UBC Faculty Research and Publications

WMAP 5-year data: Let’s test Inflation Halpern, Mark Apr 18, 2008

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During today’s  talk, WMAP will survey 1/3 of the sky (again).While we have been talking, WMAP has surveyed 1/3 of the sky.Sun shadow linesWMAP 5-year data: Let’s test InflationMark Halpern, UBCC. Bennett (PI)(JHU)J. Dunkley (Oxford)B. Gold (JHU)M. Greason (NASA)M. Halpern (UBC) R. Hill (NASA)G. Hinshaw(NASA)N. Jarosik (Princeton)A. Kogut (NASA)E. Komatsu (UTexas)D. Larson (JHU)M. Limon (Columbia) S. Meyer (Chicago)M. Nolta (CITA)N. Odegard (NASA)L. Page (Princeton)D. Spergel (Princeton)G. Tucker (Brown)J. Weiland (NASA)E. Wollack (NASA)E. Wright (UCLA)…and thanks to WMAP ‘graduates’ C. Barnes, R. Bean, O. Dore, H. Peiris, L. Verde, and especially to David Wilkinson!The WMAP Science Team:Let’s use the cosmic microwave background intensity as a pedagogic example:  What epoch does the planck function probe?Scattering time constants increase as the universe expands and cools,and a given process stops once its reaction rate becomes comparable to 1/H.   Photons stopped scattering off electrons at (1+z)~1000 and the universe became transparent.But, among the processes in this plot, only bremstrahlung and double-compton scattering can change the number of photons and bring light and matter into thermal equilibrium.  The photon-to-baryon ratio was ‘frozen’ at z~107 and the thermal spectrum tells us that there has not been a large energy release since the universe was a week old.• Hinshaw et al., “Data Processing, Sky Maps, and BasicResults” Astro-ph:0803.0732• Hill et al., “Beam Maps and Window Functions” 0803.0570• Gold et al., “Galactic Foreground Emission” 0803.0715• Wright et al., “Source Catalogue” 0803.0577• Nolta et al., “Angular Power Spectra” 0803.0593• Dunkley et al., “Likelihoods and Parameters from the WMAPdata” 0803.0586• Komatsu et al., “Cosmological Interpretation” 0803.0547There are seven papers in the WMAP 5-year data release:along with an updated WMAP Explanatory Supplement.The papers, the data and our likelihood code and results are available at http://lambda.gsfc.nasa.gov/WMAP  5 years:  what’s new?•Improved sensitivity.  We are measuring a variance, so some errors drop faster than t-1/2.•Better beam characterization and calibration•We can use Ka band in polarization along with Q and V.Our simplest 6-parameter ΛCDM model still works well.  Neither a running spectral index nor massive neutrinos help the fit.  Sudden reionization at z=6 is rejected, while a cosmic neutrino background is supported at 3σ. We have found 390  point sources.  The catalogue is complete at 2Jy.  The typical WMAP point source is only weakly polarized, while many of them are strongly variable.Wright et al., 803.0577Gold et al.  0803.0715Each pixel in the map is fit to a model of Synchrotron, Free-free and thermal Dust brightness, with synchrotron and dust spectral indices as free parameters using a Monte-Carlo Markhov chain.Gold et al.  0803.0715The procedure produces maps of the sky for each emission mechanism.In the 85% of the sky masked for CMB analysis the residuals to the fit are consistent with noise at the expected level.  The image below shows residuals/noise in W-bandHinshaw et al. 0803.0732Hinshaw et al. 0803.0732 Stokes Q mapsStokes U mapsThe 5-year Internal Linear Combination (ILC) map is a sum of the five single frequency maps which cancels galactic foreground emission.The two window functions are for  0.1 deg FWHM beams with a 1% difference in solid angle. Only WMAP has achieved anything like this accuracy.We will need to understand our beam shapes very well to understand our maps. Overall normalization, spectral index, tilt and unscrambling matter densities all rely on knowing our beam area and beam shape to high precision.Jupiter (Measured )(-40dB to 0.)Model (-40dB to 0)Difference(+/- ~3%)Hill et al. 0803.0570We have more data from Jupiter and better maps of the CMB, which confuse our Jupiter maps.A major improvement is that we now have high fidelity models of both sides of our optical system.  The models let us extend beam integrals beyond the angular range of high S/N Jupiter data.Black: Yr3-Yr5 window functions.Red: Yr-3  1-σ uncertaintiesOur beam uncertainties have dropped by almost a factor of two, while the difference between the beam shape we inferred at Yr-3 and Yr-5 is less than the Yr-3 1σuncertainties.Notice that the total beam solid angle has gone up for all V and W band by from 0.5% to 1.5%.  Much of this change is within the primary beam.Hill et al. 0803.0570Dunkley et al. 0803.0586The 5-yr TT spectrum is cosmic variance limited to l = 530, and the 3rd harmonic is resolved!Dots show values for individual lsNolta et al. 0803.0593Agreement with small angular scale measurements is goodRed line is ΛCDM fit to WMAP-5 aloneDunkley et al. 0803.0586Ground based experiments almost see the 5th harmonic and confirm the slope of the Silk tailBaryons (2.27+/- 0.06) /h2 %CDM  (10.99+/-0.62)/h2 %Optical Depth 0.087+/- 0.017Spectral Index 0.965+/-0.014σ8   0.796+/-0.036 Λ   0.742+/− 0.036The simple 6-parameter fit still works (yawn).  Values are consistent with Spergel et al. (2007) and precision has nearly doubled.Dunkley et al. 0803.0586OK--so let’s test inflation.Inflation was invented to solve the horizon problem (how is the universe so homogeneous on scales larger than the horizon at decoupling)  and the flatness problem (why is the universe still here when its natural time constant is the planck time?).Inflation models predict:•The universe is nearly flat;•Primordial fluctuations are gaussian; •Fluctuations are adiabatic;•Fluctuations are almost scale invariant. (ns is just less than unity); and•There should be a modest level of gravitational radiation.In addition to solving the horizon and flatness problems and imprinting super-horizon scale motion,Dunkley et al. 0803.0586The CMB alone can not establish flatness.Additional astrophysical data are required to set a distance scaleBaryon Acoustic Oscillations (BAO) measured in surveys of nearby galaxies set an angular-diameter distance.  Here, data from Percival et al. (2007) are compared to our best fit ΛCDM model.(Strictly speaking, the acoustic peaks in the CMB are also baryon-acoustic oscillations, but the term ‘BAO’ is typically restricted to very low-z situations.) Dunkley et al. 0803.0586Type 1A supernovae set a luminosity distance.  Here, data from HST, Essence and SNLS,  as binned by Wright (2007), are compared to our ΛCDM modelDunkley et al. 0803.0586The combined result: The Universe is flat: -0.018<Ωk<.007In this particular case, BAO provides the tighter constraint because its distance scale is absolute.  ( We have only used relative intensities of the supernovae.)Komatsu et al., 803.0547The Minkowsik FunctionalsKomatsu et al., 803.0547The WMAP maps are Gaussian.We find-137 < fNLlocal < 2  (68%)from Minkowski, and-9 < fNLlocal < 111  (95%)from the bi-spectrum.These numbers mean primordial iso-curvature fluctuations are gaussianto  0.1%.The 5-year TE power spectrum confirms Adiabatic fluctuations.  The green curve above l=30 is obtained from TT via super-horizon flow, with no free parameters.“Non-adiabatic” power would fill in the trough at l >100.Nolta et al. 0803.0593Green curve is NOT fit to these data.Entropic perturbations not correlated with curvature, such as axions,   are adiabatic to within 8.6%Komatsu et al., 803.0547Pedagogical illustration of searching for r, the ratio of tensor to scalar perturbations: the low l TT spectrum does most of the work once redundancy with tau is broken.Komatsu et al., 803.0547Gravitational radiation is expected to be present at the end of inflation and de-couples right away.  It produces tensor perturbations and a unique polarization signature.  The spectral index is less than 1, and gravitational radiation is not excessive.Komatsu et al., 803.0547As the universe “lingers” in inflation the spectral index is driven to unity and the amplitude of tensors to 0.  Some popular models have survived, others have not.…and don’t forget neutrinos.    Once again, the distance scale set by BAO is helpful.  It sharpens the resolution of the neutrino mass.There is still an order of magnitude between the mass lower limit set at SNO and Kamiokande and the upper limit set astro-physically.   Precise data on σ8 would help a lot.SNO kkKomatsu et al., 803.0547There is a Cosmic Neutrino Background! (cnb)Dunkley et al. 0803.0586The red curve is for 3 relativistic, weakly interacting species which de-couple at 2 Mev ( z~1010). This is a treat, but not a surprise.The number of relativistic species is very correlated with matter density.  We constrain the ratio better than the amount.  But the likelihood vanishes as one approaches zero.The power of this constraint does not depend on including the distance scales from supernovae or the  BAO.  ..and we are consistent with the obvious correct answer!Komatsu et al., 803.0547Hinshaw et al. 0803.0732Dunkley et al. 0803.0586Wright et al., 803.0577Gold et al.  0803.0715Hill et al. 0803.0570Hinshaw et al. 0803.0732Nolta et al. 0803.0593Komatsu et al., 803.0547Nolta et al. 0803.0593


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