Small-scale structure of cosmic superstrings with time-varying tension

This thesis project investigates the small-scale structure of cosmic superstrings with time variable tension. Building on the framework of Polchinski and Rocha for constant tension strings, we extend this by allowing the tension to vary as μ(t) ∼ t−m. The correlator constructed from the scalar product of left- or right-moving unit vectors at different points along the string obeys the same evolution equation as in the original framework, but with a modified scaling exponent χ′. Crucially, this depends on κ = 1 − mn/4, related to the modified Hubble parameter entering the equations of motion, and on ¯α = 1 − 2¯v2. Interestingly, χ′ remains positive both when the variation of the tension dominates over the expansion of the Universe (mn > 4) and viceversa (mn < 4). This is due to the squared velocity ¯v2 interpolating between values greater or smaller than 1/2, thereby affecting the sign of ¯α. Therefore, within the generalized framework considered, the time variation of the tension does not alter the smooth small-scale structure of the strings. We further investigate corrections to the squared velocity of the network and circular loops as proxies for subhorizon physics, to understand the effect of the varying tension at different scales. Notably, the Velocity-One-Scale model gives a correction to the network velocity proportional to mn − 4. Conversely, the formal and perturbative loop analyses show the corrections are extremely suppressed by the subhorizon nature of the system, appearing at order O((HL)2). Furthermore, the deviation of the correlations between left- and right-moving unit vectors from the original framework is shown to be suppressed by O(ℓ/t) beyond leading order. Overall, the time-dependent tension affects the network velocity and loop amplitudes, but the leading smooth small-scale structure predicted by the Polchinski-Rocha framework remains valid.