Simulating Cosmic Microwave Background Fluctuations

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1 Simulating Cosmic Microwave Background Fluctuations Mario Bisi Emma Kerswill Picture taken from:

2 Introduction What is the CMB and how was it formed? Why is the CMB interesting? How do we simulate CMB fluctuations? Solving degeneracies using supernovae data Polarisation of the CMB

3 About the CMB Discovered in 1964 by Robert Wilson and Arno Penzias Provides strong evidence of the Big Bang Snapshot of the early Universe Originates from the Surface of Last Scattering Temperature of CMB photons now ~2.73K

4 Surface of Last Scattering CMB photons originate from the Surface of Last Scattering Temperature ~3000K at this time Photons after this time can travel unimpeded through the Universe The epoch when the Universe went from being opaque to transparent Temperature fluctuations in the CMB photons reflect density perturbations in the early Universe

5 The CMB Monopole Dipole Increasing Resolution Anisotropies Pictures taken from:

6 Origins of the CMB anisotropies Quantum noise creates density fluctuations in primordial matter This creates potential hills and wells Radiation pressure versus the gravitational attraction causes acoustic oscillations in the matter Animation taken from:

7 What we observe Picture taken from: An angular variation of temperature is found on the scale of tens of µk Foreground noise is larger than the temperature fluctuations Therefore, measure the temperature difference across the sky from one point to another

8 What we obtain Temperature Power Spectrum T in µk Multipole, l

9 What these observations tell us We already know that the Universe is defined by parameters Enables us to home-in on values of these parameters Some examples of these parameters: Ω Total, Ω b, Ω cdm, Ω Λ, H 0, etc Identifying the values of these parameters will tell us about the type of Universe in which we live and its eventual fate

10 Using CMBfast to simulate the CMB power spectrum Can input parameter values which affect the characteristics of the Universe Uses statistical methods to model the scattering of photons during the period of recombination Produces data which can be plotted to give a simulated power spectrum of the CMB

11 Parameter Degeneracies Altering some parameters can affect the power spectrum in the same way as other parameters CMB temperature data therefore does not always give the necessary information to discern one variable s effects from another Need alternative ways of evaluating the values for these parameters

12 Degeneracy between Ω m and Ω Λ Variation of ΩΜ and ΩΛ, with ΩT = T in K ΩΛ = 0.45 ΩΛ = 0.5 ΩΛ = 0.55 ΩΛ = 0.60 ΩΛ = 0.65 ΩΛ = 0.70 ΩΛ = 0.75 ΩΛ = 0.80 ΩΛ = Multipole, l

Type Ia Supernovae Picture taken from: http://www.pitt.

13 Type Ia Supernovae Picture taken from: Characterised by absence of Hydrogen in their spectra Most likely to be a white dwarf exploding Observed peak luminosity varies greatly Normalisation using light curve shape allows them to be used as standard candles

14 Type Ia SNe as Standard Candles c m = 5log z + 5log + M H At low redshifts, z < 0.1, curvature is negligible, the above formula links the apparent magnitude of an object to its redshift Calibration with Cepheid variables shows Type Ia Supernovae are reliable distance indicators At high redshifts a more complex formula is used, involving Ω m and Ω Λ

15 Models of the Universe and SNe Ia observations Varying Ω m and Ω Λ within the magnituderedshift equation allows us to plot curves for specific models of the Universe These curves can then be compared with observational data to identify values of Ω m and Ω Λ Graph taken from: ApJ 517: , 1999 June 1

16 Combining SNe Ia and CMB data Individually both sets of data have degeneracies within the Ω m Ω Λ plane Each set of observations is totally separate from the other When the results are combined tighter constraints on Ω m and Ω Λ are achieved Picture taken from: astro-ph/ v3

17 How the CMB is polarised Animation taken from:

Types of CMB Polarisation Density perturbations give (linear) scalar polarisation Vorticity in the plasma gives vector polarisation (thought not to be significant during

18 Types of CMB Polarisation Density perturbations give (linear) scalar polarisation Vorticity in the plasma gives vector polarisation (thought not to be significant during recombination at time of last scattering) Gravity Waves give (linear and asymmetric) tensor polarisation Picture taken from:

19 Why the polarisation data of the CMB is useful Can be used to break certain parameter degeneracies seen in the temperature power spectrum Polarisation can only be generated by Thomson Scattering Provides a direct snapshot of the conditions on the surface of last scattering The temperature data may have contributions in it caused between last scattering and now, but polarisation cannot

20 Example of Thomson Scattering Electron cannot vibrate in the direction of incident photon propagation Non-isotropic temperature so therefore get a linear polarisation of the resulting photon Animation taken from:

21 Polarisation Power Spectrum Polarisation power spectrum approximately 1/10 amplitude of the temperature power spectrum T in µ K Polarisation Power Spectrum of the Variation of Ω Λ and therefore Ω k, with a constant Ω mh 2 = ΩΛ = ΩΛ = ΩΛ = ΩΛ = ΩΛ = E-Mode only from linear polarisations Multipole, l

22 Spectrum Comparison Comparison between the Temperature and Polarisation Power Spectrums 80 T in µ K ΩΛ = ΩΛ = ΩΛ = ΩΛ = ΩΛ = Miltipole, l

23 Summary The CMB provides our earliest view of the Universe We measure the temperature and polarisation power spectra of the CMB CMBfast simulates the effect different parameters have on the power spectra When combined with data from other sources gives us information about our Universe, its characteristics and its fate

Lecture 03. The Cosmic Microwave Background

Lecture 03. The Cosmic Microwave Background The Cosmic Microwave Background 1 Photons and Charge Remember the lectures on particle physics Photons are the bosons that transmit EM force Charged particles interact by exchanging photons But since they