Cosmic Microwave Background Cosmological Overview/Definitions Temperature Polarization
Download ReportTranscript Cosmic Microwave Background Cosmological Overview/Definitions Temperature Polarization
Cosmic Microwave Background Cosmological Overview/Definitions Temperature Polarization Ramifications Scott Dodelson Academic Lecture V Goal: Explain the Physics and Ramifications of this Plot Coherent picture of formation of structure in the universe t 10 34 sec t ~100,000 years Quantum Mechanical Fluctuations during Inflation Perturbation Growth: Pressure vs. Gravity V ( ) m, r , b , f Photons freestream: Inhomogeneities turn into anisotropies zreion , de , w Matter perturbations grow into nonlinear structures observed today Review of Notation Scale Factor a(t) Conformal time/comoving horizon dt/a(t) Gravitational Potential Photon distribution Will use Fourier transforms x d3k keikx /(2)3 k is comoving wavenumber Wavelength k-1 Photon Distribution Distribution depends on position x (or wavenumber k), direction n and time t (or η). Moments Monopole: Dipole: Quadrupole: You might think we care only about at our position because we can’t measure it anywhere else, but … We see photons today from last scattering surface at z=1100 accounts for D* redshifting is distanceout to last of scattering potential surface well Can rewrite as integral over Hubble radius (aH)-1 Perturbations outside the horizon Perturbations can be decomposed into Fourier modes + = Combine Fourier Modes to Produce Structure in our Universe + = + = In this simple example, all modes have same wavelength/frequency More generally, at each wavelength/frequency, need to average over many modes to get spectrum Inflation produces perturbations Quantum mechanical fluctuations in gravitational potential <(k) k’>3 3k-k’Pk Inflation stretches wavelength beyond horizon: k,tbecomes constant Infinite number of independent perturbations w/ independent amplitudes Evolution of Fluctuations To see how perturbations evolve, need to solve an infinite hierarchy of coupled differential equations Perturbations in metric induce photon, dark matter perturbations Evolution upon re-entry Pressure of radiation acts against clumping If a region gets overdense, pressure acts to reduce the density: restoring force Similar to height of guitar string (pressure replaced by tension) Before recombination, electrons and photons are tightly coupled: equations reduce to Temperature perturbation Very similar to … Displacement of a string What spectrum is produced by a stringed instrument C string on a ukulele Compare the ukulele spectrum to CMB spectrum CMB is different because … Fourier Transform of spatial, not temporal, signal Time scale much longer (400,000 yrs vs. 1/260 sec) No finite length: all k allowed! Largest Wavelength/ Smallest Frequency Smallest Wavelength/ Largest Frequency Why peaks and troughs? Vibrating String: Characteristic frequencies because ends are tied down Temperature in the Universe: Small scale modes enter the horizon earlier than large scale modes The spectrum at last scattering is: Θ0 + Ψ ~ cos[k rs(η*) ] Peaks at k = nπ/rs(η*) One more effect: Damping on small scales But So On scales smaller than D (or k>kD) perturbations are damped Cl simply related to [0+]RMS(k=l/D*) Fourier transform of temperature at Last Scattering Surface Anisotropy spectrum today Remember that at any wavelength, we are averaging over many modes with different direction. Puzzle: Why are all modes in phase? The perturbation corresponding to each mode can either have zero initial velocity or zero initial amplitude We implicitly assumed that every mode started with zero velocity. Interference could destroy peak structure There are many, many modes with similar values of k. All have different initial amplitude. But all are in phase. First Peak An infinite number of ukuleles are synchronized Similarly, all modes corresponding to first trough are in phase: they all have zero amplitude at recombination Without synchronization: First “Peak” First “Trough” All modes remain constant until they re-enter horizon. Inflation synchronizes all modes How do inhomogeneities at last scattering show up as anisotropies today? Perturbation w/ wavelength k-1 shows up as anisotropy on angular scale ~k-1/D* ~l-1 When we see this, we conclude that modes were set in phase during inflation! NASA/WMAP Bennett et al. 2003 Compton Scattering produces polarized radiation field Polarization field decomposes into 2-modes: B-mode smoking gun signature of tensor perturbations, dramatic proof of inflation... We will focus on E. Three Step argument for <TE> E-Polarization proportional to quadrupole Quadrupole proportional to dipole Dipole out of phase with monopole Isotropic radiation field produces no polarization after Compton scattering Modern Cosmology Adapted from Hu & White 1997 Radiation with a dipole produces no polarization A quadrupole is needed (ve Quadrupole proportional to dipole ve ve x MFP ) (ve x MFP ) Dipole is out of phase with monopole v 0 1 0 t Roughly, 0 (k ,* ) A cos[krs (* )] 1 (k ,* ) B sin[krs (* )] The product of monopole and dipole is initially positive (but small, since dipole vanishes as k goes to zero); and then switches signs several times. DASI initially detected TE signal Kovac et al. 2002 WMAP has indisputable evidence that monopole and dipole are out of phase NASA/ WMAP This is most remarkable for scales around l~100, which were not in causal contact at recombination. Different Geometries Possible Inflation predicts a flat universe We now have a solid argument that the total density is flat Object with known physical size Parameter I: Curvature Same wavelength subtends smaller angle in an open universe Peaks appear on smaller scales in open universe Hot/cold spots of known physical size has been observed Angular size demonstrates flatness Parameters II Reionization lowers the signal on small scales A tilted primordial spectrum (n<1) increasingly reduces signal on small scales Tensors reduce the scalar normalization, and thus the small scale signal n is degenerate w/ reionization, but polarization pins down the latter: we now know n to within a few percent. Parameters III Baryons accentuate odd/even peak disparity Less matter implies changing potentials, greater driving force, higher peak amplitudes Cosmological constant changes the distance to LSS E.g.: Baryon density x x F 2 Here, F is forcing term due to gravity. kcs k 3(1 3b / 4 ) As baryon density goes up, frequency goes down. Greater odd/even peak disparity. Bottom line h often used instead of m h b h 1 h2 2 2 CMB data says matter density is only 30% of critical: Need Dark Energy and Dark Matter Conclusions Strong evidence for inflation from CMB anisotropy/polarization spectra Baryon and matter densities tightly constrained, consistent with other determinations. Dark energy & dark matter needed Connection between particle physics & cosmology (inflation, dark matter, dark energy) more solid than ever. We need new tools … Available at www.amazon.com