Flat universe

Show that, in a flat Universe model with a cosmological constant, Eq. (12.17) reduces to... 

Because the matter density VLmh2 was fairly well constrained by the amplitudes, the positions of a point in Figure 9.21 served to define a value of the Hubble constant. The size of the points in Figure 9.21 indicates how well this derived Hubble constant agrees with the H0 = 72 8 from the HST Key Project (Freedman et al., 2001). Shown as contours are the Ax2 = 1, 4, 9 contours from my fits to 230 SNe la (Tonry et al., 2003). Clearly the CMB data, the HST data, and the SNe data are all consistent at a three-way crossing that is very close to the flat Universe line. Assuming the Universe actually is flat, the age of the Universe is very well determined 13.7 0.2 Gyr. 

In a flat Universe, dominated by pressureless matter like Cold Dark Matter, we have a, oc2/3 and, by definition, p = cs = 0. The solution to the second-order equation is = A t2/3 + The first term, proportional to f2// 3 oc... 

Within this paradigm, the results are consistent with a flat Universe (Qm = 1.02 0.02) and a nearly scale-invariant initial spectrum of perturbations ns = 0.93 0.03. Both of these are as expected if inflation acted in the early Universe. 

Figure 12.2. Likelihood distribution for 17a vs. 17m- The input data are from Tonry et al. 2003. This diagram should be compared to similar ones in Riess et al. 1998 Perlmutter et al. 1999 Leibundgut 2001 Perlmutter et al. 2003 Barris 2004 Knop et al. 2004. The degeneracy along 0.817a — 0.617m is obvious. The overlap with the flat universe model is not within the 68% likelihood area here. The grey contour lines show the dynamical age of the universe Ho-to. Clearly the SN data favour an age near 1.

De Bernadis, P and 35 others, 2000. A flat universe from high resolution maps of the cosmic microwave background radiation. Nature, 404, 955-9. 

Multipole fluctuation strength of the cosmic microwave background radiation as a function of the spherical harmonic index I. The location and the height of the first minimum favors a spatially flat Universe, while the level of the fluctuations in the higher multipoles (/ > 400) Indicates the presence of a low-density baryonic component (<5%). The measurements cover already the damping region (/ > 1,000). Wilkinson Microwave Anisotropy Probe (WMAP) data are displayed together with results of earlier balloon observations (Reprinted from Nolta et al. 2009 with kind permission of the first author, the WMAP Science Team, and AAS)... 

The parameter 77 also depends on fij, = /tb IPo i-C-> the ratio of the baryon density to the critical density Pc needed for a flat Universe. 

In this section we continue to explore the consequences of the existence of the low temperature excitations in amorphous substances, which, as argued in Section III, are really resonances that arise from residual molecular motions otherwise representative of the molecular rearrangements in the material at the temperature of vitrification. We were able to see why these degrees of freedom should exist in glasses and explain their number density and the nearly flat energy spectrum, as well as the universal nature of phonon scattering off these excitations at low T < 1 K). 

Vertical cylindrical tanks, with flat bases and conical roofs, are universally used for the bulk storage of liquids at atmospheric pressure. Tank sizes vary from a few hundred gallons (tens of cubic metres) to several thousand gallons (several hundred cubic metres). 

Chemical Engineering Faculty, Kiev National Technical University, Polytechnik Institute (NTUU KPI), 7 Peremogy Prospekt, 03056 Kiev, Ukraine, flat andriiko. kiev.ua... 

Orion Constellation This is a mosaic picture of 18 (6x3) frames. Additional four frames are added around the Barnard Loop region to increase S/N. Vignetting of the telescope is corrected by flat fielding, using proprietary software written in IDL. Distortion correction and initial colour match is done in Registar, with final colour correction and mosaic processed using Photoshop. (Reproduced by permission of Wei-Hao Wang, Institute for Astronomy at University of Hawaii)... 

There is no evidence that Minkowski space is flat on the large scale. The assumption of euclidean Minkowski space could therefore be, and probably is an illusion, like the flat earth. In fact, there is compelling evidence from observed spectroscopic red shifts that space is curved over galactic distances. These red shifts are proportional to distances from the source, precisely as required by a curved space-time[52j. An alternative explanation, in terms of an expanding-universe model that ascribes the red shifts to a Doppler... 

CDT, based in Cambridge, U.K., was founded after initial work done at the Cambridge University. Researchers in Cambridge discovered that poly(/>-phenylenevinylene) (PPV, Figure 11.16) and its derivatives can be used as emitters to construct OLEDs, which were the first examples of PLEDs [4], The invention has brought flat-panel displays to the verge of commercialization. 

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