Cosmology ASTR 2120 Sarazin. Hubble Ultra-Deep Field

Size: px
Start display at page:

Download "Cosmology ASTR 2120 Sarazin. Hubble Ultra-Deep Field"

Transcription

1 Cosmology ASTR 2120 Sarazin Hubble Ultra-Deep Field

2 Cosmology - Da Facts! 1) Big Universe of Galaxies 2) Sky is Dark at Night 3) Isotropy of Universe Cosmological Principle = Universe Homogeneous 4) Hubble Expansion of Universe

3 Cosmology - Da Facts! (Cont.) 4) Hubble Expansion of Universe Hubble Law is only homogeneous expanion law Universe is expanding everywhere, not away from a single point

4 Cosmology - Da Facts! (Cont.) 5) Cosmic Microwave Background (CMB) (Penzias & Wilson 1965)

5 Cosmology - Da Facts! (Cont.) 5) Cosmic Microwave Background (CMB) (Penzias & Wilson 1965) Predicted by Gamow in 1940 s Hot Big Bang explained fusion of H & He in early Universe Heat of Big Bang explosion T = ± K (from COBE satellite) MEMORIZE Redshifted today very hot in past

6 Cosmology - Da Facts! (Cont.) 5) Cosmic Microwave Background (CMB) Cold, but everywhere a) Most of photons in Universe b) Most of known heat and free energy in Universe (not including rest mass energy and Dark Energy) c) Most of entropy in Universe Spectrum and intensity = blackbody to 10-5 Agrees with prediction

7 CMB Spectrum COBE Satellite CMB Spectrum

8 CMB Distribution on Sky 1) Extremely Uniform (part in 10 3 ) 2) Dipole due to Doppler shift from Earth s motion Around Sun, Sun around Milky Way, Milky Way and Local Group (630 km/s) 3) Fluctuations at 10-5 level

9 Cosmology - Da Facts! (Cont.) 6) Composition of Universe a) Ordinary, baryonic matter p, n, e, most of observed mass i. Matter, not antimatter ii. Why? Aren t laws of physics symmetric? Mainly H (75% of mass, 90% of atoms) & He (25% of mass, 10% of atoms) b) Photons (CMB, most of free energy?) c) Dark Matter (most of mass, what is it?) d) Dark Energy (come back to later, most of energy?)

10 Composition of Universe

11 Cosmology - Da Facts! 1) Big Universe of Galaxies 2) Sky is Dark at Night 3) Isotropy of Universe Cosmological Principle = Universe Homogeneous 4) Hubble Expansion of Universe 5) Cosmic Microwave Background (CMB) 6) Composition of Universe

12 Cosmology - Standard Models ASTR 2120 Sarazin Positive and Negative Curvature

13 No Dark Energy Work started with Einstein, after development of General Relativity (~1920)

14 No Dark Energy Work started with Einstein, after development of General Relativity (~1920) Contributions from desitter, Lemaitre, Friedmann, others

15 No Dark Energy Gravity decelerates expansion v = H (t) r dh dt 0

16 No Dark Energy Standard Models assume: 1) Cosmological Principle Averaged over a large volume <density>, etc. the same everywhere at the same time Co-moving frame: Measure properties, time in frame moving at <v> for that location (= rest frame of CMB) Cosmic time t: measure in co-moving frame start t = 0 at Big Bang

17 No Dark Energy Standard Models assume: 1) Cosmological Principle History is universal <ρ> = ρ(t) is the same everywhere

18 No Dark Energy Standard Models assume: 1) Cosmological Principle 2) Gravity = General Relativity Gravity due to curvature of spacetime Note: in HW, you show that there is NO solution in Newtonian gravity

19 No Dark Energy Standard Models assume: 1) Cosmological Principle 2) Gravity = General Relativity 3) Only force is gravity Only long range force known

20 No Dark Energy Standard Models assume: 1) Cosmological Principle 2) Gravity = General Relativity 3) Only force is gravity 4) Matter dominates over energy (Mass) c 2 >> Energy Universe is a cold gas of galaxies (now, Dark Matter)

21 No Dark Energy Standard Models assume: 1) Cosmological Principle 2) Gravity = General Relativity 3) Only force is gravity 4) Matter dominates over energy All consistent with all known physics, but... Observed expansion implies Dark Energy (accelerating expansion) - at least one assumption is wrong

22 General Relativity tensor calculus, differential geometry tough mathematics Then, a miracle occurs... Oh no, my head is going to explode!!

23 1) Cosmological Principle A Wonderful Trick a) Every small piece of Universe reflects history and dynamics of whole Universe b) The Universe is spherically symmetric about any point 2) Birkoff s Theorem (General Relativity), & Newton s Theorem Spherical symmetry solution only depends on interior mass Consider a small sphere Throw away the rest of Universe!!

24 A Wonderful Trick (Cont.) Dynamics of entire Universe is contained in the expansion of a small, isolated, uniform density sphere!! 3) Correspondence Principle: General Relativity Newtonian physics if v << c PE << rest mass energy 4) Small sphere: r << d H c / H 0 (~ size of observable Universe) v = H r H 0 r << c GM/r << c 2 General Relativity Newtonian physics M r

25 A Wonderful Trick (Cont.) Dynamics of entire Universe is contained in the Newtonian expansion of a small, isolated, uniform density sphere!! Consider a small test mass m on the surface of the sphere All mass interior, acts like at center, fixed potential Symmetry: motion is r purely radial M m r

26 No Dark Energy The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. ma = m dv dt = GMm r 2 Conservation of energy : 1 2 mv2 GMm = constant r v 2 2GM = 2 constant r m = constan t $ = Kr 2 o c 2 Let "o" denote present - time values. v 2 = 2GM r Kr o 2 c 2 Great - mass drops out M m r

27 No Dark Energy v 2 = 2GM r The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Kr o 2 c 2 M = 4π 3 r 3 ρ = 4π 3 r o3 ρ o = constant M r v = H(t)r, H o 2 r o 2 = 2G r o H o = v o = H o r o 4π 3 r 3 o ρ o Kr 2 o c 2 8πG 3 ρ o Kc2 Great - r o drops out gets Hubble law correct!

28 No Dark Energy The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. H o = 8πG 3 ρ o Kc 2 Constant K = 0 if ρ o = ρ crit, where 8πG 3 ρ 2 crit = H o ρ crit 3H 2 o 8πG ' H = 0.95 o * 10 29), ( 71 km/s/mpc+ Interesting - not too far from actual density! 2 gm/cm 3

29 No Dark Energy The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Define Ω M ρ o ρ crit K = H 2 o c 2 ( Ω M 1) = curvature of space K has units 1/cm 2, K ~ 1 d H 2 (from General Relativity)

30 Curvature - Review K K > K < Plane K = 0 Sphere K > 0 Saddle-shape K < 0 (hyperbolic)

31 No Dark Energy Going back : The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Going back : Kr 2 o c 2 v 2 = 2GM r v = dr dt % ' & dr dt ( * ) 2 M = 4π 3 r 3 o ρ o = 8πGr 3 o ρ o 3r Divide by r o 2 +, - d(r /r o ) dt. / 0 2 = 8πGρ o 3 Kr o 2 c 2 r o r Kc2 8πG 3 ρ = H 2 crit o 8πG 2 3 = H o Ω M ρ o ρ crit ρ o = Ω M ρ crit K = H 2 o c 2 ( ) * d(r /r o ) dt ( Ω M 1) +, - 2 ρ crit 2 r = Ω M H o o r + H 2 o ( 1 Ω M )

32 No Dark Energy The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. " # $ d(r /r o ) dt % & ' Take square root d(r /r o ) dt 2 2 r = Ω M H o o r + H 2 o ( 1 Ω M ) = H o Ω M (r /r o ) +1 Ω M Equation of Cosmic Dynamics Friedmann Equation Depends only on (r / r o ) small sphere drops out, (r / r o ) = any size or distance in Universe relative to present H o t = t / t H, time scale is Hubble time

33 Metric - Review Distance: τ proper time time measured by observer following path in spacetime s c τ proper distance metric connects changes in s or τ to small changes in coordinates ct r x

34 Robertson-Walker Metric Assuming only Cosmological Principle (spherical coordinates) ( ds) 2 = ( cdt) 2 # % $ dr 1 K r 2 & ( ' 2 ( r dθ) 2 ( r sinθ dφ) 2 K = K(t) curvature of space, function of cosmic time

35 No Dark Energy The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Returning to the Standard Models and the Equation of Cosmic Dynamics: d(r /r o ) dt = H o Ω M (r /r o ) +1 Ω M Ω M ρ o ρ crit K = H 2 o c 2 ( Ω M 1) Three cases : Ω M =1, Ω M <1, Ω M >1

36 No Dark Energy The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Ω M =1, K = 0, ρ o = ρ crit d(r /r o ) dt Ω = H M o (r /r o ) +1 Ω = H (r /r M o o ) 1/2 (r /r o ) 1/2 d(r /r o ) = H o dt 2 3(r /r o ) 3/2 = H o t + constant = H o t Cosmic time r = 0 at t = 0 & r ) ( + = 3H t 2/3 & ) o ( + ' r o * ' 2 * Today r = r o t o = ( 2 3)H 1 0 = ( 2 3)t H 1 1

37 No Dark Energy The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Ω M <1, K < 0, ρ o < ρ crit $ & % r r o ' ) = Ω $ M 1 sinh 2 & ( 1 Ω M % 2 θ ' ) ( H o t = Ω M sinh( θ) θ ( ) 3/2 2 1 Ω M [ ] parametric solution Today ( 2 3)t H < t o t H

38 No Dark Energy The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Ω M >1, K > 0, ρ o > ρ crit $ & % r r o ' ) = Ω $ M 1 ( Ω M 1 sin2 & % 2 θ ' ) ( H o t = Ω M 2 Ω M 1 ( ) Today t o < ( 2 3)t H θ sin θ 3/2 [ ( )] parametric solution Note: Ω M <1 Ω M >1 with θ iθ

39 No Dark Energy The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.

40 Expansion The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Ω M < 1 Ω M = 1 Ω M > 1

41 Expansion The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Analogy to ballistic motion on Earth (Mass = constant, sphere and Earth) v < v esc Ω M > 1 v = v esc Ω M = 1 v > v esc Ω M < 1

42 Deceleration Parameter Another notation q = deceleration parameter The image cannot be displayed. Your computer may have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. $ r(t) d 2 r(t) ' & dt 2 ) % ( q(t) 2 $ d r(t) ' % & dt ( ) q o present - time value Standard models w/o Dark Energy q o = Ω M 2 Ω M <1 q o <1 2 Ω M =1 q o =1 2 Ω M >1 q o >1 2

43 Current Age The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Given current expansion: higher mass more deceleration faster expansion in past smaller age

44 Current Age The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Age/Hubble time 2/3

45 Curvature and Shape The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Ω M > 1, K > 0 Uniform positive curvature space Sphere Finite, closed Universe Ω M < 1, K < 0 Uniform negative curvature space Hyperbolic Infinite, open Universe Ω M = 1, K = 0 Flat space, no curvature Infinite, open Universe

46 No Dark Energy The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Which model (if any) is correct?

Cosmology Dark Energy Models ASTR 2120 Sarazin

Cosmology Dark Energy Models ASTR 2120 Sarazin Cosmology Dark Energy Models ASTR 2120 Sarazin Late Homeworks Last day Wednesday, May 1 My mail box in ASTR 204 Maximum credit 50% unless excused (but, better than nothing) Final Exam Thursday, May 2,

More information

Tuesday: Special epochs of the universe (recombination, nucleosynthesis, inflation) Wednesday: Structure formation

Tuesday: Special epochs of the universe (recombination, nucleosynthesis, inflation) Wednesday: Structure formation Introduction to Cosmology Professor Barbara Ryden Department of Astronomy The Ohio State University ICTP Summer School on Cosmology 2016 June 6 Today: Observational evidence for the standard model of cosmology

More information

Astr 2320 Tues. May 2, 2017 Today s Topics Chapter 23: Cosmology: The Big Bang and Beyond Introduction Newtonian Cosmology Solutions to Einstein s

Astr 2320 Tues. May 2, 2017 Today s Topics Chapter 23: Cosmology: The Big Bang and Beyond Introduction Newtonian Cosmology Solutions to Einstein s Astr 0 Tues. May, 07 Today s Topics Chapter : Cosmology: The Big Bang and Beyond Introduction Newtonian Cosmology Solutions to Einstein s Field Equations The Primeval Fireball Standard Big Bang Model Chapter

More information

Cosmology. Assumptions in cosmology Olber s paradox Cosmology à la Newton Cosmology à la Einstein Cosmological constant Evolution of the Universe

Cosmology. Assumptions in cosmology Olber s paradox Cosmology à la Newton Cosmology à la Einstein Cosmological constant Evolution of the Universe Cosmology Assumptions in cosmology Olber s paradox Cosmology à la Newton Cosmology à la Einstein Cosmological constant Evolution of the Universe Assumptions in Cosmology Copernican principle: We do not

More information

Cosmology. Thornton and Rex, Ch. 16

Cosmology. Thornton and Rex, Ch. 16 Cosmology Thornton and Rex, Ch. 16 Expansion of the Universe 1923 - Edwin Hubble resolved Andromeda Nebula into separate stars. 1929 - Hubble compared radial velocity versus distance for 18 nearest galaxies.

More information

Kinetic Theory of Dark Energy within General Relativity

Kinetic Theory of Dark Energy within General Relativity Kinetic Theory of Dark Energy within General Relativity Author: Nikola Perkovic* percestyler@gmail.com University of Novi Sad, Faculty of Sciences, Institute of Physics and Mathematics Abstract: This paper

More information

Cosmology. An Analogy 11/28/2010. Cosmology Study of the origin, evolution and future of the Universe

Cosmology. An Analogy 11/28/2010. Cosmology Study of the origin, evolution and future of the Universe Cosmology Cosmology Study of the origin, evolution and future of the Universe Obler s Paradox If the Universe is infinite why is the sky dark at night? Newtonian Universe The Universe is infinite and unchanging

More information

3.1 Cosmological Parameters

3.1 Cosmological Parameters 3.1 Cosmological Parameters 1 Cosmological Parameters Cosmological models are typically defined through several handy key parameters: Hubble Constant Defines the Scale of the Universe R 0 H 0 = slope at

More information

A Bit of History. Hubble s original redshiftdistance

A Bit of History. Hubble s original redshiftdistance XKCD: April 7, 2014 Cosmology Galaxies are lighthouses that trace the evolution of the universe with time We will concentrate primarily on observational cosmology (how do we measure important cosmological

More information

The early and late time acceleration of the Universe

The early and late time acceleration of the Universe The early and late time acceleration of the Universe Tomo Takahashi (Saga University) March 7, 2016 New Generation Quantum Theory -Particle Physics, Cosmology, and Chemistry- @Kyoto University The early

More information

Olbers Paradox. Lecture 14: Cosmology. Resolutions of Olbers paradox. Cosmic redshift

Olbers Paradox. Lecture 14: Cosmology. Resolutions of Olbers paradox. Cosmic redshift Lecture 14: Cosmology Olbers paradox Redshift and the expansion of the Universe The Cosmological Principle Ω and the curvature of space The Big Bang model Primordial nucleosynthesis The Cosmic Microwave

More information

2.1 Basics of the Relativistic Cosmology: Global Geometry and the Dynamics of the Universe Part I

2.1 Basics of the Relativistic Cosmology: Global Geometry and the Dynamics of the Universe Part I 1 2.1 Basics of the Relativistic Cosmology: Global Geometry and the Dynamics of the Universe Part I 2 Special Relativity (1905) A fundamental change in viewing the physical space and time, now unified

More information

VU lecture Introduction to Particle Physics. Thomas Gajdosik, FI & VU. Big Bang (model)

VU lecture Introduction to Particle Physics. Thomas Gajdosik, FI & VU. Big Bang (model) Big Bang (model) What can be seen / measured? basically only light _ (and a few particles: e ±, p, p, ν x ) in different wave lengths: microwave to γ-rays in different intensities (measured in magnitudes)

More information

Model Universe Including Pressure

Model Universe Including Pressure Model Universe Including Pressure The conservation of mass within the expanding shell was described by R 3 ( t ) ρ ( t ) = ρ 0 We now assume an Universe filled with a fluid (dust) of uniform density ρ,

More information

Cosmology: An Introduction. Eung Jin Chun

Cosmology: An Introduction. Eung Jin Chun Cosmology: An Introduction Eung Jin Chun Cosmology Hot Big Bang + Inflation. Theory of the evolution of the Universe described by General relativity (spacetime) Thermodynamics, Particle/nuclear physics

More information

Redshift-Distance Relationships

Redshift-Distance Relationships Redshift-Distance Relationships George Jones April 4, 0. Distances in Cosmology This note considers two conceptually important definitions of cosmological distances, look-back distance and proper distance.

More information

The Early Universe: A Journey into the Past

The Early Universe: A Journey into the Past Gravity: Einstein s General Theory of Relativity The Early Universe A Journey into the Past Texas A&M University March 16, 2006 Outline Gravity: Einstein s General Theory of Relativity Galileo and falling

More information

The Early Universe: A Journey into the Past

The Early Universe: A Journey into the Past The Early Universe A Journey into the Past Texas A&M University March 16, 2006 Outline Galileo and falling bodies Galileo Galilei: all bodies fall at the same speed force needed to accelerate a body is

More information

Cosmology - Redshift and Radiation ASTR 2120 Sarazin

Cosmology - Redshift and Radiation ASTR 2120 Sarazin Cosmology - Redshift and Radiation ASTR 2120 Sarazin Test #1 Monday, February 26, 11-11:50 am ASTR 265 (classroom) Bring pencils, paper, calculator You may not consult the text, your notes, or any other

More information

26. Cosmology. Significance of a dark night sky. The Universe Is Expanding

26. Cosmology. Significance of a dark night sky. The Universe Is Expanding 26. Cosmology Significance of a dark night sky The Universe is expanding The Big Bang initiated the expanding Universe Microwave radiation evidence of the Big Bang The Universe was initially hot & opaque

More information

Physics 133: Extragalactic Astronomy and Cosmology

Physics 133: Extragalactic Astronomy and Cosmology Physics 133: Extragalactic Astronomy and Cosmology Week 2 Spring 2018 Previously: Empirical foundations of the Big Bang theory. II: Hubble s Law ==> Expanding Universe CMB Radiation ==> Universe was hot

More information

Ay1 Lecture 17. The Expanding Universe Introduction to Cosmology

Ay1 Lecture 17. The Expanding Universe Introduction to Cosmology Ay1 Lecture 17 The Expanding Universe Introduction to Cosmology 17.1 The Expanding Universe General Relativity (1915) A fundamental change in viewing the physical space and time, and matter/energy Postulates

More information

The Friedmann Equation R = GM R 2. R(t) R R = GM R GM R. d dt. = d dt 1 2 R 2 = GM R + K. Kinetic + potential energy per unit mass = constant

The Friedmann Equation R = GM R 2. R(t) R R = GM R GM R. d dt. = d dt 1 2 R 2 = GM R + K. Kinetic + potential energy per unit mass = constant The Friedmann Equation R = GM R R R = GM R R R(t) d dt 1 R = d dt GM R M 1 R = GM R + K Kinetic + potential energy per unit mass = constant The Friedmann Equation 1 R = GM R + K M = ρ 4 3 π R3 1 R = 4πGρR

More information

Third Year: General Relativity and Cosmology. 1 Problem Sheet 1 - Newtonian Gravity and the Equivalence Principle

Third Year: General Relativity and Cosmology. 1 Problem Sheet 1 - Newtonian Gravity and the Equivalence Principle Third Year: General Relativity and Cosmology 2011/2012 Problem Sheets (Version 2) Prof. Pedro Ferreira: p.ferreira1@physics.ox.ac.uk 1 Problem Sheet 1 - Newtonian Gravity and the Equivalence Principle

More information

Lecture 16 : Cosmological Models I

Lecture 16 : Cosmological Models I Lecture 16 : Cosmological Models I Hubble s law and redshift in the new picture Standard cosmological models - 3 cases Hubble time and other terminology The Friedmann equation The Critical Density and

More information

THE DARK SIDE OF THE COSMOLOGICAL CONSTANT

THE DARK SIDE OF THE COSMOLOGICAL CONSTANT THE DARK SIDE OF THE COSMOLOGICAL CONSTANT CAMILO POSADA AGUIRRE University of South Carolina Department of Physics and Astronomy 09/23/11 Outline 1 Einstein s Greatest Blunder 2 The FLRW Universe 3 A

More information

Implications of the Hubble Law: - it is not static, unchanging - Universe had a beginning!! - could not have been expanding forever HUBBLE LAW:

Implications of the Hubble Law: - it is not static, unchanging - Universe had a beginning!! - could not have been expanding forever HUBBLE LAW: Cosmology and the Evolution of the Universe Edwin Hubble, 1929: -almost all galaxies have a redshift -moving away from us -greater distance greater redshift Implications of the Hubble Law: - Universe is

More information

Cosmology and the Evolution of the Universe. Implications of the Hubble Law: - Universe is changing (getting bigger!) - it is not static, unchanging

Cosmology and the Evolution of the Universe. Implications of the Hubble Law: - Universe is changing (getting bigger!) - it is not static, unchanging Cosmology and the Evolution of the Edwin Hubble, 1929: -almost all galaxies have a redshift -moving away from us -exceptions in Local Group -with distance measurements - found a relationship greater distance

More information

Cosmology (Cont.) Lecture 19

Cosmology (Cont.) Lecture 19 Cosmology (Cont.) Lecture 19 1 General relativity General relativity is the classical theory of gravitation, and as the gravitational interaction is due to the structure of space-time, the mathematical

More information

The Expanding Universe

The Expanding Universe Cosmology Expanding Universe History of the Universe Cosmic Background Radiation The Cosmological Principle Cosmology and General Relativity Dark Matter and Dark Energy Primitive Cosmology If the universe

More information

Astronomy 182: Origin and Evolution of the Universe

Astronomy 182: Origin and Evolution of the Universe Astronomy 182: Origin and Evolution of the Universe Prof. Josh Frieman Lecture 7 Oct. 30, 2015 Today Relativistic Cosmology Dark Side of the Universe I: Dark Matter Assignments This week: read Hawley and

More information

Lecture 2: Cosmological Background

Lecture 2: Cosmological Background Lecture 2: Cosmological Background Houjun Mo January 27, 2004 Goal: To establish the space-time frame within which cosmic events are to be described. The development of spacetime concept Absolute flat

More information

PAPER 71 COSMOLOGY. Attempt THREE questions There are seven questions in total The questions carry equal weight

PAPER 71 COSMOLOGY. Attempt THREE questions There are seven questions in total The questions carry equal weight MATHEMATICAL TRIPOS Part III Friday 31 May 00 9 to 1 PAPER 71 COSMOLOGY Attempt THREE questions There are seven questions in total The questions carry equal weight You may make free use of the information

More information

Introduction. How did the universe evolve to what it is today?

Introduction. How did the universe evolve to what it is today? Cosmology 8 1 Introduction 8 2 Cosmology: science of the universe as a whole How did the universe evolve to what it is today? Based on four basic facts: The universe expands, is isotropic, and is homogeneous.

More information

Introduction to Cosmology

Introduction to Cosmology Introduction to Cosmology João G. Rosa joao.rosa@ua.pt http://gravitation.web.ua.pt/cosmo LECTURE 2 - Newtonian cosmology I As a first approach to the Hot Big Bang model, in this lecture we will consider

More information

General Relativity ASTR 2110 Sarazin. Einstein s Equation

General Relativity ASTR 2110 Sarazin. Einstein s Equation General Relativity ASTR 2110 Sarazin Einstein s Equation Curvature of Spacetime 1. Principle of Equvalence: gravity acceleration locally 2. Acceleration curved path in spacetime In gravitational field,

More information

Modeling the Universe Chapter 11 Hawley/Holcomb. Adapted from Dr. Dennis Papadopoulos UMCP

Modeling the Universe Chapter 11 Hawley/Holcomb. Adapted from Dr. Dennis Papadopoulos UMCP Modeling the Universe Chapter 11 Hawley/Holcomb Adapted from Dr. Dennis Papadopoulos UMCP Spectral Lines - Doppler λ λ em 1+ z = obs z = λ obs λ λ em em Doppler Examples Doppler Examples Expansion Redshifts

More information

Astronomy, Astrophysics, and Cosmology

Astronomy, Astrophysics, and Cosmology Astronomy, Astrophysics, and Cosmology Luis A. Anchordoqui Department of Physics and Astronomy Lehman College, City University of New York Lesson VI March 15, 2016 arxiv:0706.1988 L. A. Anchordoqui (CUNY)

More information

Astroparticle physics the History of the Universe

Astroparticle physics the History of the Universe Astroparticle physics the History of the Universe Manfred Jeitler and Wolfgang Waltenberger Institute of High Energy Physics, Vienna TU Vienna, CERN, Geneva Wintersemester 2016 / 2017 1 The History of

More information

Is inflation really necessary in a closed Universe? Branislav Vlahovic, Maxim Eingorn. Please see also arxiv:

Is inflation really necessary in a closed Universe? Branislav Vlahovic, Maxim Eingorn. Please see also arxiv: Is inflation really necessary in a closed Universe? Branislav Vlahovic, Maxim Eingorn North Carolina Central University NASA University Research Centers, Durham NC Please see also arxiv:1303.3203 Chicago

More information

Galaxies 626. Lecture 3: From the CMBR to the first star

Galaxies 626. Lecture 3: From the CMBR to the first star Galaxies 626 Lecture 3: From the CMBR to the first star Galaxies 626 Firstly, some very brief cosmology for background and notation: Summary: Foundations of Cosmology 1. Universe is homogenous and isotropic

More information

PAPER 73 PHYSICAL COSMOLOGY

PAPER 73 PHYSICAL COSMOLOGY MATHEMATICAL TRIPOS Part III Wednesday 4 June 2008 1.30 to 4.30 PAPER 73 PHYSICAL COSMOLOGY Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight. STATIONERY

More information

6. Cosmology. (same at all points) probably true on a sufficiently large scale. The present. ~ c. ~ h Mpc (6.1)

6. Cosmology. (same at all points) probably true on a sufficiently large scale. The present. ~ c. ~ h Mpc (6.1) 6. 6. Cosmology 6. Cosmological Principle Assume Universe is isotropic (same in all directions) and homogeneous (same at all points) probably true on a sufficiently large scale. The present Universe has

More information

Large Scale Structure in the Universe

Large Scale Structure in the Universe Large Scale Structure in the Universe We seem to be located at the edge of a Local Supercluster, which contains dozens of clusters and groups over a 40 Mpc region. Galaxies and clusters seem to congregate

More information

Astronomy: The Big Picture. Outline. What does Hubble s Law mean?

Astronomy: The Big Picture. Outline. What does Hubble s Law mean? Last Homework is due Friday 11:50 am Honor credit need to have those papers this week! Estimated grades are posted. Does not include HW 8 or Extra Credit THE FINAL IS DECEMBER 15 th : 7-10pm! Astronomy:

More information

! Expansion of the Universe! Difference between expansion and explosion

! Expansion of the Universe! Difference between expansion and explosion This Class (Lecture 32): The Big Bang! Expansion of the Universe! Difference between expansion and explosion HW 11 due on Dec 5 th Music: The Universe Song Animaniacs! In a homogenous Universe, what does

More information

Cosmology. Jörn Wilms Department of Physics University of Warwick.

Cosmology. Jörn Wilms Department of Physics University of Warwick. Cosmology Jörn Wilms Department of Physics University of Warwick http://astro.uni-tuebingen.de/~wilms/teach/cosmo Contents 2 Old Cosmology Space and Time Friedmann Equations World Models Modern Cosmology

More information

Cosmology & the CMB - Cosmology: Overview - Cosmic Microwave Background - Large Scale Structure (Wed) - CMB Fluctuations (Wed)

Cosmology & the CMB - Cosmology: Overview - Cosmic Microwave Background - Large Scale Structure (Wed) - CMB Fluctuations (Wed) Oct 16, 2017 Cosmology & the CMB - Cosmology: Overview - Cosmic Microwave Background - Large Scale Structure (Wed) - CMB Fluctuations (Wed) Wednesday: HW#5 due History of the universe Discovery of Quasars

More information

AST1100 Lecture Notes

AST1100 Lecture Notes AST1100 Lecture Notes 23-24: Cosmology: models of the universe 1 The FRW-metric Cosmology is the study of the universe as a whole. In the lectures on cosmology we will look at current theories of how the

More information

New Blackhole Theorem and its Applications to Cosmology and Astrophysics

New Blackhole Theorem and its Applications to Cosmology and Astrophysics New Blackhole Theorem and its Applications to Cosmology and Astrophysics I. New Blackhole Theorem II. Structure of the Universe III. New Law of Gravity IV. PID-Cosmological Model Tian Ma, Shouhong Wang

More information

AST1100 Lecture Notes

AST1100 Lecture Notes AST1100 Lecture Notes 23-24: Cosmology: models of the universe 1 The FRW-metric Cosmology is the study of the universe as a whole. In the lectures on cosmology we will look at current theories of how the

More information

Chapter 17 Cosmology

Chapter 17 Cosmology Chapter 17 Cosmology Over one thousand galaxies visible The Universe on the Largest Scales No evidence of structure on a scale larger than 200 Mpc On very large scales, the universe appears to be: Homogenous

More information

General Relativity Lecture 20

General Relativity Lecture 20 General Relativity Lecture 20 1 General relativity General relativity is the classical (not quantum mechanical) theory of gravitation. As the gravitational interaction is a result of the structure of space-time,

More information

You may not start to read the questions printed on the subsequent pages until instructed to do so by the Invigilator.

You may not start to read the questions printed on the subsequent pages until instructed to do so by the Invigilator. MATHEMATICAL TRIPOS Part III Thursday 3 June, 2004 9 to 12 PAPER 67 PHYSICAL COSMOLOGY Attempt THREE questions. There are four questions in total. The questions carry equal weight. You may not start to

More information

Island Universes. Up to 1920 s, many thought that Milky Way encompassed entire universe.

Island Universes. Up to 1920 s, many thought that Milky Way encompassed entire universe. Island Universes Up to 1920 s, many thought that Milky Way encompassed entire universe. Observed three types of nebulas (clouds): - diffuse, spiral, elliptical - many were faint, indistinct - originally

More information

Lecture Outlines. Chapter 26. Astronomy Today 8th Edition Chaisson/McMillan Pearson Education, Inc.

Lecture Outlines. Chapter 26. Astronomy Today 8th Edition Chaisson/McMillan Pearson Education, Inc. Lecture Outlines Chapter 26 Astronomy Today 8th Edition Chaisson/McMillan Chapter 26 Cosmology Units of Chapter 26 26.1 The Universe on the Largest Scales 26.2 The Expanding Universe 26.3 The Fate of the

More information

Unication models of dark matter and dark energy

Unication models of dark matter and dark energy Unication models of dark matter and dark energy Neven ƒaplar March 14, 2012 Neven ƒaplar () Unication models March 14, 2012 1 / 25 Index of topics Some basic cosmology Unication models Chaplygin gas Generalized

More information

CH 14 MODERN COSMOLOGY The Study of Nature, origin and evolution of the universe Does the Universe have a center and an edge? What is the evidence

CH 14 MODERN COSMOLOGY The Study of Nature, origin and evolution of the universe Does the Universe have a center and an edge? What is the evidence CH 14 MODERN COSMOLOGY The Study of Nature, origin and evolution of the universe Does the Universe have a center and an edge? What is the evidence that the Universe began with a Big Bang? How has the Universe

More information

Astronomy 122 Outline

Astronomy 122 Outline Astronomy 122 Outline This Class (Lecture 26): The Primeval Fireball Next Class: Dark Matter & Dark Energy ICES Form!!! HW10 due Friday Hubble s Law implications An expanding Universe! Run in movie in

More information

Testing the Big Bang Idea

Testing the Big Bang Idea Reading: Chapter 29, Section 29.2-29.6 Third Exam: Tuesday, May 1 12:00-2:00 COURSE EVALUATIONS - please complete these online (recitation and lecture) Last time: Cosmology I - The Age of the & the Big

More information

Arvind Borde / MTH 675, Unit 20: Cosmology

Arvind Borde / MTH 675, Unit 20: Cosmology Arvind Borde / MTH 675, Unit 20: Cosmology 1. Review (1) What do we do when we do GR? We try to solve Einstein s equation. (2) What is Einstein s equation? and R ab = e[ 1 2 ged ( a g bd + b g ad d g ab

More information

Astronomy 114. Lecture35:TheBigBang. Martin D. Weinberg. UMass/Astronomy Department

Astronomy 114. Lecture35:TheBigBang. Martin D. Weinberg. UMass/Astronomy Department Astronomy 114 Lecture35:TheBigBang Martin D. Weinberg weinberg@astro.umass.edu UMass/Astronomy Department A114: Lecture 35 09 May 2005 Read: Ch. 28,29 Astronomy 114 1/18 Announcements PS#8 due Monday!

More information

A A + B. ra + A + 1. We now want to solve the Einstein equations in the following cases:

A A + B. ra + A + 1. We now want to solve the Einstein equations in the following cases: Lecture 29: Cosmology Cosmology Reading: Weinberg, Ch A metric tensor appropriate to infalling matter In general (see, eg, Weinberg, Ch ) we may write a spherically symmetric, time-dependent metric in

More information

II. The Universe Around Us. ASTR378 Cosmology : II. The Universe Around Us 23

II. The Universe Around Us. ASTR378 Cosmology : II. The Universe Around Us 23 II. The Universe Around Us ASTR378 Cosmology : II. The Universe Around Us 23 Some Units Used in Astronomy 1 parsec distance at which parallax angle is 1 ; 1 pc = 3.086 10 16 m ( 3.26 light years; 1 kpc

More information

Modeling the Universe A Summary

Modeling the Universe A Summary Modeling the Universe A Summary Questions to Consider 1. What does the darkness of the night sky tell us about the nature of the universe? 2. As the universe expands, what, if anything, is it expanding

More information

8. The Expanding Universe, Revisited

8. The Expanding Universe, Revisited 8. The Expanding Universe, Revisited A1143: History of the Universe, Autumn 2012 Now that we have learned something about Einstein s theory of gravity, we are ready to revisit what we have learned about

More information

FURTHER COSMOLOGY Book page T H E M A K E U P O F T H E U N I V E R S E

FURTHER COSMOLOGY Book page T H E M A K E U P O F T H E U N I V E R S E FURTHER COSMOLOGY Book page 675-683 T H E M A K E U P O F T H E U N I V E R S E COSMOLOGICAL PRINCIPLE Is the Universe isotropic or homogeneous? There is no place in the Universe that would be considered

More information

Physics 133: Extragalactic Astronomy ad Cosmology

Physics 133: Extragalactic Astronomy ad Cosmology Physics 133: Extragalactic Astronomy ad Cosmology Lecture 4; January 15 2014 Previously The dominant force on the scale of the Universe is gravity Gravity is accurately described by the theory of general

More information

B. The blue images are a single BACKGROUND galaxy being lensed by the foreground cluster (yellow galaxies)

B. The blue images are a single BACKGROUND galaxy being lensed by the foreground cluster (yellow galaxies) ASTR 1040 Accel Astro: Stars & Galaxies Today s s `Cosmological Events Look at models for our universe,, and what prompted ideas about big-bang bang beginnings Cosmic Microwave Background Simulation: Large-scale

More information

Outline. Covers chapter 2 + half of chapter 3 in Ryden

Outline. Covers chapter 2 + half of chapter 3 in Ryden Outline Covers chapter + half of chapter 3 in Ryden The Cosmological Principle I The cosmological principle The Cosmological Principle II Voids typically 70 Mpc across The Perfect Cosmological Principle

More information

Cosmology: The History of the Universe

Cosmology: The History of the Universe Cosmology: The History of the Universe The Universe originated in an explosion called the Big Bang. Everything started out 13.7 billion years ago with zero size and infinite temperature. Since then, it

More information

Physics 133: Extragalactic Astronomy ad Cosmology

Physics 133: Extragalactic Astronomy ad Cosmology Physics 133: Extragalactic Astronomy ad Cosmology Lecture 2; January 8 2014 Previously on PHYS133 Units in astrophysics Olbers paradox The night sky is dark. Inconsistent with and eternal, static and infinite

More information

PROBLEM SET 6 EXTRA CREDIT PROBLEM SET

PROBLEM SET 6 EXTRA CREDIT PROBLEM SET MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.286: The Early Universe May 3, 2004 Prof. Alan Guth PROBLEM SET 6 EXTRA CREDIT PROBLEM SET CAN BE HANDED IN THROUGH: Thursday, May 13,

More information

Introduction to Inflation

Introduction to Inflation Introduction to Inflation Miguel Campos MPI für Kernphysik & Heidelberg Universität September 23, 2014 Index (Brief) historic background The Cosmological Principle Big-bang puzzles Flatness Horizons Monopoles

More information

Astro Assignment 1 on course web page (due 15 Feb) Instructors: Jim Cordes & Shami Chatterjee

Astro Assignment 1 on course web page (due 15 Feb) Instructors: Jim Cordes & Shami Chatterjee Astro 2299 The Search for Life in the Universe Lecture 4 This time: Redshifts and the Hubble Law Hubble law and the expanding universe The cosmic microwave background (CMB) The elements and the periodic

More information

Lecture 1 General relativity and cosmology. Kerson Huang MIT & IAS, NTU

Lecture 1 General relativity and cosmology. Kerson Huang MIT & IAS, NTU A Superfluid Universe Lecture 1 General relativity and cosmology Kerson Huang MIT & IAS, NTU Lecture 1. General relativity and cosmology Mathematics and physics Big bang Dark energy Dark matter Robertson-Walker

More information

Lecture 14: Cosmological Principles

Lecture 14: Cosmological Principles Lecture 14: Cosmological Principles The basic Cosmological Principles The geometry of the Universe The scale factor R and curvature constant k Comoving coordinates Einstein s initial solutions 3/28/11

More information

6. Cosmology. (same at all points)ñprobably true on a sufficiently large scale. The present. (h ~ 0.7) 2 g cm. -29 h. Scale L Object Mass L/R H

6. Cosmology. (same at all points)ñprobably true on a sufficiently large scale. The present. (h ~ 0.7) 2 g cm. -29 h. Scale L Object Mass L/R H 6. 6. Cosmology 6. Cosmological Principle Assume Universe is isotropic (same in all directions) and homogeneous (same at all points)ñprobably true on a sufficiently large scale. The present Universe has

More information

The Big Bang. Olber s Paradox. Hubble s Law. Why is the night sky dark? The Universe is expanding and We cannot see an infinite Universe

The Big Bang. Olber s Paradox. Hubble s Law. Why is the night sky dark? The Universe is expanding and We cannot see an infinite Universe The Big Bang Olber s Paradox Why is the night sky dark? The Universe is expanding and We cannot see an infinite Universe Hubble s Law v = H0 d v = recession velocity in km/sec d = distance in Mpc H 0 =

More information

The Cosmological Principle

The Cosmological Principle Cosmological Models John O Byrne School of Physics University of Sydney Using diagrams and pp slides from Seeds Foundations of Astronomy and the Supernova Cosmology Project http://www-supernova.lbl.gov

More information

PROBLEM SET 10 (The Last!)

PROBLEM SET 10 (The Last!) MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.286: The Early Universe December 8, 2016 Prof. Alan Guth PROBLEM SET 10 (The Last!) DUE DATE: Wednesday, December 14, 2016, at 4:00 pm.

More information

Cosmology: Building the Universe.

Cosmology: Building the Universe. Cosmology: Building the Universe. The term has several different meanings. We are interested in physical cosmology - the study of the origin and development of the physical universe, and all the structure

More information

Why is the Universe Expanding?

Why is the Universe Expanding? Why is the Universe Expanding? In general relativity, mass warps space. Warped space makes matter move, which changes the structure of space. Thus the universe should be dynamic! Gravity tries to collapse

More information

Cosmic Microwave Background

Cosmic Microwave Background Cosmic Microwave Background Following recombination, photons that were coupled to the matter have had very little subsequent interaction with matter. Now observed as the cosmic microwave background. Arguably

More information

Uniformity of the Universe

Uniformity of the Universe Outline Universe is homogenous and isotropic Spacetime metrics Friedmann-Walker-Robertson metric Number of numbers needed to specify a physical quantity. Energy-momentum tensor Energy-momentum tensor of

More information

Week 2 Part 2. The Friedmann Models: What are the constituents of the Universe?

Week 2 Part 2. The Friedmann Models: What are the constituents of the Universe? Week Part The Friedmann Models: What are the constituents of the Universe? We now need to look at the expansion of the Universe described by R(τ) and its derivatives, and their relation to curvature. For

More information

1 Cosmological Principle

1 Cosmological Principle Notes on Cosmology April 2014 1 Cosmological Principle Now we leave behind galaxies and beginning cosmology. Cosmology is the study of the Universe as a whole. It concerns topics such as the basic content

More information

Problem Set 8 (Cosmology)

Problem Set 8 (Cosmology) Massachusetts Institute of Technology Department of Physics Physics 8.033 Out: Friday 3 November 2006 Due: Friday 17 November 2006 Problem Set 8 (Cosmology) Due: Friday 17 November 2006 at 4:00PM. Please

More information

The Dawn of Time - II. A Cosmos is Born

The Dawn of Time - II. A Cosmos is Born The Dawn of Time - II. A Cosmos is Born Learning Objectives! Why does Olbers paradox show the Universe began?! How does Hubble s Law tell us the age of the Universe? If Hubble s Constant is large, is the

More information

Chapter 1 Introduction. Particle Astrophysics & Cosmology SS

Chapter 1 Introduction. Particle Astrophysics & Cosmology SS Chapter 1 Introduction Particle Astrophysics & Cosmology SS 2008 1 Ptolemäus (85 165 b.c.) Kopernicus (1473 1543) Kepler (1571 1630) Newton (1643 1727) Kant (1724 1630) Herschel (1738 1822) Einstein (1917)

More information

Cosmology: The Origin and Evolution of the Universe Chapter Twenty-Eight. Guiding Questions

Cosmology: The Origin and Evolution of the Universe Chapter Twenty-Eight. Guiding Questions Cosmology: The Origin and Evolution of the Universe Chapter Twenty-Eight Guiding Questions 1. What does the darkness of the night sky tell us about the nature of the universe? 2. As the universe expands,

More information

Lecture 37 Cosmology [not on exam] January 16b, 2014

Lecture 37 Cosmology [not on exam] January 16b, 2014 1 Lecture 37 Cosmology [not on exam] January 16b, 2014 2 Structure of the Universe Does clustering of galaxies go on forever? Looked at very narrow regions of space to far distances. On large scales the

More information

In the expanding Universe, a comoving volume element expands along with the cosmological flow, getting physically larger over time.

In the expanding Universe, a comoving volume element expands along with the cosmological flow, getting physically larger over time. Cosmological models In the expanding Universe, a comoving volume element expands along with the cosmological flow, getting physically larger over time. The expansion is described by the scale factor R(t).

More information

Lecture 34. General relativity

Lecture 34. General relativity Lecture 34 The Shape of Space General Relativity Curvature of Space Critical Density Dark Energy Apr 17, 2006 Astro 100 Lecture 34 1 General relativity So far, just needed simple Newton's Gravity. Because

More information

Hubble's Law. H o = 71 km/s / Mpc. The further a galaxy is away, the faster it s moving away from us. V = H 0 D. Modern Data.

Hubble's Law. H o = 71 km/s / Mpc. The further a galaxy is away, the faster it s moving away from us. V = H 0 D. Modern Data. Cosmology Cosmology is the study of the origin and evolution of the Universe, addressing the grandest issues: How "big" is the Universe? Does it have an "edge"? What is its large-scale structure? How did

More information

Lecture 05. Cosmology. Part I

Lecture 05. Cosmology. Part I Cosmology Part I What is Cosmology Cosmology is the study of the universe as a whole It asks the biggest questions in nature What is the content of the universe: Today? Long ago? In the far future? How

More information

12. Relativistic Cosmology I. Simple Solutions to the Einstein Equations

12. Relativistic Cosmology I. Simple Solutions to the Einstein Equations 12. Relativistic Cosmology I. Simple Solutions to the Einstein Equations 1. Minkowski space Initial assumptions:! no matter (T µν = 0)! no gravitation (R σ µνρ = 0; i.e., zero curvature) Not realistic!

More information

Physics Nobel Prize 2006

Physics Nobel Prize 2006 Physics Nobel Prize 2006 Ghanashyam Date The Institute of Mathematical Sciences, Chennai http://www.imsc.res.in shyam@imsc.res.in Nov 4, 2006. Organization of the Talk Organization of the Talk Nobel Laureates

More information

Cosmology ESP. Kevin Janeiro. May 26, 2015

Cosmology ESP. Kevin Janeiro. May 26, 2015 Cosmology ESP Kevin Janeiro May 26, 2015 1 Contents 1 Abstract 2 2 Fundamental Assumptions and Principles 2 2.1 The Cosmological Principle................... 2 2.2 Olbers Paradox..........................

More information

Set 3: Cosmic Dynamics

Set 3: Cosmic Dynamics Set 3: Cosmic Dynamics FRW Dynamics This is as far as we can go on FRW geometry alone - we still need to know how the scale factor a(t) evolves given matter-energy content General relativity: matter tells

More information