Arthur Kosowsky

Statistics of cosmic microwave background polarization

We present a formalism for analyzing a full-sky temperature and polarization map of the cosmic microwave background. Temperature maps are analyzed by expanding over the set of spherical harmonics to give multipole moments of the two-point correlation function. Polarization, which is described by a second-rank tensor, can be treated analogously by expanding in the appropriate tensor spherical harmonics. We provide expressions for the complete set of temperature and polarization multipole moments for scalar and tensor metric perturbations. Four sets of multipole moments completely describe isotropic temperature and polarization correlations; for scalar metric perturbations one set is identically zero, giving the possibility of a clean determination of the vector and tensor contributions. The variance with which the multipole moments can be measured in idealized experiments is evaluated, including the effects of detector noise, sky coverage, and beam width. Finally, we construct coordinate-independent polarization two-point correlation functions, express them in terms of the multipole moments, and derive small-angle limits.

A Probe of Primordial Gravity Waves and Vorticity

A formalism for describing an all-sky map of the polarization of the cosmic microwave background is presented. The polarization pattern on the sky can be decomposed into two geometrically distinct components. One of these components is not coupled to density inhomogeneities. A nonzero amplitude for this component of polarization can only be caused by tensor or vector metric perturbations. This allows unambiguous identification of long-wavelength gravity waves or large-scale vortical flows at the time of last scattering.

Cosmological-parameter determination with microwave background maps

The angular power spectrum of the cosmic microwave background (CMB) contains information on virtually all cosmological parameters of interest, including the geometry of the Universe (Ω), the baryon density, the Hubble constant (h), the cosmological constant (Λ), the number of light neutrinos, the ionization history, and the amplitudes and spectral indices of the primordial scalar and tensor perturbation spectra. We review the imprint of each parameter on the CMB. Assuming only that the primordial perturbations were adiabatic, we use a covariance-matrix approach to estimate the precision with which these parameters can be determined by a CMB temperature map as a function of the fraction of sky mapped, the level of pixel noise, and the angular resolution. For example, with no prior information about any of the cosmological parameters, a full-sky CMB map with 0.5° angular resolution and a noise level of 15 μK per pixel can determine Ω, h, and Λ with standard errors of ±0.1 or better, and provide determinations of other parameters which are inaccessible with traditional observations. Smaller beam sizes or prior information on some of the other parameters from other observations improves the sensitivity. The dependence on the underlying cosmological model is discussed.

Gravitational radiation from first-order phase transitions.

We consider the stochastic background of gravity waves produced by first-order cosmological phase transitions from two types of sources: colliding bubbles and hydrodynamic turbulence. First we discuss the fluid mechanics of relativistic spherical combustion. We then numerically collide many bubbles expanding at a velocity v and calculate the resulting spectrum of gravitational radiation in the linearized gravity approximation. Our results are expressed as simple functions of the mean bubble separation, the bubble expansion velocity, the latent heat, and the efficiency of converting latent heat to kinetic energy of the bubble walls. A first-order phase transition is also likely to excite a Kolmogoroff spectrum of turbulence. We estimate the gravity waves produced by such a spectrum of turbulence and find that the characteristic amplitude of the gravity waves produced is comparable to that from bubble collisions. Finally, we apply these results to the electroweak transition. Using the one-loop effective potential for the minimal electroweak model, the characteristic amplitude of the gravity waves produced is h≃1.5×10^-27 at a characteristic frequency of 4.1 × 10^-3 Hz corresponding to Ω∼10^-22 in gravity waves, far too small for detection. Gravity waves from more strongly first-order phase transitions, including the electroweak transition in nonminimal models, have better prospects for detection, though probably not by LIGO.

Faraday rotation of microwave background polarization by a primordial magnetic field

The existence of a primordial magnetic field at the last scattering surface may induce a measurable Faraday rotation in the polarization of the cosmic microwave background. We calculate the magnitude of this effect by evolving the radiative transfer equations for the microwave background polarization through the epoch of last scatter, in the presence of a magnetic field. For a primordial field amplitude corresponding to a present value of

Weighing the universe with the cosmic microwave background

10^{-9}{\rm G}

Cosmic Microwave Background Polarization

(which would account for the observed galactic field if it were frozen in the pre-galactic plasma), we find a rotation angle of around

Detectability of inflationary gravitational waves with microwave background polarization

1^\circ

Determining cosmological parameters from the microwave background

at a frequency of 30 GHz. The statistical detection of this signal is feasible with future maps of the microwave background.

Primordial nucleosynthesis in conformal Weyl gravity

Variations in Ω, the total density of the Universe, leave an imprint on the power spectrum of temperature fluctuations in the cosmic microwave background (CMB). We evaluate the precision with which Ω can be determined by a CMB map as a function of sky coverage, pixel noise, and beam size. Assuming only that the primordial density perturbations were adiabatic and with no prior information on the values of any other cosmological parameters, a full-sky CMB map at 0.5° angular resolution and a noise level of 15 μK per pixel can determine Ω with a standard error of 5%. If all other cosmological parameters are fixed, Ω can be measured to better than 1%.