We study string interaction rates in the Brandenberger-Vafa scenario, the very early universe cosmology of a gas of strings. This cosmology starts with the assumption that all spatial dimensions are compact and initially have string scale radii; some dimensions grow due to some thermal or quantum fluctuation which acts as an initial expansion velocity. Based on simple arguments from the low energy equations of motion and string thermodynamics, we demonstrate that the interaction rates of strings are negligible, so the common assumption of thermal equilibrium cannot apply. We also present a new analysis of the cosmological evolution of strings on compact manifolds of large radius. Then we discuss modifications that should be considered to the usual Brandenberger-Vafa scenario. To confirm our simple arguments, we give a numerical calculation of the annihilation rate of winding strings. In calculating the rate, we also show that the quantum mechanics of strings in small spaces is important.

We discuss the signature of a cosmic string wake in 21cm redshift surveys. Since 21cm surveys probe higher redshifts than optical large-scale structure surveys, the signatures of cosmic strings are more manifest in 21cm maps than they are in optical galaxy surveys. We find that, provided the tension of the cosmic string exceeds a critical value (which depends on both the redshift when the string wake is created and the redshift of observation), a cosmic string wake will generate an emission signal with a brightness temperature which approaches a limiting value which at a redshift of z + 1 = 30 is close to 400 mK in the limit of large string tension. The signal will have a specific signature in position space: the excess 21cm radiation will be confined to a wedge-shaped region whose tip corresponds to the position of the string, whose planar dimensions are set by the planar dimensions of the string wake, and whose thickness (in redshift direction) depends on the string tension. For wakes created at zi + 1 = 10 3 , then at a redshift of z + 1 = 30 the critical value of the string tension µ is Gµ = 6 × 10 −7 , and it decreases linearly with redshift (for wakes created at the time of equal matter and radiation, the critical value is a factor of two lower at the same redshift). For smaller tensions, cosmic strings lead to an observable absorption signal with the same wedge geometry.

We describe a new code to search for signatures of cosmic strings in cosmic microwave anisotropy maps. The code implements the Canny Algorithm, an edge detection algorithm designed to search for the lines of large gradients in maps. Such a gradient signature which is coherent in position space is produced by cosmic strings via the Kaiser-Stebbins effect. We test the power of our new code to set limits on the tension of the cosmic strings by analyzing simulated data with and without cosmic strings. We compare maps with a pure Gaussian scale-invariant power spectrum with maps which have a contribution of a distribution of cosmic strings obeying a scaling solution. The maps have angular scale and angular resolution comparable to what current and future ground-based smallscale cosmic microwave anisotropy experiments will achieve. We present tests of the codes, indicate the limits on the string tension which could be set with the current code, and describe various ways to refine the analysis. Our results indicate that when applied to the data of ongoing cosmic microwave experiments such as the South Pole Telescope project, the sensitivity of our method to the presence of cosmic strings will be more than an order of magnitude better than the limits from existing analyses.

We calculate a signature of cosmic strings in the polarization of the cosmic microwave background (CMB). We find that ionization in the wakes behind moving strings gives rise to extra polarization in a set of rectangular patches in the sky whose length distribution is scale-invariant. The length of an individual patch is set by the co-moving Hubble radius at the time the string is perturbing the CMB. The polarization signal is largest for string wakes produced at the earliest post-recombination time, and for an alignment in which the photons cross the wake close to the time the wake is created. The maximal amplitude of the polarization relative to the temperature quadrupole is set by the overdensity of free electrons inside a wake which depends on the ionization fraction f inside the wake. The signal can be as high as 0.06µK in degree scale polarization for a string at high redshift (near recombination) and a string tension µ given by Gµ = 10 −7 .

Even with recent progress, it is still very much an open question to understand how all compactification moduli are stabilized, since there are several mechanisms. For example, it is possible to generate a scalar potential either classically or through nonperturbative effects, such as gaugino condensation. Such a potential can stabilize certain of the moduli fields, for example the dilaton. On the other hand, a background of thermal matter with moduli-dependent masses can also stabilize certain of the moduli, e.g., the radion. It is important to understand whether these two distinct mechanisms are compatible with each other, that is, that there are no interference terms that could spoil the moduli stabilization. In this paper, we study heterotic string theory on an N=1 orbifold near an enhanced symmetry point. We then consider both a nonperturbatively generated potential and a gas of strings with moduli-dependent masses to stabilize the dilaton and radial modulus, respectively. We conclude that, given certain approximations, these two moduli stabilization mechanisms are compatible.Comment: 13pg, 1 fig; v2. minor clarifications & reference addition