Origin of Structure Formation of Structure. Projected slice of 200,000 galaxies, with thickness of a few degrees.
|
|
- Beverly Norris
- 6 years ago
- Views:
Transcription
1 Origin of Structure Formation of Structure Projected slice of 200,000 galaxies, with thickness of a few degrees.
2 Redshift Surveys Modern survey: Sloan Digital Sky Survey, probes out to nearly 1000 Mpc. 800 Mpc 400 Mpc Earth Structures limited to linear dimensions <~ 100 h -1 Mpc. Universe is homogeneous if averaged over scales >~ 200 Mpc. On smaller scales, Universe is very inhomogeneous. There is structure. Courtesy of Michael Blanton.
3 Origin of Structure Global Projection of the Earth s Map
4 COBE/DIRBE Satellite Black Body T=2.725 K
5 COBE/DIRBE Satellite Thermal component subtracted, ΔT=3.353 mk
6 COBE/DIRBE Satellite Dipole component subtracted, ΔT = 18 μk
7 Origin of Structure WMAP image
8 Fluctuations are ΔT/T ~ Universe had inhomogeneities at z~1000. Origin of Structure WMAP image All components removed but background fluctuations
9 Dark Matter evolves under influence of gravitational physics millennium simulation of structure formation courtesy V. Springel
10 Dark Matter evolves under influence of gravitational physics millennium simulation of structure formation courtesy V. Springel
11 Dark Matter evolves under influence of galaxy clusters gravitational physics clustering amplitude ΛCDM prediction galaxy groups galaxies object number density Papovich (2008)
12 At z~1000, fluctuations were ~10-5. Gravity will cause positive fluctuations to grow with time. Today, massive clusters are more than 200x the critical density. (Galaxies, planets are even larger overdensities). Define Density Fluctuation as δ(r, t) = ρ(r, t) ρ(t) ρ(t) where ρ(t) is mean cosmic matter density at time t. From this definition, δ > -1 because ρ > 0. At z ~ 1000, δ << 1 because, ΔT/T~ Dynamics of cosmic expansion is dictated by ρ, whereas the density fluctuations, δ, generate an additional gravitational field that affects local dynamics.
13 Consider region with δ > 0, so that gravity is stronger than average. Extra gravity means this region expands slowly than cosmic mean. Hence the contrast in this region increases. As relative density increases, region expands less slowly, and so on. This causes a Gravitational Instability.
14 Equations of Motion. Continuity Equation ρ t + (ρv) =0 Euler Equation v t +(v )v = P ρ Φ Here the potential gradient is the gravitational field, which satisfies the Poisson equation: 2 Φ=4πGρ And again we assume pressureless dust, so P = 0. For δ << 1 these 3 equations can be solved analytically (for this approximation). Otherwise we resort to N- body simulations.
15 Equations of Motion. Consider the problem in comoving coordinates, where r = a(t) x. v(r,t)=ȧ a r + u( r a,t) First term is cosmic expansion, 2nd term is peculiar velocity, which describes deviations from homogeneous expansion. Transform other equations from partial derivatives in time with fixed r to partial derivations in time with fixed x. Define ρx(x,t) = ρ(ax,t), etc.
16 Continuity Equation Now use notation, ρx=ρ, and δx=δ, and note that partial derivatives w.r.t. time imply fixed x. ρ = ρ(1 + δ) ρ a 3 Yields: Gravitational Potential is 1st term is potential for homogeneous density field, and 2nd term satisfies
17 In the homogeneous case, δ=0, u=0, ϕ=0, ρ=ρ Equations above imply ρ +3H ρ =0 ( Which we derived earlier from the 1st law of Thermodynamics for a pressureless expansion. ) Now consider approximate solutions from small deviations in density. 1st order approximation : keep 1st order terms in δ and u (disregard higher order terms uδ or u 2
18 Euler Equation in Comoving coordinates becomes Combining this with the time derivative of for P=0 leads to this equation contains only derivatives w.r.t. time. Therefore, the solutions must have the form:
19 D(t) is the Growth Factor, and satisfies the equation: General solutions are D(t) ~ t 2/3 and D(t) ~ t -1. Growing solution will dominate at late times, and decaying solution will be irrelevant. Normalizing D(t0) = 1 forces density contrast to be δ(x,t)=d(t) δ 0 (x) Linear Perturbation Theory yields: - Spatial Shape of density fluctuations is frozen in comoving coordinates. Only Amplitude increases as described by Growth Factor. - Growth factor D(t) follows simple differential equation, which depends on cosmological model.
20 Linear Perturbation Theory yields: - Spatial Shape of density fluctuations is frozen in comoving coordinates. Only Amplitude increases as described by Growth Factor. - Growth factor D(t) follows simple differential equation, which depends on cosmological model. D(a) H(a) H 0 a 0 [Ω m a 1 +Ω Λ a 2 (Ω m +Ω Λ 1)] 3/2 with the boundary condition D(t0) = D(a=1) = 1. Note!! δ0(x) would be the density fluctuations today if evolution was linear and δ0(x) << 1. This is clearly not going to be the case for virialized structures. Therefore, we refer to δ0(x) as the linearly extrapolated density fluctuation field.
21 EXAMPLE: Consider the dynamics of an unperturbed region with the mean density of mass m = 4πρ0 a0 3 /3, expanding with the Universe. (Taken from Peebles 1980, and Lacey & Cole 1993). Dynamical equations are the following. (Assume no mass shells cross, so m is a constant here): a Mass m d 2 a dt 2 = Gm r 2 2 da = 2Gm dt a + C Dust For C > 0 (positive total energy), solution to these equations takes the form: a = A(cosh η 1), t = B(sinh η η) A where the constants are related by 3 B 2 =4πGρ 0a 3 0/3
22 EXAMPLE: Consider the dynamics of an unperturbed region with the mean density of mass m = 4πρ0 a0 3 /3, expanding with the Universe. a = A(cosh η 1), t = B(sinh η η) A 3 where the constants are related by B 2 =4πGρ 0a 3 0x 3 /3 The values of A and B are determined by present-day Hubble constant, H0 = (da/dt) / a and the density parameter Ω0=8πGρ0 / (3H0 2 ), and by choosing the present value of the radius r0 = a0 x. These give together: η 0 = cosh 1 (2Ω 1 0 1) B =(1/2)H 1 0 Ω 0 (1 Ω 0 ) 3/2
23 Now consider dynamics of the expansion and eventual recollapse of a perturbed overdense region with the same mass m as the region of the background universe with which it is being compared. r Mass m Parametric equations take the form: a p = A p (1 cos θ), t = B p (θ sin θ) where the constants are related to those for the unperturbed case by A 3 p B 2 p = A3 B 2 =4πGρ 0a 3 0x 3 /3
24 As time progresses, the perturbed region expands less rapidly than the background universe, and a density contrast develops, given by 1+δ = a 3 /a 3 p where δ = Δρ/ρ = (ρp - ρ)/ρ. The region collapses to a singularity (aka virialized, bound structure) when ap = 0 when θ = 2π. For t=bp(θ - sinθ) this yields, tcoll = 2πBp. We must now match solutions for perturbed region and the unperturbed expanding universe by considering their evolution when θ 0.
25 a = A η 2 2! + η4 4! +... t = B η 3 3! + η5 5! +... θ 2 a p = A p 2! θ4 4! +... θ 3 t = B p 3! θ5 5! +... Eliminating the parametric variables (with some algebra...) we get 2/3 t 6 2/3 2/3 a = A 1+ 62/3 t +... B B a p = A p t B p 2/3 6 2/ /3 20 t B p 2/3 +...
26 a = A Gravitational instabilities t B a p = A p t B p 2/3 6 2/3 20 2/3 6 2/ /3 Combined with 1+δ = (a/ap) 3 and keeping only terms to leading order gives δ = 3 2/3 2/3 62/ t 2/3 20 B p B 2/3 2/3 δ = 3(12π)2/ t 2/3 20 where we had defined t coll /3 20 2/3 t +... B 2/3 t +... B p t Ω =2πB = πh 1 0 Ω 0(1 Ω 0 ) 3/2 Therefore, we have shown that the perturbation grows as δ~t 2/3, the linear growing-mode solution. t Ω
27 δ = 3(12π)2/ t coll 2/3 + 1 t Ω 2/3 t 2/3 For Ω0=1, tω, and we have δ = 3(12π)2/3 20 t t coll 2/3 For spheres with tcoll = t0 we have at t=t0 that δ At later times t > tω the linear perturbation behavior departs from t 2/3, and the exact behavior follows (Peebles 1980): D(t) = And it can be shown that: 3 sinh η(sinh η η) (cosh η 1) 2 2 δ = 3 2 D(t) 1+ tω t coll 2/3
28 When the spherical perturbation collapses, we assume it reaches its virial equilibrium at then time tcoll when the expansion halts (ap=0) at a radius which is half of its radius at maximum expansion (θ=π). Therefore, 2 ρ 2π = (cosh η coll 1) 3 ρ vir sinh η coll η coll Compared to the critical density ρc = 3H(t) 2 / (8 πg) ρ =8π 2 (cosh η coll 1) 2 2 sinh η coll (sinh η coll η coll ) ρ c vir ηcoll << 1 (tcoll << tω) : ρvir = 18 π ρc ηcoll >> 1 (tcoll >> tω) : ρvir = 8 π 2 80 ρc
29 Kitayama & Suto (1996, ApJ, 469, 480) give other equations for ρvir as a function of cosmological parameters:
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 informationA5682: Introduction to Cosmology Course Notes. 11. CMB Anisotropy
Reading: Chapter 8, sections 8.4 and 8.5 11. CMB Anisotropy Gravitational instability and structure formation Today s universe shows structure on scales from individual galaxies to galaxy groups and clusters
More informationA5682: Introduction to Cosmology Course Notes. 11. CMB Anisotropy
Reading: Chapter 9, sections 9.4 and 9.5 11. CMB Anisotropy Gravitational instability and structure formation Today s universe shows structure on scales from individual galaxies to galaxy groups and clusters
More informationIntroduction 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 informationYou may not start to read the questions printed on the subsequent pages until instructed to do so by the Invigilator.
MATHEMATICAL TRIPOS Part III Friday 8 June 2001 1.30 to 4.30 PAPER 41 PHYSICAL COSMOLOGY Answer any THREE questions. The questions carry equal weight. You may not start to read the questions printed on
More informationNEWTONIAN COSMOLOGY. Figure 2.1: All observers see galaxies expanding with the same Hubble law. v A = H 0 r A (2.1)
M. Pettini: Introduction to Cosmology Lecture 2 NEWTONIAN COSMOLOGY The equations that describe the time evolution of an expanding universe which is homogeneous and isotropic can be deduced from Newtonian
More informationModel 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 informationWeek 3: Sub-horizon perturbations
Week 3: Sub-horizon perturbations February 12, 2017 1 Brief Overview Until now we have considered the evolution of a Universe that is homogeneous. Our Universe is observed to be quite homogeneous on large
More informationBeyond the spherical dust collapse model
Beyond the spherical dust collapse model 1.5M 1.0M M=1.66 10 15 M 0.65M 0.4M 0.25M Evolution of radii of different mass shells in a simulated halo Yasushi Suto Department of Physics and RESCEU (Research
More informationCosmology ASTR 2120 Sarazin. Hubble Ultra-Deep Field
Cosmology ASTR 2120 Sarazin Hubble Ultra-Deep Field Cosmology - Da Facts! 1) Big Universe of Galaxies 2) Sky is Dark at Night 3) Isotropy of Universe Cosmological Principle = Universe Homogeneous 4) Hubble
More informationPhysics 463, Spring 07. Formation and Evolution of Structure: Growth of Inhomogenieties & the Linear Power Spectrum
Physics 463, Spring 07 Lecture 3 Formation and Evolution of Structure: Growth of Inhomogenieties & the Linear Power Spectrum last time: how fluctuations are generated and how the smooth Universe grows
More informationIntroduction. 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 information6. 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 informationformation of the cosmic large-scale structure
formation of the cosmic large-scale structure Heraeus summer school on cosmology, Heidelberg 2013 Centre for Astronomy Fakultät für Physik und Astronomie, Universität Heidelberg August 23, 2013 outline
More informationDetecting Dark Energy Perturbations
H. K. Jassal IISER Mohali Ftag 2013, IIT Gandhinagar Outline 1 Overview Present day Observations Constraints on cosmological parameters 2 Theoretical Issues Clustering dark energy Integrated Sachs Wolfe
More informationCosmology. 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 informationModeling 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 informationPreliminaries. Growth of Structure. Today s measured power spectrum, P(k) Simple 1-D example of today s P(k) Growth in roughness: δρ/ρ. !(r) =!!
Growth of Structure Notes based on Teaching Company lectures, and associated undergraduate text with some additional material added. For a more detailed discussion, see the article by Peacock taken from
More information2. What are the largest objects that could have formed so far? 3. How do the cosmological parameters influence structure formation?
Einführung in die beobachtungsorientierte Kosmologie I / Introduction to observational Cosmology I LMU WS 2009/10 Rene Fassbender, MPE Tel: 30000-3319, rfassben@mpe.mpg.de 1. Cosmological Principles, Newtonian
More informationReally, really, what universe do we live in?
Really, really, what universe do we live in? Fluctuations in cosmic microwave background Origin Amplitude Spectrum Cosmic variance CMB observations and cosmological parameters COBE, balloons WMAP Parameters
More informationAstronomy, 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 informationThe Metric and The Dynamics
The Metric and The Dynamics r τ c t a () t + r + Sin φ ( kr ) The RW metric tell us where in a 3 dimension space is an event and at which proper time. The coordinates of the event do not change as a function
More informationCosmological Structure Formation
Cosmological Structure Formation Beyond linear theory Lagrangian PT: Zeldovich approximation (Eulerian PT: Spherical collapse) Redshift space distortions Recall linear theory: When radiation dominated
More informationFluctuations of cosmic parameters in the local universe
Fluctuations of cosmic parameters in the local universe Alexander Wiegand Dominik Schwarz Fakultät für Physik Universität Bielefeld 6. Kosmologietag, Bielefeld 2011 A. Wiegand (Universität Bielefeld) Fluctuations
More informationMATHEMATICAL TRIPOS Part III PAPER 53 COSMOLOGY
MATHEMATICAL TRIPOS Part III Wednesday, 8 June, 2011 9:00 am to 12:00 pm PAPER 53 COSMOLOGY Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight. STATIONERY
More informationStructure formation. Yvonne Y. Y. Wong Max-Planck-Institut für Physik, München
Structure formation Yvonne Y. Y. Wong Max-Planck-Institut für Physik, München Structure formation... Random density fluctuations, grow via gravitational instability galaxies, clusters, etc. Initial perturbations
More informationPhysical Cosmology 12/5/2017
Physical Cosmology 12/5/2017 Alessandro Melchiorri alessandro.melchiorri@roma1.infn.it slides can be found here: oberon.roma1.infn.it/alessandro/cosmo2017 Structure Formation Until now we have assumed
More informationUnication 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 informationTutorial II Newtonian Cosmology; Hubble Expansion
Tutorial II Newtonian Cosmology; Hubble Expansion Exercise I: Newtonian Cosmology In 1934 i.e. way after Friedman derived his equations- Milne and Mc- Crea showed that relations of the Friedman form can
More information3.1 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 informationNewtonian Gravity and Cosmology
Chapter 30 Newtonian Gravity and Cosmology The Universe is mostly empty space, which might suggest that a Newtonian description of gravity (which is valid in the weak gravity limit) is adequate for describing
More informationLarge Scale Structure
Large Scale Structure L2: Theoretical growth of structure Taking inspiration from - Ryden Introduction to Cosmology - Carroll & Ostlie Foundations of Astrophysics Where does structure come from? Initial
More informationA brief history of cosmological ideas
A brief history of cosmological ideas Cosmology: Science concerned with the origin and evolution of the universe, using the laws of physics. Cosmological principle: Our place in the universe is not special
More informationDark Matter and Cosmic Structure Formation
Dark Matter and Cosmic Structure Formation Prof. Luke A. Corwin PHYS 792 South Dakota School of Mines & Technology Jan. 23, 2014 (W2-2) L. Corwin, PHYS 792 (SDSM&T) DM & Cosmic Structure Jan. 23, 2014
More informationTheory of galaxy formation
Theory of galaxy formation Bibliography: Galaxy Formation and Evolution (Mo, van den Bosch, White 2011) Lectures given by Frank van den Bosch in Yale http://www.astro.yale.edu/vdbosch/teaching.html Theory
More informationLinear Theory and perturbations Growth
Linear Theory and perturbations Growth The Universe is not homogeneous on small scales. We want to study how seed perturbations (like the ones we see in the Cosmic Microwave Background) evolve in an expanding
More informationOutline. 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 informationGalaxies are not distributed randomly in space. 800 Mpc. 400 Mpc
Formation Origin of of Structure Galaxies are not distributed randomly in space. 800 Mpc 400 Mpc If one galaxy has comoving coordinate, x, then the probability of finding another galaxy in the vicinity
More informationAST1100 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 informationBackreaction as an explanation for Dark Energy?
Backreaction as an explanation for Dark Energy? with some remarks on cosmological perturbation theory James M. Bardeen University of Washington The Very Early Universe 5 Years On Cambridge, December 17,
More informationToday. Course Evaluations Open. Modern Cosmology. The Hot Big Bang. Age & Fate. Density and Geometry. Microwave Background
Today Modern Cosmology The Hot Big Bang Age & Fate Density and Geometry Microwave Background Course Evaluations Open Cosmology The study of the universe as a physical system Historically, people have always
More informationAST1100 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 informationGrowth of structure in an expanding universe The Jeans length Dark matter Large scale structure simulations. Large scale structure
Modern cosmology : The Growth of Structure Growth of structure in an expanding universe The Jeans length Dark matter Large scale structure simulations effect of cosmological parameters Large scale structure
More information8.1 Structure Formation: Introduction and the Growth of Density Perturbations
8.1 Structure Formation: Introduction and the Growth of Density Perturbations 1 Structure Formation and Evolution From this (Δρ/ρ ~ 10-6 ) to this (Δρ/ρ ~ 10 +2 ) to this (Δρ/ρ ~ 10 +6 ) 2 Origin of Structure
More informationAST4320: LECTURE 10 M. DIJKSTRA
AST4320: LECTURE 10 M. DIJKSTRA 1. The Mass Power Spectrum P (k) 1.1. Introduction: the Power Spectrum & Transfer Function. The power spectrum P (k) emerged in several of our previous lectures: It fully
More informationAY202a Galaxies & Dynamics Lecture 7: Jeans Law, Virial Theorem Structure of E Galaxies
AY202a Galaxies & Dynamics Lecture 7: Jeans Law, Virial Theorem Structure of E Galaxies Jean s Law Star/Galaxy Formation is most simply defined as the process of going from hydrostatic equilibrium to gravitational
More informationEnergy and Matter in the Universe
Chapter 17 Energy and Matter in the Universe The history and fate of the Universe ultimately turn on how much matter, energy, and pressure it contains: 1. These components of the stress energy tensor all
More informationClusters: Context and Background
Clusters: Context and Background We re about to embark on a subject rather different from what we ve treated before, so it is useful to step back and think again about what we want to accomplish in this
More informationThe oldest science? One of the most rapidly evolving fields of modern research. Driven by observations and instruments
The oldest science? One of the most rapidly evolving fields of modern research. Driven by observations and instruments Intersection of physics (fundamental laws) and astronomy (contents of the universe)
More informationInhomogeneous Universe: Linear Perturbation Theory
Inhomogeneous Universe: Linear Perturbation Theory We have so far discussed the evolution of a homogeneous universe. The universe we see toy is, however, highly inhomogeneous. We see structures on a wide
More informationN-body Simulations and Dark energy
N-Body Simulations and models of Dark Energy Elise Jennings Supported by a Marie Curie Early Stage Training Fellowship N-body Simulations and Dark energy elise jennings Introduction N-Body simulations
More informationCosmic 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 informationChapter 9. Cosmic Structures. 9.1 Quantifying structures Introduction
Chapter 9 Cosmic Structures 9.1 Quantifying structures 9.1.1 Introduction We have seen before that there is a very specific prediction for the power spectrum of density fluctuations in the Universe, characterised
More informationCosmology with CMB & LSS:
Cosmology with CMB & LSS: the Early universe VSP08 lecture 4 (May 12-16, 2008) Tarun Souradeep I.U.C.A.A, Pune, India Ω +Ω +Ω +Ω + Ω +... = 1 0 0 0 0... 1 m DE K r r The Cosmic Triangle (Ostriker & Steinhardt)
More informationCosmological Issues. Consider the stress tensor of a fluid in the local orthonormal frame where the metric is η ab
Cosmological Issues Radiation dominated Universe Consider the stress tensor of a fluid in the local orthonormal frame where the metric is η ab ρ 0 0 0 T ab = 0 p 0 0 0 0 p 0 () 0 0 0 p We do not often
More informationTuesday: 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 informationCosmology. Clusters of galaxies. Redshift. Late 1920 s: Hubble plots distances versus velocities of galaxies. λ λ. redshift =
Cosmology Study of the structure and origin of the universe Observational science The large-scale distribution of galaxies Looking out to extremely large distances The motions of galaxies Clusters of galaxies
More informationAy1 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 informationCosmology. 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 informationBAO & RSD. Nikhil Padmanabhan Essential Cosmology for the Next Generation VII December 2017
BAO & RSD Nikhil Padmanabhan Essential Cosmology for the Next Generation VII December 2017 Overview Introduction Standard rulers, a spherical collapse picture of BAO, the Kaiser formula, measuring distance
More informationhalo merger histories
Physics 463, Spring 07 Lecture 5 The Growth and Structure of Dark Mater Halos z=7! z=3! z=1! expansion scalefactor z=0! ~milky way M>3e12M! /h c vir ~13 ~virgo cluster M>3e14M! /h, c vir ~6 halo merger
More informationThe 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 informationStructures in the early Universe. Particle Astrophysics chapter 8 Lecture 4
Structures in the early Universe Particle Astrophysics chapter 8 Lecture 4 overview problems in Standard Model of Cosmology: horizon and flatness problems presence of structures Need for an exponential
More information1 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 informationA 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 informationPower spectrum exercise
Power spectrum exercise In this exercise, we will consider different power spectra and how they relate to observations. The intention is to give you some intuition so that when you look at a microwave
More informationThe Early Universe John Peacock ESA Cosmic Vision Paris, Sept 2004
The Early Universe John Peacock ESA Cosmic Vision Paris, Sept 2004 The history of modern cosmology 1917 Static via cosmological constant? (Einstein) 1917 Expansion (Slipher) 1952 Big Bang criticism (Hoyle)
More informationFuture evolution of bound supercluster in an accelerating Universe
Future evolution of bound supercluster in an accelerating Universe P.A. Araya-Melo, A. Reisenegger, A. Meza, R. van de Weygaert, R. Dünner and H. Quintana August 27, 2010 Mon. Not. R. Astron. Soc. 399,97-120
More informationarxiv: v1 [astro-ph.co] 4 Sep 2009
Spherical collapse model with and without curvature Seokcheon Lee 1,2 arxiv:99.826v1 [astro-ph.co] 4 Sep 29 1 Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, R.O.C. 2 Leung Center for Cosmology
More informationWhy 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 informationASTR 610 Theory of Galaxy Formation Lecture 4: Newtonian Perturbation Theory I. Linearized Fluid Equations
ASTR 610 Theory of Galaxy Formation Lecture 4: Newtonian Perturbation Theory I. Linearized Fluid Equations Frank van den Bosch Yale University, spring 2017 Structure Formation: The Linear Regime Thus far
More informationOlbers 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 informationPhysics of the Large Scale Structure. Pengjie Zhang. Department of Astronomy Shanghai Jiao Tong University
1 Physics of the Large Scale Structure Pengjie Zhang Department of Astronomy Shanghai Jiao Tong University The observed galaxy distribution of the nearby universe Observer 0.7 billion lys The observed
More informationModern Cosmology Solutions 4: LCDM Universe
Modern Cosmology Solutions 4: LCDM Universe Max Camenzind October 29, 200. LCDM Models The ansatz solves the Friedmann equation, since ȧ = C cosh() Ωm sinh /3 H 0 () () ȧ 2 = C 2 cosh2 () sinh 2/3 () (
More informationCMB Anisotropies: The Acoustic Peaks. Boom98 CBI Maxima-1 DASI. l (multipole) Astro 280, Spring 2002 Wayne Hu
CMB Anisotropies: The Acoustic Peaks 80 T (µk) 60 40 20 Boom98 CBI Maxima-1 DASI 500 1000 1500 l (multipole) Astro 280, Spring 2002 Wayne Hu Physical Landscape 100 IAB Sask 80 Viper BAM TOCO Sound Waves
More informationAstro 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 informationGalaxy Formation! Lecture Seven: Galaxy Formation! Cosmic History. Big Bang! time! present! ...fluctuations to galaxies!
Galaxy Formation Lecture Seven: Why is the universe populated by galaxies, rather than a uniform sea of stars? Galaxy Formation...fluctuations to galaxies Why are most stars in galaxies with luminosities
More informationStructures in the early Universe. Particle Astrophysics chapter 8 Lecture 4
Structures in the early Universe Particle Astrophysics chapter 8 Lecture 4 overview Part 1: problems in Standard Model of Cosmology: horizon and flatness problems presence of structures Part : Need for
More informationarxiv:astro-ph/ v1 27 Nov 2000
A&A manuscript no. (will be inserted by hand later) Your thesaurus codes are: 02 (3.13.18) - methods: N-body simulations ASTRONOMY AND ASTROPHYSICS The mass of a halo Martin White arxiv:astro-ph/0011495v1
More informationClusters: Context and Background
Clusters: Context and Background We reabouttoembarkon asubjectratherdifferentfrom what we vetreatedbefore, soit is useful to step back and think again about what we want to accomplish in this course. We
More informationarxiv:astro-ph/ v1 22 Sep 2005
Mass Profiles and Shapes of Cosmological Structures G. Mamon, F. Combes, C. Deffayet, B. Fort (eds) EAS Publications Series, Vol.?, 2005 arxiv:astro-ph/0509665v1 22 Sep 2005 MONDIAN COSMOLOGICAL SIMULATIONS
More informationNew 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 informationThe mass of a halo. M. White
A&A 367, 27 32 (2001) DOI: 10.1051/0004-6361:20000357 c ESO 2001 Astronomy & Astrophysics The mass of a halo M. White Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA e-mail: mwhite@cfa.harvard.edu
More informationLecture #25: Plan. Cosmology. The early Universe (cont d) The fate of our Universe The Great Unanswered Questions
Lecture #25: Plan Cosmology The early Universe (cont d) The fate of our Universe The Great Unanswered Questions Announcements Course evaluations: CourseEvalUM.umd.edu Review sheet #3 was emailed to you
More informationCosmology: 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 informationI Structure formation 2
Contents I Structure formation 2 1 Introduction 2 1.1 Seeds for structure formation............................... 2 1.2 Why expanding background is important........................ 2 1.3 The plan for
More informationIntroduction to Observational Cosmology II
Introduction to Observational Cosmology II Summer-semester 2010 in collaboration with Dr. Stefanie Phelps and Dr. Rene Fassbender Hans Böhringer Max-Planck Institut für extraterrestrische Physik, Garching
More informationENVIRONMENTAL EFFECTS IN MODIFIED GRAVITY MODELS
University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations Fall 12-22-2009 ENVIRONMENTAL EFFECTS IN MODIFIED GRAVITY MODELS Matthew C. Martino University of Pennsylvania, mcmarti2@sas.upenn.edu
More informationThe Effects of Inhomogeneities on the Universe Today. Antonio Riotto INFN, Padova
The Effects of Inhomogeneities on the Universe Today Antonio Riotto INFN, Padova Frascati, November the 19th 2004 Plan of the talk Short introduction to Inflation Short introduction to cosmological perturbations
More informationClusters of Galaxies Groups: Clusters poor rich Superclusters:
Clusters of Galaxies Galaxies are not randomly strewn throughout space. Instead the majority belong to groups and clusters of galaxies. In these structures, galaxies are bound gravitationally and orbit
More informationDark Energy in Light of the CMB. (or why H 0 is the Dark Energy) Wayne Hu. February 2006, NRAO, VA
Dark Energy in Light of the CMB (or why H 0 is the Dark Energy) Wayne Hu February 2006, NRAO, VA If its not dark, it doesn't matter! Cosmic matter-energy budget: Dark Energy Dark Matter Dark Baryons Visible
More informationCHAPTER 20. Collisions & Encounters of Collisionless Systems
CHAPTER 20 Collisions & Encounters of Collisionless Systems Consider an encounter between two collisionless N-body systems (i.e., dark matter halos or galaxies): a perturber P and a system S. Let q denote
More informationThird 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 informationBAO AS COSMOLOGICAL PROBE- I
BAO AS COSMOLOGICAL PROBE- I Introduction Enrique Gaztañaga, ICE (IEEC/CSIC) Barcelona PhD Studenships (on simulations & galaxy surveys) Postdoctoral oportunities: www.ice.cat (or AAS Job: #26205/26206)
More informationIntroduction to Cosmology
1 Introduction to Cosmology Mast Maula Centre for Theoretical Physics Jamia Millia Islamia New Delhi - 110025. Collaborators: Nutty Professor, Free Ride Mast Maula (CTP, JMI) Introduction to Cosmology
More informationClusters of Galaxies Groups: Clusters poor rich Superclusters:
Clusters of Galaxies Galaxies are not randomly strewn throughout space. Instead the majority belong to groups and clusters of galaxies. In these structures, galaxies are bound gravitationally and orbit
More informationHalo Model. Vinicius Miranda. Cosmology Course - Astro 321, Department of Astronomy and Astrophysics University of Chicago
Introduction program Thanks Department of Astronomy and Astrophysics University of Chicago Cosmology Course - Astro 321, 2011 Introduction program Thanks Outline 1 Introduction 2 Linear Theory Press -
More informationLecture 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 informationCOBE/DIRBE Satellite. Black Body T=2.725 K. Tuesday, November 27, 12
COBE/DIRBE Satellite Black Body T=2.725 K COBE/DIRBE Satellite Thermal component subtracted, ΔT=3.353 mk COBE/DIRBE Satellite Dipole component subtracted, ΔT = 18 μk Origin of Structure WMAP image Fluctuations
More informationThe Search for the Complete History of the Cosmos. Neil Turok
The Search for the Complete History of the Cosmos Neil Turok * The Big Bang * Dark Matter and Energy * Precision Tests * A Cyclic Universe? * Future Probes BIG Questions * What are the Laws of Nature?
More information