Physical Foundations of Cosmology

380 Cosmic microwave background anisotropies Problem 9.9Show thatηx/η 0 Iz−x^1 /^2 ,where I≡ 3 ( (^)  (^) m ) 1 / 6 ⎡ ⎣ ∫y 0 ...

9.7 Anisotropies on small angular scales 381 This estimate is not very reliable because the imperfect fluid approximation breaks ...

382 Cosmic microwave background anisotropies recombination. This is why the parameter!and the location of the acoustic peaks in ...

9.7 Anisotropies on small angular scales 383 Problem 9.13Using the stationary (saddle) point method, verify that for a slowly va ...

384 Cosmic microwave background anisotropies where the integrals Im ( l/lf ) ≡ ∫∞ 1 (lnx)m x^2 √ x^2 − 1 e−(l/lf) (^2) x 2 dx (9 ...

9.8 Determining cosmic parameters 385 0 2 4 6 400 800 1200 l Fig. 9.2. 9.8 Determining cosmic parameters Assuming a Gaussian, ad ...

386 Cosmic microwave background anisotropies the plateau can be used to determine the primordial spectral amplitude and spectral ...

9.8 Determining cosmic parameters 387 in the current best-fit model. However, for some choices of parameters the destruc- tive i ...

388 Cosmic microwave background anisotropies changes in the baryon and cold dark matter densities. If the baryon density is made ...

9.8 Determining cosmic parameters 389 showed that to keep the first peak heightH 1 fixed, the baryon density can be increased on ...

390 Cosmic microwave background anisotropies constant. The dependence of the peak location onh 75 is modest, so a very accu- rat ...

9.9 Gravitational waves 391 index. The dark energy may comprise quintessence, rather than vacuum energy. In this case, we must i ...

392 Cosmic microwave background anisotropies and substituting (9.116) in the Boltzmann equation (9.7), we find that the temper- ...

9.9 Gravitational waves 393 Introducing the new variablex≡k(η 0 −η)instead ofη,and noting that (l 1 k) k =− ∂ i∂x e−i kl 1 kx, ( ...

394 Cosmic microwave background anisotropies (9.128), we can calculate the integral with the help of (9.43). The result, valid f ...

9.10 Polarization of the cosmic microwave background 395 10 100 1000 0.01 0.1 1 10 100 1000 S+ T T l l(l + l)C (l (^2) T /2 π) [ ...

396 Cosmic microwave background anisotropies primordial spectrum of gravitational waves produced by inflation, one of the most c ...

9.10 Polarization of the cosmic microwave background 397 characterized entirely by the two-dimensional, second rank symmetric po ...

398 Cosmic microwave background anisotropies In the orthonormal basis,whereea·eb=δab,one can define the Stokes param- eters Q≡ 2 ...

9.10 Polarization of the cosmic microwave background 399 n l x z y e Fig. 9.5. components of the electric field along vectoreaar ...