How to detect gravitational waves through the cross-correlation of the galaxy distribution with the CMB polarization

Thompson scattering of cosmic microwave background (CMB) photons off of free electrons during the reionization epoch induces a correlation between the distribution of galaxies and the polarization pattern of the CMB, the magnitude of which is proportional to the quadrupole moment of radiation at the time of scattering. Since the quadrupole moment generated by gravitational waves (GWs) gives rise to a different polarization pattern than that produced by scalar modes, one can put interesting constraints on the strength of GWs on large scales by cross-correlating the small scale galaxy distribution and CMB polarization. We use this method together with Fisher analysis to predict how well future surveys can measure the tensor-to-scalar ratio $r$. We find that with a future CMB experiment with detector noise Delta_P = 2 mu K-arcmin and a beam width theta_FWHM = 2 and a future galaxy survey with limiting magnitude I<25.6 one can measure the tensor-to-scalar ratio with an error sigma_r simeq 0.09. To measure r approx 0.01, however, one needs Delta_P simeq 0.5 mu K-radian and theta_FWHM simeq 1. We also investigate a few systematic effects, none of which turn out to add any biases to our estimators, but they increase the error bars by adding to the cosmic variance. The incomplete sky coverage has the most dramatic effect on our constraints on r for large sky cuts, with a reduction in signal-to-noise smaller than one would expect from the naive estimate (S/N)^2 propto f_sky. Specifically, we find a degradation factor of f_deg=0.32 pm 0.01 for a sky cut of |b|>10^circ (f_sky=0.83) and f_deg=0.056 pm 0.004 for a sky cut of |b|>20^circ (f_sky=0.66). Nonetheless, given that our method has different systematics than the more conventional method of observing the large scale B modes directly, it may be used as an important check in the case of a detection.

Molecular hydrogen in the cosmic recombination epoch

The advent of precise measurements of the cosmic microwave background (CMB) anisotropies has motivated correspondingly precise calculations of the cosmic recombination history. Cosmic recombination proceeds far out of equilibrium because of a bottleneck at the $n=2$ level of hydrogen: atoms can only reach the ground state via slow processes: two-photon decay or Lyman-$alpha$ resonance escape. However, even a small primordial abundance of molecules could have a large effect on the interline opacity in the recombination epoch and lead to an additional route for hydrogen recombination. Therefore, this paper computes the abundance of the H$_2$ molecule during the cosmic recombination epoch. Hydrogen molecules in the ground electronic levels X$^1Sigma^+_g$ can either form from the excited H$_2$ electronic levels B$^1Sigma^+_u$ and C$^1Pi_u$ or through the charged particles H$_2^+$, HeH$^+$ and H$^-$. We follow the transitions among all of these species, resolving the rotational and vibrational sub-levels. Since the energies of the X$^1Sigma^+_g$--B$^1Sigma^+_u$ (Lyman band) and X$^1Sigma^+_g$-C$^1Pi_u$ (Werner band) transitions are near the Lyman-$alpha$ energy, the distortion of the CMB spectrum caused by escaped H Lyman-line photons accelerates both the formation and the destruction of H$_2$ due to this channel relative to the thermal rates. This causes the populations of H$_2$ molecules in X$^1Sigma^+_g$ energy levels to deviate from their thermal equilibrium abundances. We find that the resulting H$_2$ abundance is $10^{-17}$ at $z=1200$ and $10^{-13}$ at $z=800$, which is too small to have any significant influence on the recombination history.

Dark matter halo merger and accretion probabilities in the excursion set formalism

The merger and accretion probabilities of dark matter halos have so far only been calculated for an infinitesimal time interval. This means that a Monte-Carlo simulation with very small time steps is necessary to find the merger history of a parent halo. In this paper we use the random walk formalism to find the merger and accretion probabilities of halos for a finite time interval. Specifically, we find the number density of halos at an early redshift that will become part of a halo with a specified final mass at a later redshift, given that they underwent $n$ major mergers, $n=0,1,2,...$ . We reduce the problem into an integral equation which we then solve numerically. To ensure the consistency of our formalism we compare the results with Monte-Carlo simulations and find very good agreement. Though we have done our calculation assuming a flat barrier, the more general case can easily be handled using our method. This derivation of finite time merger and accretion probabilities can be used to make more efficient merger trees or implemented directly into analytical models of structure formation and evolution.