The Effects of the Small-Scale Behaviour of Dark Matter Power Spectrum on CMB Spectral Distortion
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First Year Wilkinson Microwave Anisotropy Probe (WMAP ) Observations: Determination of Cosmological Parameters
Accepted by the Astrophysical Journal First Year Wilkinson Microwave Anisotropy Probe (WMAP ) Observations: Determination of Cosmological Parameters D. N. Spergel 2, L. Verde 2 3, H. V. Peiris 2, E. Komatsu 2, M. R. Nolta 4, C. L. Bennett 5, M. Halpern 6, G. Hinshaw 5, N. Jarosik 4, A. Kogut 5, M. Limon 5 7, S. S. Meyer 8, L. Page 4, G. S. Tucker 5 7 9, J. L. Weiland 10, E. Wollack 5, & E. L. Wright 11 [email protected] ABSTRACT WMAP precision data enables accurate testing of cosmological models. We find that the emerging standard model of cosmology, a flat ¡ −dominated universe seeded by a nearly scale-invariant adiabatic Gaussian fluctuations, fits the WMAP data. For the WMAP data 2 2 £ ¢ ¤ ¢ £ ¢ ¤ ¢ £ ¢ only, the best fit parameters are h = 0 ¢ 72 0 05, bh = 0 024 0 001, mh = 0 14 0 02, ¥ +0 ¦ 076 ¢ £ ¢ § ¢ £ ¢ = 0 ¢ 166− , n = 0 99 0 04, and = 0 9 0 1. With parameters fixed only by WMAP 0 ¦ 071 s 8 data, we can fit finer scale CMB measurements and measurements of large scale structure (galaxy surveys and the Lyman ¨ forest). This simple model is also consistent with a host of other astronomical measurements: its inferred age of the universe is consistent with stel- lar ages, the baryon/photon ratio is consistent with measurements of the [D]/[H] ratio, and the inferred Hubble constant is consistent with local observations of the expansion rate. We then fit the model parameters to a combination of WMAP data with other finer scale CMB experi- ments (ACBAR and CBI), 2dFGRS measurements and Lyman ¨ forest data to find the model’s 1WMAP is the result of a partnership between Princeton University and NASA's Goddard Space Flight Center. -
THE NONLINEAR MATTER POWER SPECTRUM1 Online Material
The Astrophysical Journal, 665:887– 898, 2007 August 20 A # 2007. The American Astronomical Society. All rights reserved. Printed in U.S.A. THE NONLINEAR MATTER POWER SPECTRUM1 Zhaoming Ma Department of Astronomy and Astrophysics and Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637; [email protected] Received 2006 October 6; accepted 2007 April 30 ABSTRACT We modify the public PM code developed by Anatoly Klypin and Jon Holtzman to simulate cosmologies with arbitrary initial power spectra and the equation of state of dark energy. With this tool in hand, we perform the follow- ing studies on the matter power spectrum. With an artificial sharp peak at k 0:2 h MpcÀ1 in the initial power spec- trum, we find that the position of the peak is not shifted by nonlinear evolution. An upper limit of the shift at the level of 0.02% is achieved by fitting the power spectrum local to the peak using a power law plus a Gaussian. We also find that the existence of a peak in the linear power spectrum would boost the nonlinear power at all scales evenly. This is contrary to what the HKLM scaling relation predicts, but roughly consistent with that of the halo model. We construct dark energy models with the same linear power spectra today but different linear growth histories. We demonstrate that their nonlinear power spectra differ at the level of the maximum deviation of the corresponding linear power spectra in the past. Similarly, two constructed dark energy models with the same growth histories result in consistent nonlinear power spectra. -
Planck Early Results. XVIII. the Power Spectrum of Cosmic Infrared Background Anisotropies
A&A 536, A18 (2011) Astronomy DOI: 10.1051/0004-6361/201116461 & c ESO 2011 Astrophysics Planck early results Special feature Planck early results. XVIII. The power spectrum of cosmic infrared background anisotropies Planck Collaboration: P. A. R. Ade74, N. Aghanim48,M.Arnaud60, M. Ashdown58,4, J. Aumont48, C. Baccigalupi72,A.Balbi30, A. J. Banday78,8,65,R.B.Barreiro55, J. G. Bartlett3,56,E.Battaner80, K. Benabed49, A. Benoît47,J.-P.Bernard78,8, M. Bersanelli27,42,R.Bhatia5,K.Blagrave7,J.J.Bock56,9, A. Bonaldi38, L. Bonavera72,6,J.R.Bond7,J.Borrill64,76, F. R. Bouchet49, M. Bucher3,C.Burigana41, P. Cabella30, J.-F. Cardoso61,3,49, A. Catalano3,59, L. Cayón20, A. Challinor52,58,11, A. Chamballu45,L.-YChiang51,C.Chiang19,P.R.Christensen69,31,D.L.Clements45, S. Colombi49, F. Couchot63, A. Coulais59, B. P. Crill56,70, F. Cuttaia41,L.Danese72,R.D.Davies57,R.J.Davis57,P.deBernardis26,G.deGasperis30,A.deRosa41, G. de Zotti38,72, J. Delabrouille3, J.-M. Delouis49, F.-X. Désert44,H.Dole48, S. Donzelli42,53,O.Doré56,9,U.Dörl65, M. Douspis48, X. Dupac34, G. Efstathiou52,T.A.Enßlin65,H.K.Eriksen53, F. Finelli41, O. Forni78,8, P. Fosalba50, M. Frailis40, E. Franceschi41, S. Galeotta40, K. Ganga3,46,M.Giard78,8, G. Giardino35, Y. Giraud-Héraud3, J. González-Nuevo72,K.M.Górski56,82,J.Grain48, S. Gratton58,52, A. Gregorio28, A. Gruppuso41,F.K.Hansen53, D. Harrison52,58,G.Helou9, S. Henrot-Versillé63, D. Herranz55, S. R. Hildebrandt9,62,54,E.Hivon49, M. Hobson4,W.A.Holmes56, W. Hovest65,R.J.Hoyland54,K.M.Huffenberger81, A. -
Clusters, Cosmology and Reionization from the SZ Power Spectrum
Clusters, Cosmology and Reionization from the SZ Power Spectrum Shaw et al. (10,11) Reichardt, LS, Zahn + (11) Zahn, Reichardt, LS + (11) Collaborators: D. Nagai, D. Rudd (Yale), G. Holder (McGill), Suman Bhattacharya (LANL), O. Zahn (Berkeley), O. Dore (Caltech), the SPT team. Tremendous recent progress measuring the CMB damping tail Small scales provide additional constraints Keisler+ on ★ Helium abundance ★ ns & running ★ neutrinos ..and beyond thermal & kinetic SZ CMB lensing CIB (dusty galaxies) Radio sources Reichardt+ 11 ..and beyond thermal & kinetic SZ CMB lensing CIB (dusty galaxies) Radio sources Reichardt+ 11 primordial signal secondaries & E.G. foregrounds Statistical detection of the SZE by searching for anisotropy power at small angular scales primary cmb thermal SZ kinetic SZ Amplitude of SZ power spectrum is particularly sensitive to matter power spectrum normalization simulated tsz map (Shaw+, 09) 10deg Sensitive to both the abundance of collapsed structures and the thermal pressure of the intra-cluster medium Halo model approach to calculating the tSZ power spectrum Calculate SZ power spectrum by integrating the mass function over M and z, weighted by cluster signal at a given angular scale. zmax dV Mmax dn(M, z) C = g2 dz dM y (M, z) 2 l ν dz dM | l | 0 0 volume integral cluster mass function Fourier transform of projected gas thermal pressure profiles Where does tSZ power come from? distribution of power at ell = 3000 (~3.6’) 10% 50% 90% Shaw+ (10) Low mass, high redshift contribution significant. Modelling the tSZ Power Spectrum Simple parameterized model, calibrated to observations and including cosmological scaling [Shaw+ (10), Ostriker+ (05)] ★ Gas resides in hydrostatic equilibrium in NFW dark matter halos with polytropic EoS ★ Assume some gas has radiatively cooled + formed stars. -
FIRST-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) 1 OBSERVATIONS: DETERMINATION of COSMOLOGICAL PARAMETERS D. N. Spergel,2
The Astrophysical Journal Supplement Series, 148:175–194, 2003 September E # 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A. FIRST-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP)1 OBSERVATIONS: DETERMINATION OF COSMOLOGICAL PARAMETERS D. N. Spergel,2 L. Verde,2,3 H. V. Peiris,2 E. Komatsu,2 M. R. Nolta,4 C. L. Bennett,5 M. Halpern,6 G. Hinshaw,5 N. Jarosik,4 A. Kogut,5 M. Limon,5,7 S. S. Meyer,8 L. Page,4 G. S. Tucker,5,7,9 J. L. Weiland,10 E. Wollack,5 and E. L. Wright11 Received 2003 February 11; accepted 2003 May 20 ABSTRACT WMAP precision data enable accurate testing of cosmological models. We find that the emerging standard model of cosmology, a flat Ã-dominated universe seeded by a nearly scale-invariant adiabatic Gaussian fluctuations, fits the WMAP data. For the WMAP data only, the best-fit parameters are h ¼ 0:72 Æ 0:05, 2 2 þ0:076 bh ¼ 0:024 Æ 0:001, mh ¼ 0:14 Æ 0:02, ¼ 0:166À0:071, ns ¼ 0:99 Æ 0:04, and 8 ¼ 0:9 Æ 0:1. With parameters fixed only by WMAP data, we can fit finer scale cosmic microwave background (CMB) measure- ments and measurements of large-scale structure (galaxy surveys and the Ly forest). This simple model is also consistent with a host of other astronomical measurements: its inferred age of the universe is consistent with stellar ages, the baryon/photon ratio is consistent with measurements of the [D/H] ratio, and the inferred Hubble constant is consistent with local observations of the expansion rate. -
Cosmological Structure Formation with Modified Gravity
Cosmological Structure Formation with Modified Gravity A THESIS SUBMITTED TO THE UNIVERSITY OF MANCHESTER FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF ENGINEERING AND PHYSICAL SCIENCES 2015 Samuel J. Cusworth School of Physics and Astronomy 2 Simulations with Modified Gravity Contents Abstract . 10 Declarations . 11 Acknowledgements . 12 The Author . 14 Supporting Publications . 15 1 Introduction 17 1.1 Introduction to Modern Cosmology . 17 1.1.1 Cosmological Principle . 17 1.1.2 Introduction to General Relativity . 18 1.1.3 Einstein’s Equations from an Action Principle . 20 1.2 Concordance Cosmology . 21 1.2.1 Background Cosmology . 21 1.2.2 The Perturbed ΛCDM universe . 23 1.2.3 Non-linear Structure Formation . 27 1.3 Observational Cosmology . 30 1.3.1 SN1a . 30 1.3.2 CMB . 30 1.3.3 Galaxy Clusters . 33 1.4 f(R) as Dark Energy . 34 1.4.1 Gravitational Field Equations . 35 1.4.2 Einstein Frame . 36 Samuel Cusworth 3 CONTENTS 1.4.3 Screening Mechanism . 37 1.4.4 Viable Models . 39 2 Simulations of Structure Formation 43 2.1 Initial Condition Generation . 44 2.2 N-body Solvers . 45 2.2.1 Tree-Based Methods . 46 2.2.2 Particle Mesh Methods . 47 2.2.3 Adaptive Grid Methods . 49 2.3 Hydrodynamics . 50 2.3.1 Smoothed Particle Hydrodynamics . 51 2.4 Measuring Large Scale Structure Statistics . 54 2.4.1 Matter Power Spectrum . 54 2.4.2 Cluster Mass Function . 55 2.5 Known Limitations . 59 2.5.1 Choice of Initial Conditions . -
CMBEASY:: an Object Oriented Code for the Cosmic Microwave
www.cmbeasy.org CMBEASY:: an Object Oriented Code for the Cosmic Microwave Background Michael Doran∗ Department of Physics & Astronomy, HB 6127 Wilder Laboratory, Dartmouth College, Hanover, NH 03755, USA and Institut f¨ur Theoretische Physik der Universit¨at Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany We have ported the cmbfast package to the C++ programming language to produce cmbeasy, an object oriented code for the cosmic microwave background. The code is available at www.cmbeasy.org. We sketch the design of the new code, emphasizing the benefits of object orienta- tion in cosmology, which allow for simple substitution of different cosmological models and gauges. Both gauge invariant perturbations and quintessence support has been added to the code. For ease of use, as well as for instruction, a graphical user interface is available. I. INTRODUCTION energy, dark matter, baryons and neutrinos. The dark energy can be a cosmological constant or quintessence. The cmbfast computer program for calculating cos- There are three scalar field field models implemented, or mic microwave background (CMB) temperature and po- alternatively one may specify an equation-of-state his- larization anisotropy spectra, implementing the fast line- tory. Furthermore, the modular code is easily adapted of-sight integration method, has been publicly available to new problems in cosmology. since 1996 [1]. It has been widely used to calculate spec- In the next section IIA we explain object oriented pro- cm- tra for open, closed, and flat cosmological models con- gramming and its use in cosmology. The design of beasy taining baryons and photons, cold dark matter, massless is presented in section II B, while the graphical and massive neutrinos, and a cosmological constant. -
Year 1 Cosmology Results from the Dark Energy Survey
Year 1 Cosmology Results from the Dark Energy Survey Elisabeth Krause on behalf of the Dark Energy Survey collaboration TeVPA 2017, Columbus OH Our Simple Universe On large scales, the Universe can be modeled with remarkably few parameters age of the Universe geometry of space density of atoms density of matter amplitude of fluctuations scale dependence of fluctuations [of course, details often not quite as simple] Our Puzzling Universe Ordinary Matter “Dark Energy” accelerates the expansion 5% dominates the total energy density smoothly distributed 25% acceleration first measured by SN 1998 “Dark Matter” 70% Our Puzzling Universe Ordinary Matter “Dark Energy” accelerates the expansion 5% dominates the total energy density smoothly distributed 25% acceleration first measured by SN 1998 “Dark Matter” next frontier: understand cosmological constant Λ: w ≡P/ϱ=-1? 70% magnitude of Λ very surprising dynamic dark energy varying in time and space, w(a)? breakdown of GR? Theoretical Alternatives to Dark Energy Many new DE/modified gravity theories developed over last decades Most can be categorized based on how they break GR: The only local, second-order gravitational field equations that can be derived from a four-dimensional action that is constructed solely from the metric tensor, and admitting Bianchi identities, are GR + Λ. Lovelock’s theorem (1969) [subject to viability conditions] Theoretical Alternatives to Dark Energy Many new DE/modified gravity theories developed over last decades Most can be categorized based on how they break GR: The only local, second-order gravitational field equations that can be derived from a four-dimensional action that is constructed solely from the metric tensor, and admitting Bianchi identities, are GR + Λ. -
The Optical Depth to Reionization As a Probe of Cosmological and Astrophysical Parameters Aparna Venkatesan University of San Francisco, [email protected]
The University of San Francisco USF Scholarship: a digital repository @ Gleeson Library | Geschke Center Physics and Astronomy College of Arts and Sciences 2000 The Optical Depth to Reionization as a Probe of Cosmological and Astrophysical Parameters Aparna Venkatesan University of San Francisco, [email protected] Follow this and additional works at: http://repository.usfca.edu/phys Part of the Astrophysics and Astronomy Commons, and the Physics Commons Recommended Citation Aparna Venkatesan. The Optical Depth to Reionization as a Probe of Cosmological and Astrophysical Parameters. The Astrophysical Journal, 537:55-64, 2000 July 1. http://dx.doi.org/10.1086/309033 This Article is brought to you for free and open access by the College of Arts and Sciences at USF Scholarship: a digital repository @ Gleeson Library | Geschke Center. It has been accepted for inclusion in Physics and Astronomy by an authorized administrator of USF Scholarship: a digital repository @ Gleeson Library | Geschke Center. For more information, please contact [email protected]. THE ASTROPHYSICAL JOURNAL, 537:55È64, 2000 July 1 ( 2000. The American Astronomical Society. All rights reserved. Printed in U.S.A. THE OPTICAL DEPTH TO REIONIZATION AS A PROBE OF COSMOLOGICAL AND ASTROPHYSICAL PARAMETERS APARNA VENKATESAN Department of Astronomy and Astrophysics, 5640 South Ellis Avenue, University of Chicago, Chicago, IL 60637; aparna=oddjob.uchicago.edu Received 1999 December 17; accepted 2000 February 8 ABSTRACT Current data of high-redshift absorption-line systems imply that hydrogen reionization occurred before redshifts of about 5. Previous works on reionization by the Ðrst stars or quasars have shown that such scenarios are described by a large number of cosmological and astrophysical parameters. -
Cosmology from Cosmic Shear and Robustness to Data Calibration
DES-2019-0479 FERMILAB-PUB-21-250-AE Dark Energy Survey Year 3 Results: Cosmology from Cosmic Shear and Robustness to Data Calibration A. Amon,1, ∗ D. Gruen,2, 1, 3 M. A. Troxel,4 N. MacCrann,5 S. Dodelson,6 A. Choi,7 C. Doux,8 L. F. Secco,8, 9 S. Samuroff,6 E. Krause,10 J. Cordero,11 J. Myles,2, 1, 3 J. DeRose,12 R. H. Wechsler,1, 2, 3 M. Gatti,8 A. Navarro-Alsina,13, 14 G. M. Bernstein,8 B. Jain,8 J. Blazek,7, 15 A. Alarcon,16 A. Ferté,17 P. Lemos,18, 19 M. Raveri,8 A. Campos,6 J. Prat,20 C. Sánchez,8 M. Jarvis,8 O. Alves,21, 22, 14 F. Andrade-Oliveira,22, 14 E. Baxter,23 K. Bechtol,24 M. R. Becker,16 S. L. Bridle,11 H. Camacho,22, 14 A. Carnero Rosell,25, 14, 26 M. Carrasco Kind,27, 28 R. Cawthon,24 C. Chang,20, 9 R. Chen,4 P. Chintalapati,29 M. Crocce,30, 31 C. Davis,1 H. T. Diehl,29 A. Drlica-Wagner,20, 29, 9 K. Eckert,8 T. F. Eifler,10, 17 J. Elvin-Poole,7, 32 S. Everett,33 X. Fang,10 P. Fosalba,30, 31 O. Friedrich,34 E. Gaztanaga,30, 31 G. Giannini,35 R. A. Gruendl,27, 28 I. Harrison,36, 11 W. G. Hartley,37 K. Herner,29 H. Huang,38 E. M. Huff,17 D. Huterer,21 N. Kuropatkin,29 P. Leget,1 A. R. Liddle,39, 40, 41 J. -
Cosmic Microwave Background
1 29. Cosmic Microwave Background 29. Cosmic Microwave Background Revised August 2019 by D. Scott (U. of British Columbia) and G.F. Smoot (HKUST; Paris U.; UC Berkeley; LBNL). 29.1 Introduction The energy content in electromagnetic radiation from beyond our Galaxy is dominated by the cosmic microwave background (CMB), discovered in 1965 [1]. The spectrum of the CMB is well described by a blackbody function with T = 2.7255 K. This spectral form is a main supporting pillar of the hot Big Bang model for the Universe. The lack of any observed deviations from a 7 blackbody spectrum constrains physical processes over cosmic history at redshifts z ∼< 10 (see earlier versions of this review). Currently the key CMB observable is the angular variation in temperature (or intensity) corre- lations, and to a growing extent polarization [2–4]. Since the first detection of these anisotropies by the Cosmic Background Explorer (COBE) satellite [5], there has been intense activity to map the sky at increasing levels of sensitivity and angular resolution by ground-based and balloon-borne measurements. These were joined in 2003 by the first results from NASA’s Wilkinson Microwave Anisotropy Probe (WMAP)[6], which were improved upon by analyses of data added every 2 years, culminating in the 9-year results [7]. In 2013 we had the first results [8] from the third generation CMB satellite, ESA’s Planck mission [9,10], which were enhanced by results from the 2015 Planck data release [11, 12], and then the final 2018 Planck data release [13, 14]. Additionally, CMB an- isotropies have been extended to smaller angular scales by ground-based experiments, particularly the Atacama Cosmology Telescope (ACT) [15] and the South Pole Telescope (SPT) [16]. -
6 Structure Formation – I
6 Structure formation – I 6.1 Newtonian equations of motion We have decided that perturbations will in most cases effectively be described by the Newtonian potential, Φ. Now we need to develop an equation of motion for Φ, or equivalently for the density fluctuation ρ (1 + δ)¯ρ. In the Newtonian approach, we treat dynamics of cosmological≡ matter exactly as we would in the laboratory, by finding the equations of motion induced by either pressure or gravity. We begin by casting the problem in comoving units: x(t) = a(t)r(t) (177) δv(t) = a(t)u(t), so that x has units of proper length, i.e. it is an Eulerian coordinate. First note that the comoving peculiar velocity u is just the time derivative of the comoving coordinate r: x˙ =a ˙r + ar˙ = Hx + ar˙, (178) where the rhs must be equal to the Hubble flow Hx, plus the peculiar velocity δv = au. The equation of motion follows from writing the Eulerian equation of motion as x¨ = g0 + g, where g = Φ/a is the peculiar −∇∇∇∇∇∇∇ acceleration, and g0 is the acceleration that acts∇∇∇ on a particle in a homogeneous universe (neglecting pressure forces to start with, for simplicity). Differentiating x = ar twice gives a¨ x¨ = au˙ + 2˙au + x = g0 + g. (179) a The unperturbed equation corresponds to zero peculiar velocity and zero peculiar acceleration: (¨a/a) x = g0; subtracting this gives the perturbed equation of motion u˙ + 2(˙a/a)u = g/a = Φ/a. (180) −∇∇∇∇∇∇∇∇∇∇ This equation of motion for the peculiar velocity shows that u is affected by gravitational acceleration and by the Hubble drag term, 2(˙a/a)u.