David P. Bennett and Francois R. Bouchet- Cosmic Strings: A Problem or a Solution?

8/3/2019 David P. Bennett and Francois R. Bouchet- Cosmic Strings: A Problem or a Solution?

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0 Fermi National Accelerator LaboratoryFERMILAB-Conf-87/164-AOctober 1987

COSMIC STRINGS: A PROBLEM OR A SOLUTION?DAVID P . BENNETT

NASA/Fermilab Astrophysics Center, FermiNational Accelerator Laboratory, Batavia, li'linois 60510

andAstronomy and Astrophysics Center, The

University of Chicago, Chicago, Illinois 60637and

FRANCOIS R. BOUCHET*Department of Astronomy, University of California, Berkeley, California

andIGPP, Lawrence Livermore National Laboratory, Livermore, California

ABSTRACTWe address, by means of Numerical Simulations, the most fundamental issuein the theory of cosmic strings: the existence of a scaling solution. The resolutionof this question will determine whether cosmic strings can form the basis of anattractive theory of galaxy formation or prove to be a cosmological disaster likemagnetic monopoles or domain walls. After a brief discussion of our numericaltechnique, we present our results which, though st ill preliminary, offer the bestsupport to date of this scaling hypothesis.

Talk presented at the NATO ASI,The post-recombination universe:Cambridge, England, July 27-Aug. 7, 1987

* On leave from Institut dA&ophyaiquc de Pa&

e Operated by Unlversitiea Research Association Inc. under contract w ith the United States Department ot Energy


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INTRODUCTIONAlthough Cosmic strings are often discussed as possible sources of the pri-mordial density fluctuations: the fundamental question of how a string networkevolves in the early universe haa not been resolved. Strings form when the uni-verse is at a GUT scale temperature, but they are expected to be relevant at muchlater times because the majority of the string length at the time of formation isin the form of infinitely long strings. These infinitely long strings cannot radiateaway into gravitational radiation, so they are expected to survive indefinitely.This is the reason that cosmic strings might be relevant for galaxy formation,but it also poses a potential problem for the cosmic string scenario.

If the interactions between strings are neglected, it can be shown that theenergy density of the infinite strings scales roughly like non-relativistic matter.So if interactions were not important this would imply that imply that cosmicstrings (or their gravitational radiation) would dominate the universe soon af-ter the strings are formed. This diiaster is supposed to be avoided by theprocess by which the infinitely long strings cross themselves and break off smallloops which can decay into gravitational radiation. This scenario has been stud-ied analytically by Kibblez and Bennett? Their work has shown that there aretwo possibilities: either the loop production is not sufficient to avoid a string-dominated universe, or the strings will settle down to a scaling solution in whichthe number of strings crossing a given horizon volume is Sxed.

A great deal of work has already been done on the cosmic string theory ofgalaxy formation, assuming that a scaling solution does indeed exist, and therehas been a great deal of speculation as to the characteristics of the assumed scal-ing solution. So far, however, all of this work is on uncertain ground because thebasic details of string evolution are not understood. Albrecht and Turok4 havepublished preliminary results from their simulation two years ago. However, theirprogram was fairly crude, and these results were criticized ss inconsistent on thebasis of analytical work?

NUMERICAL TECHNIQUETo Generate the initia l conditions, we follow the general procedure introduced

by Vachaspati and Viler&in! To minimize the problems caused by the degenera-eies of these initia l conditions, we have replaced the generated sharp corners byarcs of circles, and added small transverse velocities on the curved segments.

To evolve the generated configuration, we solve the partial differential equa-tions which describe cosmic string motion in an expanding universe using a

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stressed, however, that our value for pLt/p is an order of magnitude larger thanthe value quoted by Albrecht and Turok, so our results cannot be considered tobe consistent with theirs.

In fact, our results differ substantially from many of the generally acceptedideas about string evolution. The standard scenario for loop production holdsthat horizon sized parent loops break off the infinite string network and frag-ment into roughly 10 child loops of roughly equal sizes, but we find that inaddition to the horizon sized parent loops, the infinite strings lose significantamounts of energy directly into small loops. The reason for this is presumablythat the strings have a lot of short wavelength structure in the form of the kinksthat are formed whenever strings cross. In addition, the large parent loops frag-ment much more efficiently than was previously thought, so that most (but notall) of the loops that are created are close enough to our lower cutoff on loopsize (usually 10 points per loop) so that their chances of fragmenting further aresignificantly (or completely) suppressed.

The fact that these very small loops play such an important role presentssome difficult numerical problems. The most obvious problem is we cannot besure of the correct loop distribution function because we dont know which ofthese small loops would fragment further if we had better resolution. Anotherdifficulty is that our result for p,#/p has some dependence on our small loopcutoff. This is mainly because loop reconnection to the infinite strings is muchless efficient for very small loops than for larger ones. Thus, reducing the lowercutoff increases the efficiency of loop production and decreases the scaling solutionvalue of pL/tz. Thus, our determination of pL/t suffers from a systematic errordue to our small loop cutoff. Only by fitting the free parameters of the analyticmodel of Refs. 2 and 3 to these numerical results will we be able to resolve thesequestions.

CONCLUSIONOur results, though not definitive, lend support to the hypothesis of ezistence

of a scaling solution although the string density at the scaling solution is an orderof magnitude larger than that reported by Albrecht and Turok. Neverthelessmore work is necessary in order to disentangle the precise characteristics of thescaling regime from numerical effects such ss the cutoff on small loops.


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ACKNOWLEDGEMENTSWe would like to thank Andy Albrecht and Neil Turok for many stimulating

discussions. This work wss supported in part by the DOE (at Fermilab andIGPP), the NSF (at Chicago and Berkeley), and NASA (at Fermilab).

REFERENCES[l] See the papers by R. Brandenberger, B. Rudak, A. Stebbins, and

S. Veeraraghavan in these proceedings.[2] A. Albrecht, and N. Turok, Phys. Rev. Lett. 64, 1868 (1985).[S] D. P. Bennett, Phys. Rev. D33, 872, and D34, 3592 (1986).[4] T. W. B. Kibble, Nucl. Phys. B262,227 (1985).[5] N. Turok, and P. Bhattacharjee, Phys. Rev. D29, 1557 (1984).[6] T. Vachaspati, and A. Viler&in, Phys. Rev. DSO, 2036 (1984).

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David P. Bennett and Francois R. Bouchet- Cosmic Strings: A Problem or a Solution?