Aspects of spherically symmetric cosmological models.

Thesis (M.Sc.)-University of Natal, Durban, 1998.In this thesis we consider spherically symmetric cosmological models when the shear is nonzero and also cases when the shear is vanishing. We investigate the role of the Emden-Fowler equation which governs the behaviour of the gravitational field. The Einstein field equations are derived in comoving coordinates for a spherically symmetric line element and a perfect fluid source for charged and uncharged matter. It is possible to reduce the system of field equations under different assumptions to the solution of a particular Emden-Fowler equation. The situations in which the Emden-Fowler equation arises are identified and studied. We analyse the Emden-Fowler equation via the method of Lie point symmetries. The conditions under which this equation is reduced to quadratures are obtained. The Lie analysis is applied to the particular models of Herlt (1996), Govender (1996) and Maharaj et al (1996) and the role of the Emden-Fowler equation is highlighted. We establish the uniqueness of the solutions of Maharaj et al (1996). Some physical features of the Einstein-Maxwell system are noted which distinguishes charged solutions. A charged analogue of the Maharaj et al (1993) spherically symmetric solution is obtained. The Gutman-Bespal'ko (1967) solution is recovered as a special case within this class of solutions by fixing the parameters and setting the charge to zero. It is also demonstrated that, under the assumptions of vanishing acceleration and proper charge density, the Emden-Fowler equation arises as a governing equation in charged spherically symmetric models

Observing the Sunyaev-Zel'dovich Effect Closer to Home

Hot gas trapped in a dark matter halo will produce a decrement in the surface brightness of the microwave background, the Sunyaev-Zel'dovich (SZ) effect. While massive clusters produce the strongest central SZ decrements, we point out that a local galaxy halo, specifically the halo of M31, may be one of the brightest integrated SZ sources in the sky. For various realistic gas distributions consistent with current X-ray limits, we show that the integrated SZ decrement from M31 will be comparable to decrements already detected in more distant sources, provided its halo contains an appreciable quantity of hot gas. A measurement of this decrement would provide direct information on the mass, spatial distribution and thermodynamic state of hot gas in a low-mass halo, and could place important constraints on current models of galaxy formation. Detecting such an extended (~ 10 degree), low-amplitude signal will be challenging, but should be possible with all-sky SZ maps from satellite missions such as the Wilkinson Microwave Anisotropy Probe or the Planck Surveyor.Comment: 5 pages, 3 figures; submitted to MNRA

Measurement of the pairwise kinematic Sunyaev-Zeldovich effect with Planck and BOSS data

We present a new measurement of the kinetic Sunyaev-Zeldovich effect (kSZ) using Planck cosmic microwave background (CMB) and Baryon Oscillation Spectroscopic Survey (BOSS) data. Using the `LowZ North/South' galaxy catalogue from BOSS DR12, and the group catalogue from BOSS DR13, we evaluate the mean pairwise kSZ temperature associated with BOSS galaxies. We construct a `Central Galaxies Catalogue' (CGC) which consists of isolated galaxies from the original BOSS data set, and apply the aperture photometry (AP) filter to suppress the primary CMB contribution. By constructing a halo model to fit the pairwise kSZ function, we constrain the mean optical depth to be $\bar{\tau}=(0.53\pm0.32)\times10^{-4}(1.65\,\sigma)$ for `LowZ North CGC', $\bar{\tau}=(0.30\pm0.57)\times10^{-4}(0.53\,\sigma)$ for `LowZ South CGC', and $\bar{\tau}=(0.43\pm0.28)\times10^{-4}(1.53\,\sigma)$ for `DR13 Group'. In addition, we vary the radius of the AP filter and find that the AP size of $7\,{\rm arcmin}$ gives the maximum detection for $\bar{\tau}$. We also investigate the dependence of the signal with halo mass and find $\bar{\tau}=(0.32\pm0.36)\times10^{-4}(0.8\,\sigma)$ and $\bar{\tau}=(0.67\pm0.46)\times10^{-4}(1.4\,\sigma)$ for `DR13 Group' with halo mass restricted to, respectively, less and greater than its median halo mass, $10^{12}\, h^{-1}{\rm M}_{\odot}$. For the `LowZ North CGC' sample restricted to $M_{\rm h} \gtrsim 10^{14}\, h^{-1}{\rm M}_\odot$ there is no detection of the kSZ signal because these high mass halos are associated with the high-redshift galaxies of the LowZ North catalogue, which have limited contribution to the pairwise kSZ signals.Comment: 11 pages, 11 figures, 2 table

A cross-bispectrum estimator for CMB-HI intensity mapping correlations

Intensity mapping of 21cm emission from neutral hydrogen (HI) promises to be a powerful probe of large-scale structure in the post-reionisation epoch. However, HI intensity mapping (IM) experiments will suffer the loss of long-wavelength line-of-sight HI modes in the galactic foreground subtraction process. The loss of these modes is particularly problematic for detecting HI IM cross-correlations with projected large-scale structure tracers, such as CMB secondary anisotropies. Here, we propose a cross-bispectrum estimator to recover the cross-correlation of the HI IM field, $\delta T_{21},$ with the CMB lensing field, $\kappa,$ constructed by correlating the position-dependent HI power spectrum with the mean overdensity traced by CMB lensing. We study the cross-bispectrum estimator, $B^{\bar \kappa \delta T_{21} \delta T_{21}},$ in the squeezed limit and forecast its detectability based on HI IM measurements from HIRAX and CMB lensing measurements from AdvACT. The cross-bispectrum improves constraints on cosmological parameters; in particular, the constraint on the dark energy equation-of-state parameter, $w_0,$ improves on the HI IM auto-power spectra constraint by 44\% (to 0.014), while the constraint on $w_a$ improves by 33\% (to 0.08), assuming Planck priors in each case. These results are robust to HI IM foreground removal because they largely derive from small-scale HI modes. The HI-HI-$\kappa$ cross-bispectrum thus provides a novel way to recover HI correlations with CMB lensing and constrain cosmological parameters at a level that is competitive with next-generation galaxy redshift surveys. As a striking example of this, we find that the combined constraint on the sum of the neutrino masses, while varying all redshift and standard cosmological parameters within a $w_0w_a\Omega_K$CDM model, is 5.5 meV.Comment: 11 pages, 4 figure

CMB Lensing Reconstruction in Real Space

We explore the reconstruction of the gravitational lensing field of the cosmic microwave background in real space showing that very little statistical information is lost when estimators of short range on the celestial sphere are used in place of the customary estimators in harmonic space, which are nonlocal and in principle require a simultaneous analysis of the entire sky without any cuts or excisions. Because virtually all the information relevant to lensing reconstruction lies on angular scales close to the resolution scale of the sky map, the gravitational lensing dilatation and shear fields (which unlike the deflection field or lensing potential are directly related to the observations in a local manner) may be reconstructed by means of quadratic combinations involving only very closely separated pixels. Even though harmonic space provides a more natural context for understanding lensing reconstruction theoretically, the real space methods developed here have the virtue of being faster to implement and are likely to prove useful for analyzing realistic maps containing a galactic cut and possibly numerous small excisions to exclude point sources that cannot be reliably subtracted.Comment: 21 pages, 8 figure