non-BPS strings, the function ϵ ( β ) is given in [481]. This is the case for F - and D -strings originating from brane inflation. Currently the constraints on their effects on CMB is among the most stringent observation and is directly relevant to inflationary physics when they are formed close to or at the end of inflation. In this case, their formation affects the normalization of the fluctuation power spectrum by imposing an additional contribution. This can be described by an additional contribution to the temperature quadrupole anisotropy [73, 482–484] T ∣$^{2}$ Q T ∣$^{2}$ infl T ∣$^{2}$ CS where ( δT/T )$_{CS}$ = y 2 πϵ ( β ) v $^{2}$/M2 $_{p}$. The constant y parametrizes the density of the string network at the last scattering surface and has to be extracted from numerical simulations. The most recent simulations computing this parameter predicts y = 8 . 9 ± 2 . 7 [485], though older simulations or semi-analytical calculations give y ∈ [3 − 6] (see for e.g. [486] and references therein). The current constraints from this normalization (for example in the case of their formation at the end of F -term inflation) lead to [484, 486]: In more recent studies, the effect of a cosmic string network on the CMB anisotropies have been computed at ℓ = 10 instead of the quadrupole ℓ = 2 [487] as the latter is polluted by a large cosmic variance error. These simulations are improved compared to previous analysis since cosmic strings are described using field theory instead of modeled. Analyzing of the presence and the impact of cosmic strings in the CMB data assuming a model of inflation can therefore be made fully consistently using Monte-Carlo methods [263]. At ℓ = 10, a fraction f$_{10}$ < 0 . 11 of the temperature anisotropies from cosmic strings are found compatible with the 3 years WMAP data (at 2 σ ), assuming a 7-parameter ΛCDM model and it is shown that the fraction of cosmic strings f$_{10}$ is strongly degenerate with the spectral index (see Sec. II E). This constraint can be translated into Gµ < 7 × 10 − $^{7}$. Other CMB searches, such as direct searches in spatial map for line discontinuity gives a bound on Gµ < ∼ 3 × 10 − 7 [488]. To search for cosmic string signals in future CMB data, one should also incorporate recent developments on the small-scale signal in temperature anisotropies [489, 490], on the CMB B-mode polarization signal [264–266] or from the gen- eration of non-Gaussianities [491, 492]. Recent work have also investigated the cosmological v < ∼ 2 × 10 15 GeV , Gµ < ∼ 8 × $_{10}$− 7 , (160) 75