Percolating cosmic string networks from kination

We describe a new mechanism, whose ingredients are realized in string compactifications, for the formation of cosmic (super)string networks. Oscillating string loops grow when their tension <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>μ</a:mi></a:math> decreases with time. If <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>2</c:mn><c:mi>H</c:mi><c:mo>+</c:mo><c:mover accent="true"><c:mi>μ</c:mi><c:mo>˙</c:mo></c:mover><c:mo>/</c:mo><c:mi>μ</c:mi><c:mo>&lt;</c:mo><c:mn>0</c:mn></c:math>, where <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>H</f:mi></f:math> is the Hubble parameter, loops grow faster than the scale factor and an initial population of isolated small loops (for example, produced by nucleation) can grow, percolate, and form a network. This condition is satisfied for fundamental strings in the background of a kinating volume modulus rolling toward the asymptotic large volume region of moduli space. Such long kination epochs are motivated in string cosmology by both the electroweak hierarchy problem and the need to solve the overshoot problem. The tension of such a network today is set by the final vacuum; for phenomenologically appealing large volume scenario vacua, this would lead to a fundamental string network with <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>G</h:mi><h:mi>μ</h:mi><h:mo>∼</h:mo><h:msup><h:mn>10</h:mn><h:mrow><h:mo>−</h:mo><h:mn>10</h:mn></h:mrow></h:msup></h:math>. Published by the American Physical Society 2024