Cosmic strings increasing internal energy?

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TL;DR
Cosmic strings increasing internal energy as the Universe expands?
I was reading an article by Edward Harrison, which tackles the problems of conservation of energy at cosmological scales.

At some point (point 2.4) he cites several article, including one by Rees and Gott, which he says indicates that the internal energy of a comoving volume (e.g. a cosmic string) increases as the universe expands. However I have looke the article by Rees and Gott and I didn't understand it well. So, if a cosmic string increases its energy as the universe expands, will it increase as long as the expansion is maintained? And what is exactly this internal energy? Heat? Radiation?...

Link to the article: https://adsabs.harvard.edu/full/1995ApJ...446...63H
 
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