Abstract
In this paper, we consider the vacuum energy of a scalar field in the spacetime of two non-parallel cosmic strings. To this end, we obtain metrics for orthogonal straight cosmic strings and for slightly nonparallel strings. In the first case, we derive the separation-dependent part of the vacuum energy in the leading order of string tension. The dependence of the vacuum energy on separation differs from that known for parallel strings. For two strings inclined at a small angle to each other, the approximation used simply reproduces the result for parallel strings, since the angle dependence enters the next to leading order. The results are compared with the Casimir interaction between two inclined cylinders.
Highlights
First models of cosmic strings considered symmetry-breaking at the grand unification scale with estimated string tension Gλ/c2 ∼ 10−6
We have considered the vacuum energy of a scalar field in the spacetime of two non-parallel cosmic strings
We obtained the metrics for perpendicular straight cosmic strings and for slightly nonparallel strings
Summary
The current upper bound on the energy scale of the possible cosmic string network from pulsar timing observations is Gλ/c2 ∼ 10−11. At this level and below, no effects can be seen in the CMB, and the strings cannot be discovered by gravitational lensing (except certain microlensing models). The vacuum energy of the scalar field in the background of two parallel cosmic strings was first derived by Bordag in 1990 [8].
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