We compute the gravitational waveform produced by cosmic superstring reconnections. This is done by first constructing the superstring reconnection trajectory, which closely resembles that of classical, instantaneous reconnection but with the singularities smoothed out due to the string path integral. We then evaluate the graviton vertex operator in this background to obtain the burst amplitude. The result is compared to the detection threshold for current and future gravitational wave detectors, finding that neither bursts nor the stochastic background would be detectable by Advanced LIGO. This disappointing but anticipated conclusion holds even for the most optimistic values of the reconnection probability and loop sizes.
Deep Dive into Gravitational Wave Bursts from Cosmic Superstring Reconnections.
We compute the gravitational waveform produced by cosmic superstring reconnections. This is done by first constructing the superstring reconnection trajectory, which closely resembles that of classical, instantaneous reconnection but with the singularities smoothed out due to the string path integral. We then evaluate the graviton vertex operator in this background to obtain the burst amplitude. The result is compared to the detection threshold for current and future gravitational wave detectors, finding that neither bursts nor the stochastic background would be detectable by Advanced LIGO. This disappointing but anticipated conclusion holds even for the most optimistic values of the reconnection probability and loop sizes.
One of the most exciting products of the recent synthesis of superstring theory and cosmology has been that of cosmic superstrings [1]. Like their classical cousins [2], cosmic superstrings were briefly considered then discarded [3], but for theoretical reasons rather than observational ones. Subsequent (and largely non-perturbative) analysis [4] has shown that cosmic superstrings have been found to naturally arise in models of brane inflation [5], a string theory realization of inflationary cosmology theory.
Cosmic strings and superstrings can produce a variety of astrophysical signatures including gravitational waves [6][7][8][9][10], ultra high energy cosmic rays [11], and gamma ray bursts [12]. Very recent work has revealed a number of exciting new possibilities such as radio bursts from strings [13], effects on the cosmic 21 cm power spectrum [14], magnetogenesis [15], effects on the CMB at small angular scales [16,17], CMB polarization [18], microlensing from strings [19,20], strong lensing [21,22], and weak lensing [23].
Prior work on gravitational radiation has focused on two processes: cusps (whereby a segment of the string momentarily moves at the speed of light) and kinks (formed after two cosmic strings collide and reconnect) [6][7][8][9][10]. Here we study a third source:
the radiation emitted from the reconnection process itself. This is possible for cosmic superstrings because string theory allows us to explicitly construct the reconnection process and compute detailed interaction properties. We will do this for the bosonic string but the presence of fermions in the superstring should not change the conclusions.
In the first half of this article we compute the gravitational waveform resulting from fundamental cosmic superstring reconnection. In the second half we consider the likelihood of detection of this signal with current and future experiments.
The theory of cosmic superstring reconnection was developed in [24] [25] [26]. Consider two long, straight wound bosonic strings on a 2D torus of size L and skew angle θ as illustrated in Figure 1. In terms of the string tension (2πα ) -1 the momenta are taken
We model cosmic superstrings as straight wound modes on a large torus, which will then interact to form a kinked configuration. to be
(1, 0, 0, 0, 0), L 1 = L(0, 1, 0, 0, 0),
(1, 0, 0, v, 0), L 2 = L(0, cos θ, sin θ, 0, 0).
These satisfy the tachyonic mass-shell conditions
The relevant vertex operators are: (i = 1, 2)
where the volume V = V ⊥ L 2 sin θ is the product of the the transverse volume and the 2D torus (methods to calculate V ⊥ can be found in [27]). Here X L (z), X R (z) refer to the (anti)holomorphic components of X(z, z), so that X(z, z) = X L (z) + X R (z).
These will scatter into some kinked configuration and the amplitude for all such processes can be summed. In the large-winding limit the probability of reconnection is found to be
It is also likely that there will be radiation emitted during this reconnection. This can be included by using the reconnection process as a classical background trajectory X cl (z, z) upon which the radiation vertex operator must be integrated over [26]. Then the probability to emit a radiated state of definite momentum k will be the probability of reconnection times a factor depending on the radiated particle under consideration,
(2.4)
One might also consider the possibility that the strings will pass through each other without reconnecting but still emit radiation in the process. This is a valid possibility but one in which the amplitude is suppressed by a factor of g s due to three final strings instead of two (recall that a reconnected kinked string is considered a single string, whereas this process will produce two unconnected strings with accompanying coupling factor). So to leading order this process can be neglected.
The reconnection trajectory was computed in [26] by considering the vertex operator of the kinked string. This is done by examining the operator product expansion of the straight strings, : e ip 1L X L (z) ::
The Taylor expansion of the exponential shows the vertex operators of the infinite tower of the produced states, which will appear kinked due to their large oscillator excitation number N :
Since p 1R •p 2R = p 1L •p 2L the result will be identical for the right-moving oscillators and so Ñ = N . Now consider the state corresponding to the sum of these vertex operators (2.5):
The expectation value of the position operator in the reconnection amplitude is then easily evaluated:
While this is a technically correct answer, it is unsatisfactory in that it appears to treat string 1 different from string 2 even though of course these are unphysical labels. The reason is that the placement of vertex operators has treated them in a non-symmetric fashion, expanding V T ( ; p 1 ) around the location of V T (0; p 2 ). To remedy this we simply redo the previous calculation but expand both vertex operators around
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