The early universe resembled a tightly stretched rubber band. In some theories, this band is not just space but enormous oscillating strings whose tension made the world expand at an unimaginable rate. When the band snapped (that is, when inflation ended) the strings collapsed and annihilated like popping bubbles in a boiling pot. But instead of steam and splashes, energy was released that could go not into an ordinary 'soup' of particles but into something stranger.
The authors studied what happens right after this 'collapse' in models where stability is maintained not by quantum jumps but by smooth corrections, as if a table were held up not by magnets but by many small adjustable screws. It turns out that the released energy can drive the visible particles into a special state — a string bath (the Hagedorn phase). In this state, the temperature does not rise no matter how much heat you add, like overheated paste that stays thick even if you keep heating it. This state absorbs excess energy and prevents it from turning into extra particles.
The main practical conclusion concerns so-called dark radiation — an invisible background of light particles that slightly distorts the expansion of the universe. If ordinary matter (our branes — multidimensional sheets where particles live) is in the same 'zone' where annihilation occurred, then even a small fraction of energy entering the string bath reduces the amount of this radiation below current observational limits. If our matter is in another zone, everything depends on how quickly energy flows between zones: fast or slow transfer can still trigger the bath, but the mechanism works best when the string scale in our zone is lower than in the annihilation zone, like boiling water from a large vat being poured into a smaller one.
Thus, the end of inflation turns out not to be a chaotic explosion but a transition into a dense, almost solid state of strings that 'eats' excess energy by itself. The same rubber band, when snapped, did not fly into shreds but coiled into a tight ball that still determines how much light and heat our universe received.
as written by the authors arXiv:2606.08767
We study the post-inflationary open-string Hagedorn phase in perturbatively moduli stabilized brane-antibrane inflation. In this class of models, the volume modulus is stabilized by perturbative corrections rather than by non-perturbative effects to the superpotential, thereby avoiding the standard brane-antibrane $$\eta$$-problem. Since inflation ends through tachyon condensation and brane-antibrane annihilation, the endpoint is intrinsically stringy and need not be described immediately by an ordinary radiation bath. We analyze whether the energy released at annihilation can drive the visible sector into an open-string Hagedorn phase, and study the consequences for dark radiation. If the Standard Model (SM) branes lie in the same throat as where the annihilation occurs, we find that a modest fraction of the released energy deposited into surviving visible open strings is sufficient to enter the Hagedorn regime and can suppress the effective number of relativistic species $$\Delta N_{\rm eff}$$ below current observational bounds. If the SM lies in a different throat, the result depends on inter-throat energy transfer: prompt or delayed transfer can still yield a visible Hagedorn phase. However, the mechanism is most efficient when the local string scale in the SM throat is lower than or comparable to that in the annihilation throat.
In the string bath, the number of particle species grows so rapidly with energy that the temperature stops rising, as if you tried to heat a room, but all new calories went into creating new, previously nonexistent pieces of furniture.
In Iain Banks's novel 'Excession,' a civilization uses 'string technology' to travel between dimensions, and here the string bath serves as a natural energy regulator in the infant universe.