Abstract
The dependences of the mean expected number of cosmic strings on their redshift up to the surface of last scattering have been derived. The calculations are based on the geometric probability of a straight string segment crossing a given field and on information about the absence of strings when they are searched for via their gravitational lensing effects in optical catalogs. It is shown that there are no strings for redshifts 0 < z < 1.954, but the expected number of strings for 0 < z < 5 can be no more than 2.1 × 103 at the 95% confidence level. The expected number of strings for redshifts up to z = 1100 can be no more than 2.4 × 104 at the 95% confidence level. The latter estimate is sensitive to a priori information about the absence of cosmic strings in the redshift range 0 < z < 1.954 in a field of 4.48 square degrees in optical catalogs; it is smaller than the estimate without allowance for this information by 6%.
Similar content being viewed by others
References
A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, 1994), p. 258.
T. W. B. Kibble, J. Phys. A: Math. Gen. 9, 1387 (1976).
S. F. Shandarin and Ia. B. Zeldovich, Phys. Rev. Lett. 52, 1488 (1984).
M. V. Sazhin, G. Longo, M. Capaccioli, J. M. Alcalá, R. Silvotti, G. Covone, O. Khovanskaya, M. Pavlov, M. Pannella, M. Radovich, and V. Testa, Mon. Not. R. Astron. Soc. 343, 353 (2003).
M. V. Sazhin, M. Capaccioli, G. Longo, M. Paolillo, and O. Khovanskaya, Astrophys. J. 636, L5 (2006).
E. Morganson, P. Marshall, T. Treu, T. Schrabback, and R. D. Blandford, Month. Not. R. Astron. Soc. 406, 2452 (2010).
M. V. Sazhin, O. S. Sazhina, M. Capaccioli, G. Longo, M. Paolillo, and G. Riccio, Open Astron. J. 3, 200 (2010).
O. S. Sazhina, M. V. Sazhin, and V. N. Sementsov, JETP 106(5), 878 (2008).
S. Amsel, J. Berger, and R. H. Brandenberger, arXiv:0709.0982v3 [astro-ph].
R. J. Danos and R. H. Brandenberger, Int. J. Mod. Phys. D 19, 183 (2010).
E. Jeong, C. Baccigalupi, and G. F. Smoot, J. Cosmol. Astropart. Phys. 09, 018 (2010).
O. S. Sazhina, M. V. Sazhin, M. Capaccioli, and G. Longo, Phys.—Usp. 54(10), 1072 (2011).
O. S. Sazhina and M. V. Sazhin, JETP 113(5), 798 (2011).
R. Consiglio, O. Sazhina, G. Longo, M. Sazhin, and F. Pezzella, arXiv:1112.5186v1.
M. V. Sazhin, O. S. Khovanskaya, M. Capaccioli, G. Longo, J. M. Alcalá, R. Silvotti, and M. V. Pavlov, Astron. Lett. 31(2), 73 (2005).
B. Allen and E. P. S. Shellard, Phys. Rev. Lett. 64, 119 (1990).
T. W. B. Kibble, arXiv:astro-ph/0410073v2.
T. Vachaspati and A. Vilenkin, Phys. Rev. D: Part. Fields 30, 2036 (1984).
A. I. Kobzar’, Applied Mathematical Statistics (Fizmatlit, Moscow, 2006), p. 92 [in Russian].
A. Leauthaud, R. Massey, J.-P. Kneib, J. Rhodes, D. E. Johnston, P. Capak, C. Heymans, R. S. Ellis, A. M. Koekemoer, O. Le Fèvre, Y. Mellier, A. Réfrégier, A. C. Robin, N. Scoville, L. Tasca, J. E. Taylor, and L. Van Waerbeke, Astrophys. J., Suppl. Ser. 172, 219 (2007).
C. M. Baugh and G. Efstathiou, Mon. Not. R. Astron. Soc. 265, 145 (1993).
T. J. Broadhurst, R. S. Ellis, and T. Shanks, Mon. Not. R. Astron. Soc. 235, 827 (1988).
M. J. Colles, R. S. Ellis, T. J. Broadhurst, K. Taylor, and B. A. Peterson, Mon. Not. R. Astron. Soc. 261, 19 (1993).
O. S. Sazhina, Vestn. Mosk. Univ. 6, 93 (2010).
V. A. Rubakov and D. S. Gorbunov, Introduction to the Theory of the Early Universe: Hot Big Bang Theory (URSS, Moscow, 2008; World Scientific, Singapore, 2011), Vol. 1, p. 96.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © O.S. Sazhina, 2013, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2013, Vol. 143, No. 1, pp. 81–91.
Rights and permissions
About this article
Cite this article
Sazhina, O.S. Probabilistic estimates of the number of cosmic strings. J. Exp. Theor. Phys. 116, 71–79 (2013). https://doi.org/10.1134/S1063776113010147
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776113010147