Bound on the string tension of cosmic strings

Question

Many GUT theories contain cosmic strings with string tension near GUT scale. I would like to ask: what is the upper bound of such a string tension from, say,  cosmic microwave background and the recent BICEP2 observation?

FYI, $SO(10)$ GUT energy scales (one example): $SO(10) \to Z_2\rtimes [SO(6)\times SO(4)]  \sim_{\text{as Lie alg}} SU(4)\times [SU(2)\times SU(2)]$ $\to SU(3)\times SU(2)\times U(1)$. The first breaking [by Higgs in $54$ representation of the $SO(10)$] happens at $3.5\times 10^{15}$ GeV, and the second (by Higgs in $126$ and $126^*$ representations) around $10^{11}$ GeV. ($M_P=1.2\times 10^{19}$ GeV.)

We also have $10\times 10 =1_s +45_a +54_s$ and $16\times 16 = 10_s + 120_a +126_s$. For $SO(10) \to SU(4)\times SU(2)\times SU(2)$: $10\to (1,2,2)+(6,1,1)$ and $16\to (4,2,1)+(4^*,1,2)$.

Answer 1

Here are old bounds (without BICEP2):

http://arxiv.org/abs/1005.0479 gives $G\mu < 3\times 10^{-7}$ or $\sqrt{\mu} < 5\times 10^{-4} M_P$

http://arxiv.org/abs/1309.6637 gives $G\mu < 3\times 10^{-9}$ or $\sqrt{\mu} < 5\times 10^{-5} M_P$

Due to the unbroken $Z_2$ which leads to a cosmic string at $10^{15}$GeV, the above bound nearly rule out the breaking path $SO(10) \to Z_2\rtimes [SO(6)\times SO(4)]  \sim_{\text{as Lie alg}} SU(4)\times [SU(2)\times SU(2)]$ .