Halo Model. Vinicius Miranda. Cosmology Course - Astro 321, Department of Astronomy and Astrophysics University of Chicago
|
|
- Cornelia Heath
- 6 years ago
- Views:
Transcription
1 Introduction program Thanks Department of Astronomy and Astrophysics University of Chicago Cosmology Course - Astro 321, 2011
2 Introduction program Thanks Outline 1 Introduction 2 Linear Theory Press - Schechter Theory Dark Matter Galaxies velocities 3 program Good Qualities Bad Qualities 4 Thanks
3 Introduction program Thanks Since 1998, type IA SN indicates that the universe started to accelerate at some point in the past.
4 Introduction program Thanks Background evolution is determined by equation of state.
5 Introduction program Thanks Knowing Ω m (CMB or BAO), EOS is mainly obtained by SN assuming w constant
6 Introduction program Thanks Limitations of Kinematic Tests Theoretical alternatives: Assuming the dynamics of Dark Energy is given by a scalar field, Two very distinct possibilities are subject of intense research. Modified gravity. R µν 1 2 g µν + L µν (g µν ) = κ 2 T (m) µν (1) New non-gravitational field. R µν 1 ( ) 2 g µν = κ 2 T µν (m) + T µν (φ) (2)
7 Introduction program Thanks Example of the former approach (JF slide) Scalar Field Dark Energy aka quintessence General features: m eff < 3H 0 ~ ev (w < 0) (Potential > Kinetic Energy) V(ϕ) V ~ m 2 ϕ 2 ~ ρ crit ~ ev 4 ϕ ~ ev ~ M Planck ev (10 3 ev) 4 Ultra-light particle: Dark Energy hardly clusters, nearly smooth Equation of state: usually, w > 1 and evolves in time Hierarchy problem: Why m/φ ~ 10 61? Weak coupling: Quartic self-coupling λ φ < ϕ
8 Introduction program Thanks Example of the second approach Our Work ( V. Miranda, S. Jorás, I. Waga and M. Quartin PRL v102, p ,2009) In our work we tried to figure out if it is possible to build a viable f(r) model, without high curvature corrections, that is compatible with the existence of relativistic star and which does not suffer from Frolov s singularity. We started from the following generalization of the HSS models R f ( R) = R α R* β R * β R f ( R) = R α R* ln 1+ R* 1 n β β =1 1 f ( R) = R α R* 1 n R Hu & Sawicki s model 1+ R * n = 2 β = m α = % α / β Starobinsky s model 1 f ( R) = R % α R* 1 2 m R 1 + R*
9 Introduction program Thanks Dinamical Tests Can we differentiate the two approaches by measuring only the geometry? NO! We need the growth of structures Cluster Counts Lensing
10 Introduction program Thanks
11 Introduction program Thanks (Mortonson, Hu,Huterer) "We have shown that any observation that purports to rule out ΛCDM from the existence of massive clusters at any redshift also rules out quintessence, since quintessence models can suppress but not enhance the abundance of rare clusters compared to ΛCDM. This conclusion still holds if dark energy is a non-negligible fraction of the total density at high redshift. Once normalized to the CMB, quintessence models can only reduce the number of clusters"
12 Introduction program Thanks Gravitational Lensing: "Light Propagate as if in a medium with spatially varying index of refraction" n = 1 2Φ( x, τ) c 2 (3) JF slide Mean 3D Cluster Mass Profile from Statistical Lensing Virial mass 2-halo term NFW fit Johnston, etal 33
13 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Linear Power Spectrum In linear theory, it is possible to analyze the Dark Matter Power Spectrum with the following pieces: Initial Conditions given by inflation. R = A s ( k k norm ) ns 1 The linear growth rate of the gravitational potential as a function of time. (4) G(a) = Ψ(k norm, a) Ψ(k norm, a init ) (5)
14 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie How to calculate the linear growth rate? δ t + 2H δ t where δ(k, a) = G(a)aδ(k, 0). 4piG ρ = 0 (6) d 2 [ G 5 d(ln a) ] dg 2 w(a)ω DE(a) d ln a [1 w(a)] Ω DE(a)G = 0 (7)
15 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Transfer function that defines subhorizon evolution (Eisenstein and Hu)
16 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Press - Schechter Theory Can we estimate qualitatively the non linear power spectrum without doing a N Body simulation? ANSATZ: Choose some particle in the initial density Field. Smooth the density filed around this particle with a top hat filter of scale R. Assume the collapse of dark matter particle is spherical. For R of the other if Hubble volume, the overdensity of this smoothed field should be very small. As R decreases, the overdensity value will vary, sometimes up, sometimes down. Eventually the ovedensity will cross some threshold value δ sc (z).
17 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Press - Schechter Theory Can we estimate qualitatively the non linear power spectrum without doing a N Body simulation? ANSATZ: Choose some particle in the initial density Field. Smooth the density filed around this particle with a top hat filter of scale R. Assume the collapse of dark matter particle is spherical. For R of the other if Hubble volume, the overdensity of this smoothed field should be very small. As R decreases, the overdensity value will vary, sometimes up, sometimes down. Eventually the ovedensity will cross some threshold value δ sc (z).
18 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Press - Schechter Theory Can we estimate qualitatively the non linear power spectrum without doing a N Body simulation? ANSATZ: Choose some particle in the initial density Field. Smooth the density filed around this particle with a top hat filter of scale R. Assume the collapse of dark matter particle is spherical. For R of the other if Hubble volume, the overdensity of this smoothed field should be very small. As R decreases, the overdensity value will vary, sometimes up, sometimes down. Eventually the ovedensity will cross some threshold value δ sc (z).
19 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Press - Schechter Theory Can we estimate qualitatively the non linear power spectrum without doing a N Body simulation? ANSATZ: Choose some particle in the initial density Field. Smooth the density filed around this particle with a top hat filter of scale R. Assume the collapse of dark matter particle is spherical. For R of the other if Hubble volume, the overdensity of this smoothed field should be very small. As R decreases, the overdensity value will vary, sometimes up, sometimes down. Eventually the ovedensity will cross some threshold value δ sc (z).
20 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie First crossing of this value indicates the scale where the field is dense enough to form a virialized halo at redshift z.
21 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Spherical Collapse Equation of motion. d 2 R dt 2 = GM(R) R 2 + ΛR 3, (8) ( ) dr 2 = 2GM dt R + ΛR2 3 E i. (9) Assume Λ = 0. Make a rescale in time: dη = 2GM/R m dt/r. R = R m 2 (1 cos(η)), (10) t = R3/2 m (η sin(η)). (11) 2GM
22 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Spherical Collapse Equation of motion. d 2 R dt 2 = GM(R) R 2 + ΛR 3, (8) ( ) dr 2 = 2GM dt R + ΛR2 3 E i. (9) Assume Λ = 0. Make a rescale in time: dη = 2GM/R m dt/r. R = R m 2 (1 cos(η)), (10) t = R3/2 m (η sin(η)). (11) 2GM
23 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Spherical Collapse Equation of motion. d 2 R dt 2 = GM(R) R 2 + ΛR 3, (8) ( ) dr 2 = 2GM dt R + ΛR2 3 E i. (9) Assume Λ = 0. Make a rescale in time: dη = 2GM/R m dt/r. R = R m 2 (1 cos(η)), (10) t = R3/2 m (η sin(η)). (11) 2GM
24 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Overdensity: For δ << 1 and η << 1: 1 + δ(t) = 9 (η sin η) 2 (1 cos η) 2. (12) δ(t) = δ L (t) = 3 20 ( ) 6πt 2/3. (13) t m δ L (2t m ) = (14) Virializarion ρ(t v ) ρ(t v ) = 18π2 (15)
25 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Overdensity: For δ << 1 and η << 1: 1 + δ(t) = 9 (η sin η) 2 (1 cos η) 2. (12) δ(t) = δ L (t) = 3 20 ( ) 6πt 2/3. (13) t m δ L (2t m ) = (14) Virializarion ρ(t v ) ρ(t v ) = 18π2 (15)
26 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Overdensity: For δ << 1 and η << 1: 1 + δ(t) = 9 (η sin η) 2 (1 cos η) 2. (12) δ(t) = δ L (t) = 3 20 ( ) 6πt 2/3. (13) t m δ L (2t m ) = (14) Virializarion ρ(t v ) ρ(t v ) = 18π2 (15)
27 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Comoving number density dn = ρ νf (ν)dν M ν Spherical Collapse ν = ( ) δsc (z) 2 (16) σ(m) νf (ν) = ν 2π exp( ν/2) (17) Ellipsoidal Collapse ( ( νf (ν) = A(p) 1 + (qν) p qν ) 1/2 ) exp qν/2 2π (18) A(p) = [ p Γ(1/2 p)/ π ] 1 (19)
28 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Comoving number density dn = ρ νf (ν)dν M ν Spherical Collapse ν = ( ) δsc (z) 2 (16) σ(m) νf (ν) = ν 2π exp( ν/2) (17) Ellipsoidal Collapse ( ( νf (ν) = A(p) 1 + (qν) p qν ) 1/2 ) exp qν/2 2π (18) A(p) = [ p Γ(1/2 p)/ π ] 1 (19)
29 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Comoving number density dn = ρ νf (ν)dν M ν Spherical Collapse ν = ( ) δsc (z) 2 (16) σ(m) νf (ν) = ν 2π exp( ν/2) (17) Ellipsoidal Collapse ( ( νf (ν) = A(p) 1 + (qν) p qν ) 1/2 ) exp qν/2 2π (18) A(p) = [ p Γ(1/2 p)/ π ] 1 (19)
30 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie n_lnm
31 bias Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie δ = δ b + δ p (20) δ cp = δ c δ b (21) b(m) = 1 + qν 1 2p + [ δ c δ c 1 + (qν) p ] (22)
32 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie
33 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie z=0 Bias
34 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie NFR Profile Definition: Normalization ρ(r m) = ρ s (r/r s ) (1 + r/r s ) 2. (23) m = 4πρ s r 3 s [ ln(1 + c) c ] 1 + c (24) p(c m, z)dc = ( ) d(ln c) ln 2 [c/ c(m, z)] exp 2πσln 2 2σln 2 c c (25) c = 9 [ ] 0.20, 1+z σln m m c 0.25 and m M
35 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie NFR Profile Definition: Normalization ρ(r m) = ρ s (r/r s ) (1 + r/r s ) 2. (23) m = 4πρ s r 3 s [ ln(1 + c) c ] 1 + c (24) p(c m, z)dc = ( ) d(ln c) ln 2 [c/ c(m, z)] exp 2πσln 2 2σln 2 c c (25) c = 9 [ ] 0.20, 1+z σln m m c 0.25 and m M
36 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie
37 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie NFR Profile Normalize Fourier Transform: u(k m) = d 3 xρ( x m)e i k x d 3 xρ( x m) (26) For NFW profile: u(k m) = 4πρ sr 3 s m [ sin(kr s ) [Si([1 + c]kr s ) Si(kr s )] sin(ckr ] s) (1 + c)kr s (27) + 4πρ sr 3 s m [cos(kr s) [Ci([1 + c]kr s ) Ci(kr s )]]
38 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie
39 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie z=0 1 F_NFW M 1e 10, 1e 12, 1e 14, 1e
40 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Dark Matter Power Spectrum P(k) = P 1h (k) + P 2h (k) (28) P 1h (k) = ( d ln M M ρ m (z = 0) ) 2 dn d ln(m) u2 (k, M) (29) ( P 2h (k) = ( d ln M M ρ m (z = 0) ) ) dn 2 b(m)u(k, M) P l (k) d ln(m) (30)
41 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie z = 0 2 k Power Spectra 100 Linear Power Spectra Halo Term 2 Halo Term k
42 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Galaxy Power Spectrum P gal (k) = Pgal 1h (k) + P2h gal (k) (31) P 1h (k) = d ln M N gal(n gal 1) M n 2 gal dn d ln(m) up (k, M) (32) ( P 2h (k) = d ln M N gal M n gal dn d ln(m) ) 2 b(m)u(k, M) P l (k) (33)
43 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Galaxy Power Spectrum If N gal M < 1, then p = 1. Else p = 2. Variance: Mean: N gal (N gal 1) M = α(m) N gal where (34) ( ) α = log M/(10 11 M h 1 ) N gal M = 0 if M M h 1 (35) ( ) 0.9 = M/( ) if M M h 1 ( ) 0.8 ( ) 0.9 = 0.7 M/( ) + M/( ) if M (M h 1 )
44 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie
45 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie z = 0 k Power Spectra 100 Linear Power Spectra 1 1 Halo Term 2 Halo Term k
46 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie velocities p(v m)dv = Probability of a particle in a halo of mass m, has velocity in the range dv about v. f (v) = dmn(m)p(v m) dmmn(m) (36) Shape of p(v m) : 2 components. Virial Motions: Maxwell Boltzmann Distribution. Gaussian Field: Halo motions also obey Maxwell Boltzmann
47 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Virial Motions: σvirial 2 GM GMr 2 r r ( 3 ) 3m 2/3 ( vir ρ crit ) (37) 4π vir ρ crit ( ) ( ) H(z) 1/3 σvirial 2 m = M km/s (38) /h H 0
48 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie Halo Motions: σ halo = d log(ag) d log(a) σ 1 1 σ0 4/σ4 1 σ4 1 (39) σj 2 (R) = 1 2π 2 dkk 2+2j P lin (k)w 2 [kr] (40)
49 Introduction program Thanks Linear Theory Press - Schechter Theory Dark Matter Galaxie z = 0 k v
50 Introduction program Thanks Good Qualities Bad Qualities Good Qualities It is organized. (readable) Calculates matter power spectrum, galaxy power spectrum, and peculiar velocity distribution. Input file allows you to change many physical and optimization parameters.
51 Introduction program Thanks Good Qualities Bad Qualities Good Qualities It is organized. (readable) Calculates matter power spectrum, galaxy power spectrum, and peculiar velocity distribution. Input file allows you to change many physical and optimization parameters.
52 Introduction program Thanks Good Qualities Bad Qualities Good Qualities It is organized. (readable) Calculates matter power spectrum, galaxy power spectrum, and peculiar velocity distribution. Input file allows you to change many physical and optimization parameters.
53 Introduction program Thanks Good Qualities Bad Qualities Allows you to choose between 2 different dark energy parameterizations: w de = w 0 + w 1 z (41) z w de = w 0 + w z. Allows you to choose between 3 different concentration parameters: c = 10 (42) c = c c given by p(c).
54 Introduction program Thanks Good Qualities Bad Qualities Input.txt
55 Introduction program Thanks Good Qualities Bad Qualities
56 Introduction program Thanks Good Qualities Bad Qualities Ouput.txt
57 Introduction program Thanks Good Qualities Bad Qualities
58 Introduction program Thanks Good Qualities Bad Qualities
59 Introduction program Thanks Good Qualities Bad Qualities run: make -fmakefile.mak final_project
60 Introduction program Thanks Good Qualities Bad Qualities Optimization It is optimized. Run: seconds/point. For a entire plot: 2-10 minutes (30-45 seconds to calculate and fit sigma + 1s/point). Can be better? Use of inline functions - Integral code that double (not triple) the number of points on each call...
61 Introduction program Thanks Good Qualities Bad Qualities Bad Qualities Normalization bug (someone really should make an independent check). Not written in a C++ class style. NR copyrighted $$$ code. However, integrands are written in gsl function style. Thus, it should be simple to use GSL integration code.
62 Introduction program Thanks Good Qualities Bad Qualities Bad Qualities Normalization bug (someone really should make an independent check). Not written in a C++ class style. NR copyrighted $$$ code. However, integrands are written in gsl function style. Thus, it should be simple to use GSL integration code.
63 Introduction program Thanks Good Qualities Bad Qualities Needs to incorporate more physics: subhalos structure for k >> 1Mpc/h 1 ), weak lensing, momentum power spectra, dark matter - galaxy cross power spectrum.
64 Introduction program Thanks Thanks and sorry about the thousands of questions (some "out of phase" with the lecture subject!) Funny thing about my "impatience". First Time I attended a class on was during the 2008 BSCG. Ravi Sheth BSCG proceedings: " I thank (..) V. Miranda for raising so many interesting questions, M. Calvao for keeping him under control.." Thanks for Keeping me under control! :)
65 Introduction program Thanks Thanks and sorry about the thousands of questions (some "out of phase" with the lecture subject!) Funny thing about my "impatience". First Time I attended a class on was during the 2008 BSCG. Ravi Sheth BSCG proceedings: " I thank (..) V. Miranda for raising so many interesting questions, M. Calvao for keeping him under control.." Thanks for Keeping me under control! :)
66 Introduction program Thanks Thanks and sorry about the thousands of questions (some "out of phase" with the lecture subject!) Funny thing about my "impatience". First Time I attended a class on was during the 2008 BSCG. Ravi Sheth BSCG proceedings: " I thank (..) V. Miranda for raising so many interesting questions, M. Calvao for keeping him under control.." Thanks for Keeping me under control! :)
N-body Simulations. Initial conditions: What kind of Dark Matter? How much Dark Matter? Initial density fluctuations P(k) GRAVITY
N-body Simulations N-body Simulations N-body Simulations Initial conditions: What kind of Dark Matter? How much Dark Matter? Initial density fluctuations P(k) GRAVITY Final distribution of dark matter.
More informationDark Energy and Dark Matter Interaction. f (R) A Worked Example. Wayne Hu Florence, February 2009
Dark Energy and Dark Matter Interaction f (R) A Worked Example Wayne Hu Florence, February 2009 Why Study f(r)? Cosmic acceleration, like the cosmological constant, can either be viewed as arising from
More informationGalaxies 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 informationHalo models of large scale structure
Halo models of large scale structure Asantha Cooray Theoretical Astrophysics, California Institute of Technology, Pasadena CA 91125. E-mail: asante@caltech.edu arxiv:astro-ph/0206508v1 28 Jun 2002 Ravi
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 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 informationSimulating non-linear structure formation in dark energy cosmologies
Simulating non-linear structure formation in dark energy cosmologies Volker Springel Distribution of WIMPS in the Galaxy Early Dark Energy Models (Margherita Grossi) Coupled Dark Energy (Marco Baldi) Fifth
More informationCosmic Acceleration from Modified Gravity: f (R) A Worked Example. Wayne Hu
Cosmic Acceleration from Modified Gravity: f (R) A Worked Example Wayne Hu Aspen, January 2009 Outline f(r) Basics and Background Linear Theory Predictions N-body Simulations and the Chameleon Collaborators:
More informationLecture 6: Dark Matter Halos
Lecture 6: Dark Matter Halos Houjun Mo February 23, 2004 Hierarchical clustering, the matter in the universe condenses to form quasiequilibrium objects (dark halos) of increasing masses in the passage
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 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 informationOrigin of Structure Formation of Structure. Projected slice of 200,000 galaxies, with thickness of a few degrees.
Origin of Structure Formation of Structure Projected slice of 200,000 galaxies, with thickness of a few degrees. Redshift Surveys Modern survey: Sloan Digital Sky Survey, probes out to nearly 1000 Mpc.
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 informationdark matter haloes and galaxy formation
dark matter haloes and galaxy formation cosmology lecture (chapter 12) Haus der Astronomie and Centre for Astronomy Fakultät für Physik und Astronomie, Universität Heidelberg August 1, 2013 outline 1 repetition
More informationMeasuring Neutrino Masses and Dark Energy
Huitzu Tu UC Irvine June 7, 2007 Dark Side of the Universe, Minnesota, June 5-10 2007 In collaboration with: Steen Hannestad, Yvonne Wong, Julien Lesgourgues, Laurence Perotto, Ariel Goobar, Edvard Mörtsell
More informationCluster abundances, clustering and cosmology. Ravi K Sheth (ICTP/UPenn)
Cluster abundances, clustering and cosmology Ravi K Sheth (ICTP/UPenn) Motivation: A biased view of dark matters Observational probes Gravitational Instability The spherical (and tri-axial) collapse models
More informationCross-Correlation of CFHTLenS Galaxy Catalogue and Planck CMB Lensing
Cross-Correlation of CFHTLenS Galaxy Catalogue and Planck CMB Lensing A 5-month internship under the direction of Simon Prunet Adrien Kuntz Ecole Normale Supérieure, Paris July 08, 2015 Outline 1 Introduction
More informationSignatures of MG on. linear scales. non- Fabian Schmidt MPA Garching. Lorentz Center Workshop, 7/15/14
Signatures of MG on non- linear scales Fabian Schmidt MPA Garching Lorentz Center Workshop, 7/15/14 Tests of gravity Smooth Dark Energy (DE): unique prediction for growth factor given w(a) Use evolution
More informationThe Principal Components of. Falsifying Cosmological Paradigms. Wayne Hu FRS, Chicago May 2011
The Principal Components of Falsifying Cosmological Paradigms Wayne Hu FRS, Chicago May 2011 The Standard Cosmological Model Standard ΛCDM cosmological model is an exceedingly successful phenomenological
More informationTESTING GRAVITY WITH COSMOLOGY
21 IV. TESTING GRAVITY WITH COSMOLOGY We now turn to the different ways with which cosmological observations can constrain modified gravity models. We have already seen that Solar System tests provide
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 informationNeoClassical Probes. of the Dark Energy. Wayne Hu COSMO04 Toronto, September 2004
NeoClassical Probes in of the Dark Energy Wayne Hu COSMO04 Toronto, September 2004 Structural Fidelity Dark matter simulations approaching the accuracy of CMB calculations WMAP Kravtsov et al (2003) Equation
More informationCosmic Acceleration from Modified Gravity: f (R) A Worked Example. Wayne Hu
Cosmic Acceleration from Modified Gravity: f (R) A Worked Example Wayne Hu CalTech, December 2008 Why Study f(r)? Cosmic acceleration, like the cosmological constant, can either be viewed as arising from
More informationA look into the Dark Universe
Zentrum für Astronomie, Institut für Theoretische Astrophysik Universität Heidelberg Dark Energy dark energy: assumed to drive accelerated cosmic expansion scalar field having negative pressure? early
More informationhalo formation in peaks halo bias if halos are formed without regard to the underlying density, then δn h n h halo bias in simulations
Physics 463, Spring 07 Bias, the Halo Model & Halo Occupation Statistics Lecture 8 Halo Bias the matter distribution is highly clustered. halos form at the peaks of this distribution 3 2 1 0 halo formation
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 informationAST Cosmology and extragalactic astronomy Lecture 7
AST4320 - Cosmology and extragalactic astronomy Lecture 7 Press-Schechter Formalism: applications, origin of the `fudge factor 2, modifications Press-Schechter (PS) Formalism: Preface... PS assumes 1.
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 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 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 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 informationA 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 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 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 informationPhysical Cosmology 4/4/2016. Docente: Alessandro Melchiorri
Physical Cosmology 4/4/2016 Docente: Alessandro Melchiorri alessandro.melchiorri@roma1.infn.it Suggested textbooks Barbara Ryden, Introduction to Cosmology http://www.astro.caltech.edu/~george/ay21/readings/ryden_introcosmo.pdf
More information4. Structure of Dark Matter halos. Hence the halo mass, virial radius, and virial velocity are related by
13-4-12see http://www.strw.leidenuniv.nl/ franx/college/galaxies12 12-c04-1 13-4-12see http://www.strw.leidenuniv.nl/ franx/college/galaxies12 12-c04-2 4. Structure of Dark Matter halos Obviously, we cannot
More informationCosmology: 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 informationPhysical Cosmology 18/5/2017
Physical Cosmology 18/5/2017 Alessandro Melchiorri alessandro.melchiorri@roma1.infn.it slides can be found here: oberon.roma1.infn.it/alessandro/cosmo2017 Summary If we consider perturbations in a pressureless
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 informationObservational Cosmology
(C. Porciani / K. Basu) Lecture 7 Cosmology with galaxy clusters (Mass function, clusters surveys) Course website: http://www.astro.uni-bonn.de/~kbasu/astro845.html Outline of the two lecture Galaxy clusters
More information4. Structure of Dark Matter halos. Hence the halo mass, virial radius, and virial velocity are related by
6-4-10see http://www.strw.leidenuniv.nl/ franx/college/galaxies10 10-c04-1 6-4-10see http://www.strw.leidenuniv.nl/ franx/college/galaxies10 10-c04-2 4. Structure of Dark Matter halos Obviously, we cannot
More informationConstraining Modified Gravity and Coupled Dark Energy with Future Observations Matteo Martinelli
Coupled Dark University of Rome La Sapienza Roma, October 28th 2011 Outline 1 2 3 4 5 1 2 3 4 5 Accelerated Expansion Cosmological data agree with an accelerated expansion of the Universe d L [Mpc] 16000
More informationCosmology with high (z>1) redshift galaxy surveys
Cosmology with high (z>1) redshift galaxy surveys Donghui Jeong Texas Cosmology Center and Astronomy Department University of Texas at Austin Ph. D. thesis defense talk, 17 May 2010 Cosmology with HETDEX
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 informationModified gravity as an alternative to dark energy. Lecture 3. Observational tests of MG models
Modified gravity as an alternative to dark energy Lecture 3. Observational tests of MG models Observational tests Assume that we manage to construct a model How well can we test the model and distinguish
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 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 informationLeptogenesis via the Relaxation of Higgs and other Scalar Fields
Leptogenesis via the Relaxation of Higgs and other Scalar Fields Louis Yang Department of Physics and Astronomy University of California, Los Angeles PACIFIC 2016 September 13th, 2016 Collaborators: Alex
More informationCosmological Constraints from a Combined Analysis of Clustering & Galaxy-Galaxy Lensing in the SDSS. Frank van den Bosch.
Cosmological Constraints from a Combined Analysis of Clustering & Galaxy-Galaxy Lensing in the SDSS In collaboration with: Marcello Cacciato (Leiden), Surhud More (IPMU), Houjun Mo (UMass), Xiaohu Yang
More informationThe nonlinear dynamical stability of infrared modifications of gravity
The nonlinear dynamical stability of infrared modifications of gravity Aug 2014 In collaboration with Richard Brito, Vitor Cardoso and Matthew Johnson Why Study Modifications to Gravity? General relativity
More informationEquation of state of dark energy. Phys. Rev. D 91, (2015)
Equation of state of dark energy in f R gravity The University of Tokyo, RESCEU K. Takahashi, J. Yokoyama Phys. Rev. D 91, 084060 (2015) Motivation Many modified theories of gravity have been considered
More informationElise Jennings University of Chicago
Pacific 2014 Testing gravity with large scale structure dynamics Elise Jennings University of Chicago THE UNIVERSITY OF CHICAGO THE ENRICO FERMI INSTITUTE EJ, B. Li, C.M. Baugh, G. Zhao, K. Kazuya 2013
More informationLarge Scale Structure After these lectures, you should be able to: Describe the matter power spectrum Explain how and why the peak position depends on
Observational cosmology: Large scale structure Filipe B. Abdalla Kathleen Lonsdale Building G.22 http://zuserver2.star.ucl.ac.uk/~hiranya/phas3136/phas3136 Large Scale Structure After these lectures, you
More informationH 0 is Undervalued BAO CMB. Wayne Hu STSCI, April 2014 BICEP2? Maser Lensing Cepheids. SNIa TRGB SBF. dark energy. curvature. neutrinos. inflation?
H 0 is Undervalued BICEP2? 74 Maser Lensing Cepheids Eclipsing Binaries TRGB SBF SNIa dark energy curvature CMB BAO neutrinos inflation? Wayne Hu STSCI, April 2014 67 The 1% H 0 =New Physics H 0 : an end
More informationSPA7023P/SPA7023U/ASTM109 Stellar Structure and Evolution Duration: 2.5 hours
MSc/MSci Examination Day 28th April 2015 18:30 21:00 SPA7023P/SPA7023U/ASTM109 Stellar Structure and Evolution Duration: 2.5 hours YOU ARE NOT PERMITTED TO READ THE CONTENTS OF THIS QUESTION PAPER UNTIL
More informationSMALL COSMOLOGICAL CONSTANT FROM RUNNING GRAVITATIONAL COUPLING
SMALL COSMOLOGICAL CONSTANT FROM RUNNING GRAVITATIONAL COUPLING arxiv:1101.4995, arxiv:0803.2500 Andrei Frolov Department of Physics Simon Fraser University Jun-Qi Guo (SFU) Sternberg Astronomical Institute
More informationAstronomy 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 informationThermodynamics in Cosmology Nucleosynthesis
Thermodynamics in Cosmology Nucleosynthesis Thermodynamics Expansion Evolution of temperature Freeze out Nucleosynthesis Production of the light elements Potential barrier Primordial synthesis calculations
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 informationCosmology with Galaxy Clusters. I. A Cosmological Primer
Cosmology with Galaxy Clusters I. A Cosmological Primer Timetable Monday Tuesday Wednesday Thursday Friday 4pm 4pm 4pm 4pm no lecture 4pm Can we have lectures from 16.00-16.50? Timetable shows problems
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 informationTo Lambda or not to Lambda?
To Lambda or not to Lambda? Supratik Pal Indian Statistical Institute Kolkata October 17, 2015 Conclusion We don t know :) Partly based on my works with Dhiraj Hazra, Subha Majumdar, Sudhakar Panda, Anjan
More informationCosmology with weak-lensing peak counts
Durham-Edinburgh extragalactic Workshop XIV IfA Edinburgh Cosmology with weak-lensing peak counts Chieh-An Lin January 8 th, 2018 Durham University, UK Outline Motivation Why do we study WL peaks? Problems
More informationWhat do we really know about Dark Energy?
What do we really know about Dark Energy? Ruth Durrer Département de Physique Théorique & Center of Astroparticle Physics (CAP) ESTEC, February 3, 2012 Ruth Durrer (Université de Genève ) Dark Energy ESTEC
More informationSecondary CMB Anisotropy
Secondary CMB Anisotropy III: Dark Energy Wayne Hu Cabo, January 2009 Integrated Sachs-Wolfe Effect Smooth Energy Density & Potential Decay Regardless of the equation of state an energy component that
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 informationParameterizing. Modified Gravity. Models of Cosmic Acceleration. Wayne Hu Ann Arbor, May 2008
Parameterizing Modified Gravity Models of Cosmic Acceleration Wayne Hu Ann Arbor, May 2008 Parameterizing Acceleration Cosmic acceleration, like the cosmological constant, can either be viewed as arising
More informationGasdynamical and radiative processes, gaseous halos
Gasdynamical and radiative processes, gaseous halos Houjun Mo March 19, 2004 Since luminous objects, such as galaxies, are believed to form through the collapse of baryonic gas, it is important to understand
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 informationLarge-scale structure as a probe of dark energy. David Parkinson University of Sussex, UK
Large-scale structure as a probe of dark energy David Parkinson University of Sussex, UK Question Who was the greatest actor to portray James Bond in the 007 movies? a) Sean Connery b) George Lasenby c)
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 informationExamining the Viability of Phantom Dark Energy
Examining the Viability of Phantom Dark Energy Kevin J. Ludwick LaGrange College 12/20/15 (11:00-11:30) Kevin J. Ludwick (LaGrange College) Examining the Viability of Phantom Dark Energy 12/20/15 (11:00-11:30)
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 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 informationThe imprint of the initial conditions on large-scale structure
Stars, Planets and Galaxies 2018 Harnack House, Berlin The imprint of the initial conditions on large-scale structure Simon White Max Planck Institute for Astrophysics The Planck map of TCMB the initial
More informationarxiv: v1 [astro-ph] 2 Dec 2008
Non-linear Evolution of f(r) Cosmologies III: Halo Statistics arxiv:0812.0545v1 [astro-ph] 2 Dec 2008 Fabian Schmidt, 1, 2, Marcos Lima, 2, 3, 4 Hiroaki Oyaizu, 1,2 1, 2, 5 and Wayne Hu 1 Department of
More informationThe Los Cabos Lectures
January 2009 The Los Cabos Lectures Dark Matter Halos: 2 Simon White Max Planck Institute for Astrophysics EPS statistics for the standard ΛCDM cosmology Millennium Simulation cosmology: Ωm = 0.25, ΩΛ
More informationD. f(r) gravity. φ = 1 + f R (R). (48)
5 D. f(r) gravity f(r) gravity is the first modified gravity model proposed as an alternative explanation for the accelerated expansion of the Universe [9]. We write the gravitational action as S = d 4
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 informationAST4320: LECTURE 6 M. DIJKSTRA
AST432: LECTURE 6. DIJKSTRA. Gaussian Random Fields & The Press Schechter Formalism.. Support for Previous Lecture. The plot shown in the slides where the cooling time was compared to the collapse time
More informationBrief Introduction to Cosmology
Brief Introduction to Cosmology Matias Zaldarriaga Harvard University August 2006 Basic Questions in Cosmology: How does the Universe evolve? What is the universe made off? How is matter distributed? How
More informationCosmology (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 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 informationConcordance Cosmology and Particle Physics. Richard Easther (Yale University)
Concordance Cosmology and Particle Physics Richard Easther (Yale University) Concordance Cosmology The standard model for cosmology Simplest model that fits the data Smallest number of free parameters
More informationCosmology 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 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 informationASTR 610 Theory of Galaxy Formation Lecture 15: Galaxy Interactions
ASTR 610 Theory of Galaxy Formation Lecture 15: Galaxy Interactions Frank van den Bosch Yale University, spring 2017 Galaxy Interactions & Transformations In this lecture we discuss galaxy interactions
More informationGravitational Lensing of the CMB
Gravitational Lensing of the CMB SNAP Planck 1 Ω DE 1 w a.5-2 -1.5 w -1 -.5 Wayne Hu Leiden, August 26-1 Outline Gravitational Lensing of Temperature and Polarization Fields Cosmological Observables from
More informationPrinceton December 2009 The fine-scale structure of dark matter halos
Princeton December 2009 The fine-scale structure of dark matter halos Simon White Max Planck Institute for Astrophysics The dark matter structure of CDM halos A rich galaxy cluster halo Springel et al
More informationThe impact of relativistic effects on cosmological parameter estimation
The impact of relativistic effects on cosmological parameter estimation arxiv:1710.02477 (PRD) with David Alonso and Pedro Ferreira Christiane S. Lorenz University of Oxford Rencontres de Moriond, La Thuile,
More informationDark Universe II. The shape of the Universe. The fate of the Universe. Old view: Density of the Universe determines its destiny
Dark Universe II Prof. Lynn Cominsky Dept. of Physics and Astronomy Sonoma State University Modifications by H. Geller November 2007 11/27/2007 Prof. Lynn Cominsky 2 Dark Energy and the Shape of the Universe
More informationBaryon Acoustic Oscillations (BAO) in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample
Baryon Acoustic Oscillations (BAO) in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample BOMEE LEE 1. Brief Introduction about BAO In our previous class we learned what is the Baryon Acoustic Oscillations(BAO).
More informationThe large scale structure of the universe
The large scale structure of the universe Part 1: Deciphering the large scale structure (LSS) With statistics and physics Part 2: Tracers of LSS Broadband power spectrum, BAO, redshift distortion, weak
More informationHalo concentration and the dark matter power spectrum
Mon. Not. R. Astron. Soc. 340, 1199 1204 (2003) Halo concentration and the dark matter power spectrum Kevin M. Huffenberger and Uroš Seljak Department of Physics, Jadwin Hall, Princeton University, Princeton,
More informationClusters: Observations
Clusters: Observations Last time we talked about some of the context of clusters, and why observations of them have importance to cosmological issues. Some of the reasons why clusters are useful probes
More informationThe fine-scale structure of dark matter halos
COSMO11, Porto, August 2011 The fine-scale structure of dark matter halos Simon White Max-Planck-Institute for Astrophysics COSMO11, Porto, August 2011 Mark Vogelsberger The fine-scale structure of dark
More informationFundamental Stellar Parameters. Radiative Transfer. Stellar Atmospheres
Fundamental Stellar Parameters Radiative Transfer Stellar Atmospheres Equations of Stellar Structure Basic Principles Equations of Hydrostatic Equilibrium and Mass Conservation Central Pressure, Virial
More informationComplementarity in Dark Energy measurements. Complementarity of optical data in constraining dark energy. Licia Verde. University of Pennsylvania
Complementarity in Dark Energy measurements Complementarity of optical data in constraining dark energy Licia Verde University of Pennsylvania www.physics.upenn.edu/~lverde The situation: SN 1A (Riess
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 informationLarge Scale Structure (Galaxy Correlations)
Large Scale Structure (Galaxy Correlations) Bob Nichol (ICG,Portsmouth) QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. QuickTime and a TIFF (Uncompressed) decompressor
More informationASTR 610 Theory of Galaxy Formation
ASTR 610 Theory of Galaxy Formation Lecture 13: The Halo Model & Halo Occupation Statistics Frank van den Bosch Yale University, Fall 2018 The Halo Model & Occupation Statistics In this lecture we discuss
More information