How And To What Extent We Can Detect String Wake Signal? (Cosmology / Quantum)

A cosmic string wake produces a 21cm non-Gaussian signal in intensity maps at redshifts above that of reionization. Now, David Maibach and colleagues studied to what extent this signal can be extracted from noisy interferometric data. They found that, a wake produced by a string with tension Gµ = 3×10¯7 can be successfully detected using a telescope of specifications very similar to that of the MWA instrument. Their study recently appeared in Arxiv.

Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry-breaking phase transition in the early universe and persist, by causality, until the present time. These strings are relativistic, i.e. characterized by a tension whose magnitude is equal to the energy per unit length. Any curvature of such a string will hence induce relativistic motion. The network of strings takes on a scaling solution in which the statistical properties of the string distribution are independent of time if all lengths are scaled to the Hubble radius. Strings carry trapped energy, and their gravitational effects lead to specific non-Gaussian signatures in a wide range of cosmological observables. The search for these signatures provides an interesting interplay between particle physics and cosmology.

Fig 1: Sketch of a string wake in three-dimensional real space (dimensions not scaled) being tilted relative to the line of sight. The width of the wake, as it was defined above is marked relative to the center of the wake, here displayed as a dotted line. The dashed line represents a vector normal to the wake plane and defines the angle θ © David Maibach et al.

The network of cosmic strings consists of a random-walk-like distribution of “infinite” (or “long”) strings, and a distribution of string loops with radii R smaller than the Hubble radius. The mean curvature radius of the infinite string network is of the order of the Hubble radius. This is maintained in time by the long strings intersecting and chopping off string loops.

Space perpendicular to a cosmic string is conical with deficit angle 8πGµ, where G is Newton’s gravitational constant. The extent of the deficit angle extends to one Hubble distance away from the string. Because of the conical deficit angle, a long straight string segment moving with a speed comparable to “c” induces a planar overdensity (called a “wake”). The comoving planar dimensions of this overdensity (called a “wake”) are set by the length and distance travelled by the segment, and the thickness is set by the deficit angle. The key point is that wakes are nonlinear overdense regions which exist at arbitrarily early times after the phase transition. In particular, at any time after phase transition they lead to regions of enhanced baryon number and thus of enhanced free electron density. The extra Thomson scattering in wakes thus leads to a characteristic CMB polarization signal, a rectangle in the sky with extra polarization (including a B-mode component).

Now, David Maibach and colleagues focused on another type of signal, namely a wedge of extra 21-cm absorption or emission in 21-cm redshift maps, which is generated from the overdensity of baryons inside of a string wake.

“Since string wakes are disrupted by the Gaussian fluctuations from the ΛCDM model which are the dominant source of structure formation at redshifts smaller than that of reionization (denoted by zEoR), the 21-cm signal of strings wakes is most clearly visible for z > zEoR. In fact, at these redshifts the wakes are the dominant source of nonlinear fluctuations in the Standard Model.”

— they said

Hence, David Maibach and colleagues studied the potential of planned interferometric 21-cm redshift surveys to discover the signal of a string wake given the multitude of astrophysical and instrumental foregrounds.

They described the foregrounds which they included and explained how they model instrumental effects. They focused on two statistics which they used to differentiate between maps with and without strings: a χ² statistic and a three point function with a shape designed to pick out the string signal. They also describe signal processing techniques which they used to suppress the backgrounds relative to the string signal.

FIG. 2: Simulation of a box of angular dimensions 5° × 5° comparing the ΛCDM fluctuations with the signal of a cosmic string wake (located in the small rectangle in the center of the box). The value of Gµ was taken to be Gµ = 3 × 10¯7, and the redshift interval was 11.9 < z < 12.1. © David Maibach et al.

“We find that an experiment like MWA has the angular resolution and sensitivity to clearly identify the cosmic string signal using our three point statistic provided we apply our signal processing techniques to suppress the foregrounds. This is true even if a small patch of the sky of size 5° × 5° is analyzed. The benchmark value of the string tension which we use is Gµ = 3 × 10¯7. While this value is a factor of 2 larger than the current upper bound, they showed that strings with tensions comparable and slightly lower than this bound can also be identified, provided that a larger patch of the sky is analyzed.”

— they said.

Based on the specific geometry of the string signal they identified a particular three-point statistic which is promising in order to extract the signal (or planar structures which string wakes create), and found that, with an angular resolution of 36 arc-seconds, a wake produced by a string with tension Gµ = 3×10¯7 can be successfully extracted using a telescope of specifications very similar to that of the MWA instrument and by applying signal processing techniques like Weiner filtering and foreground subtraction scheme.

“We look forward to applying our analysis scheme to actual data. Another avenue for future research is to explore more sophisticated statistics such as wavelet analyses. It would also be interesting to consider the application of machine learning techniques”

— they concluded

Reference: David Maibach, Robert Brandenberger, Devin Crichton, and Alexandre Refregier, “Extracting the Signal of Cosmic String Wakes from 21-cm Observations”, Arxiv, pp. 1-35, 2021.

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