Causality, randomness, and the microwave background

TL;DR

Differences between these two scenarios can give rise to striking signatures in the microwave fluctuations on small scales, which should enable high resolution measurements of CMB anisotropies to distinguish between two broad classes of theories, independent of the precise details of each.

Abstract

Fluctuations in the cosmic microwave background (CMB) temperature are being studied with ever increasing precision. Two competing types of theories might describe the origins of these fluctuations: ``inflation'' and ``defects''. Here we show how the differences between these two scenarios can give rise to striking signatures in the microwave fluctuations on small scales, assuming a standard recombination history. These should enable high resolution measurements of CMB anisotropies to distinguish between these two broad classes of theories, independent of the precise details of each.

Figures (4)

• Figure 1: Perturbations from Inflation: Evolution of two different modes during the tight coupling era. While in (a) elements of the ensemble have non-zero values at $\eta_\star$, in (b), all members of the ensemble will go to zero at the final time ($\eta_\star$), due to the fixed phase of oscillation set by the "growing solution" initial conditions. The y-axis is in arbitrary units.
• Figure 2: The r.m.s. value of $\delta_r$ evaluated at decoupling ($\eta_\star$) for inflation (solid) and cosmic strings (dashed). For this figure we use ${\cal F}_{00} = (1 + 2(k\eta)^2))^{-1}$, ${\cal F}_D = 1/(1 + (2 \pi /k\eta)^2)^2$, and $\eta_c = \eta/(1 + k\eta)$.
• Figure 3: Perturbations from defects: Evolution of $\delta_r(k)$ and the corresponding source ${\Theta}_{00}$ during the tight coupling era ($\Theta_D$ is not shown). Two members of the ensemble are shown, with matching line types. Due to the randomness of the source, the ensemble includes solutions with a wide range of values at $\eta_\star$. Unlike the inflationary case (Figure 1) the phase of the temporal oscillations is not fixed. The y axis is in arbitrary units, and the source models are the same as for figure 2. The factor $\eta a/\dot a$ allows one to judge the relative importance (over time) of the $\Theta_{00}$ term in Eqn 2.
• Figure 4: Angular power spectrum of temperature fluctuations generated by cosmic strings (dashed) and arising from a typical model of scale invariant primordial fluctuations (solid) in arbitrary units. The all-sky temperature maps are decomposed into spherical harmonics ${\Delta T\over T}=a^l_m Y^l_m$ from which one defines the angular power spectrum as $C_l={1\over 2l+1}{\sum^l_{-l}}|a^l_m|^2$. The shape of the string curve for $l \stackrel{<}{\sim} 100$ (and thus the height of the peak) is very sensitive to existing uncertainties in string networks. We show only the scalar contribution, in arbitrary units. The string curve is from [13] where we use an extended Hu-Sugiyama formalism.