We present a review of the current status of cosmic strings in theoretical and observational cosmology. Two independent methods to cosmic strings' search in the Universe are considered: (a) a search for chains of gravitational lensing images of a special type in optical surveys with the help of tools of high angular resolution; (b) a study of the structure of CMB anisotropy in the data provided by WMAP and Planck missions. We also received new observational constraints on the energy of single cosmic string.

Available data on the chirp mass distribution of the coalescing black hole binaries in O1-O3 LIGO/Virgo runs are analyzed and compared statistically with the distribution calculated under the assumption that these black holes are primordial with a log-normal mass spectrum. The theoretically calculated chirp mass distribution with the inferred best acceptable mass spectrum parameters, M0=17 M⊙ and γ=0.9, perfectly describes the data. The value of M0 very well agrees with the theoretically expected one. On the opposite, the chirp mass distribution of black hole binaries originated from massive binary star evolution requires additional model adjustments to reproduce the observed chirp mass distribution.

Friedmans cosmological equations for the scale factor are analyzed for the Universe containing dark energy. The parameter of the equation of state of the dark energy is treated as an arbitrary constant whose value lies within the interval w ∈ [−1.5, −0.5], the limits of which are set by current observations. A unified analytic solution is obtained for the scale factor as a function of physical and conformal time. We obtain approximated solutions for scale factor to an accuracy of better then 1%. This accuracy is better then measurement errors of global density parameters and therefore is suitable for the approximated models of our Universe. An analitic solution is obtained for the scale factor in ΛCDM cosmological model both in physical and conformal time, for the description of the evolution of the Universe from the epoch of matter domination up to the infinite future.

This paper is aimed at setting observational limits to the number of cosmic strings (Nambu-Goto, AbelianHiggs, semilocal) and other topological defects (textures). Radio maps of CMB anisotropy, provided by the space mission Planck for various frequencies, were filtered and then processed by the method of convolution with modified Haar functions (MHF) to search for cosmic string candidates. This method was designed to search for solitary strings, without additional assumptions as regards the presence of networks of such objects. The sensitivity of the MHF method is δT ≈ 10 µK in a background of δT ≈ 100 µK. The comparison of these with previously known results on search string network shows that strings can only be semilocal in the range of 1 ÷ 5, with the upper restriction on individual string tension (linear density) of Gμ/c 2 ≤ 7.36 × 10 −7 . The texture model is also legal. There are no strings with Gμ/c 2 > 7.36×10 −7 . However, a comparison with the data for the search of non-Gaussian signals shows that the presence of several (up to three) Nambu-Goto strings is also possible. For Gμ/c 2 ≤ 4.83×10 −7 the MHF method is ineffective because of unverifiable spurious string candidates. Thus the existence of strings with tensions Gμ/c 2 ≤ 4.83 × 10 −7 is not prohibited but it is beyond the Planck data possibilities. The same string candidates have been found in the WMAP 9-year data. Independence of Planck and WMAP data sets serves as an additional argument to consider those string candidates as very promising. However, the final proof should be given by optical deep surveys.