# Gravitational waves, cosmic strings, and recent NANOGrav results

There has been intriguing news in the past week regarding gravitational waves and cosmic strings. I have yet to write about cosmic strings on this blog, a consequence of a lack of time more than anything else; but it is certainly on the list of things I want to cover, especially considering that I would like to write some papers in this area in the future. A very nice introductory article was written some time ago by my professor, Ed Copeland, which I recommend. One of my favourite papers on cosmic superstrings was in fact co-authored by Ed Copeland and Joe Polchinski alongside Robert C. Myers. They also wrote a paper together on macroscopic fundamental and Dirichlet strings, which should provide ample background material. Although I am inclined to say that I come more from the maths side of string research than the cosmology side, cosmic strings are super cool. Thinking of them now has me remember when I first arrived at Nottingham as an undergraduate, it was around the time I first met Prof. Copeland. I was sharing with him my enthusiasm for Joe Polchinski’s textbooks, when Ed shared with me that he had written with Joe on a few occasions. I recall racing home to read the papers they had written together. The next time I spoke with Ed, I had a printed copy of their paper on cosmic superstrings and told him how much I enjoyed reading it! I was only beginning to study strings in a thorough and rigorous way at that time, but his papers stimulated my interests greatly.

I will think of drafting a detailed technical essay in time, but one way to think of cosmic strings is under the Nambu-Goto approximation which describes them as one-dimensional objects. The idea is that these hypothetical objects may have formed early on in the universe, particularly while it was expanding and cooling down. If we take a model of hybrid inflation as an example, we have two scalar fields: $\psi$, which is the inflation field with a flat potential satisfying slow-roll conditions, and a more dynamical scalar $\phi$ whose mass depends on $\psi$. One argument is that, as the universe cooled, spacetime may have cracked – to give a sense of intuition think of a fissure in the ice of a frozen lake or something similar. This crack is what we term a topological defect. In a hybrid inflation model, inflation ends not so much as the slow-roll approximation breaks down but when $\phi$ becomes tachyonic, such that its mass squared becomes negative. One can study tachyons in a direct and wonderfully illuminating way in the spectrum of the bosonic string, but the main point here is that they are highly unstable. So the hybrid model signals an instability, and it is this instability where a phase transition can occur in which such topological defects can form. These are cosmic strings.

Many field-theory models predict the existence of cosmic strings, and experimental evidence of their existence would be truly extraordinary. It would mean a lot of things, not least direct experimental evidence in support of string theory. One of the brilliant properties of cosmic strings is that, like the ordinary string, they may interact and form loops. In the cosmic string case, when two strings intersect or when a single string crosses itself, intercommutation can lead to the formation of a closed loop. These loops can oscillate in different ways depending on the dynamics, but if a single loop is large enough it is very likely to meet another string and reconnect, hence we have a network of cosmic strings which would have evolved in time as the Universe expanded. It should be noted that a mathematical description of these string interactions can very insofar that, for instance, in the context of brane cosmology – think also of Brane-worlds – we have F-strings, which in certain scenarios can grow to cosmological scales. These are cosmic superstrings, and unlike standard cosmic strings they interact (and form loops) probabilistically. What is cool is that, in this string network, the loops oscillate and radiate energy, shrinking and eventually decaying. One such form of radiation is gravitational radiation, and it is through the dissipation of energy from the oscillating loops that we may describe gravitational wave emission. In the formalism, there are two primary concepts, kinks and cusps, which describe the strongest bursts of gravitational waves by the string.

To date there has been no direct evidence for the existence of cosmic strings, but last week a number of papers emerged speculating on a recent report provided by The North American Nanohertz Observatory for Gravitational Waves (NANOGrav). Pierre Auclair, a PhD candidate at Laboratoire Astroparticule et Cosmologie (APC), gave a talk for us last Friday at the Centre For Astronomy And Particle Theory to go over his research on cosmic strings, and toward the end of his presentation he mentioned some of the excitement stirring in response to this NANOGrav report (attached is a screenshot from his lecture slides, it lists a number of notable papers to appear on the archives in recent days). Right now a lot of study is being put into obtaining bounds on the string tension $G\mu$ from gravitational waves detectors (NANOGrav, LIGO, and Virgo), and experiments are searching for individual bursts in the context of stochastic backgrounds. When it comes to the NANOGrav report, the initial view by a number of researchers is that study yields strong evidence for the presence of a stochastic common-spectrum process across the 45 pulsars analysed. It is a 12.5-year data set, and while a conclusive statement on the physical origin of the signal is not immediately obtainable, with a number of qualifications required to ensure the detection of a gravitational wave signal, some have already begun to argue it is reasonable to interpret the data in terms of a stochastic gravitational-wave background emitted by a cosmic-string network.

It is exciting news, to be sure. But just as Auclair advised – and as is generally a reasonable principle to follow – one should proceed tentatively and with caution toward any claims about evidence for the existence of cosmic strings.

Currently I am preparing to submit my thesis for the end of the month, so I haven’t had a moment to properly dig into the report. A letter by Simone Blasi, Vedran Brdar, and Kai Schmitz speculating on the connection to cosmic strings can be found here. It will be great to write about all of this in more technical detail when there is time, and to also watch closely for further reports.