlycorrelated with the distance to thegalaxy.

Hubble’s Original Data, Showing VelocityVersus Distance for a Number of Galaxies

Slope of the line on this plot is the Hubble “constant”.

The Expansion of the Universe via Analogy

❑ It turns out that the complex mathematics of GR in fact reduces toa very simple equation when describing the expansion of theuniverse -- the same one that are produced for a rocket moving ata fixed speed in a gravitational field in Newtonian physics.

VelocityGravity

The Expansion of the Universe

❑ GR cosmology has a close correspondence in the rocket shipanalogy. The height of the rocket is analogous the to radius of theuniverse, the strength of the gravitational field is analogous to thedensity of matter in the cosmos, and the speed of the rocket isanalogous to the Hubble “constant” as it is measured today.

Curvature of Universe

Is the Universe Open, Closed, or Flat? Will itCollapse or Continue Expanding Forever?

❑ While Hubble’s original Cepheid variable data clearly showed theexpansion of the universe, the jury on the value of the Hubbleconstant was out for many years.

❑ Hubble’s original value (500 km/s/Mpc) was much larger than themodern value (by a factor of 7) due to errors in the calibration ofthe Cepheids.

❑ By the late 1980s, the uncertainty in the Hubble constant wasdown to a factor of 2. Enormous debates raged as to which valuewas correct, and whether the universe was open or closed.

❑ A huge dedicated effort was undertaken by numerous groups toreduce this uncertainty even further and nail once and for all whatthe ultimate fate of the universe will be.

Modern Value of Hubble Constant

❑ Fittingly, one of the major achievements of the Hubble SpaceTelescope and other parallel projects was the accuratedetermination of the Hubble constant, which is now known tobetter than 10%.

A Flat, Accelerating Universe

❑ Observations of distant type Ia supernovae (which we discusseda few weeks ago) serve as excellent standard candles.

❑ These observations are consistent with a flat, acceleratinguniverse.

Einstein’s Greatest Blunder? Maybe Not.

❑ What is causing the acceleration of the universe?

❑ It is consistent with a cosmological constant.

Cosmic Microwave Background

Large-Scale Structure of the Universe

Zoom-in of Millenium Simulation

Flythrough of Large-Scale Structure of theMillenium Simulation

Next Week : Interstellar Space Travel, Life in theUniverse, and the Ultimate Fate of the Universe

❑ Does life exist elsewhere in the universe? How can scienceaddress this age-old question?

❑ Does intelligent life exist elsewhere in the universe? How can wesearch for extraterrestrial intelligence?

❑ Is it possible for humans to travel to other stars?

❑ What is the ultimate fate of the universe?

❑ Wrapping it all up -- from ancient astronomy to the infinite farfuture of the universe