Maximal-entropy initial state of the Universe as a microscopic description of inflation

Ram Brustein, Ram Brustein, A. J.M. Medved, A. J.M. Medved

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We propose that the initial state of the Universe was an isotropic state of maximal entropy. Such a state can be described in terms of a state of closed, interacting, fundamental strings in their high-temperature Hagedorn phase, which constitutes a novel microscopic model for the state of the Universe when it is at the highest sustainable temperature. This state resolves the big-bang singularity by replacing the past of the hot big-bang Universe and sets inflationary initial conditions for the subsequent evolution of the thermal radiation and the semiclassical cosmological geometry. The entropy density in this state is equal to the square root of the energy density in Planck units, while the pressure is positive and equal to the energy density. These relations imply a maximally large entropy density and, therefore, a state that cannot be described by a semiclassical spacetime geometry. If one nevertheless insists on an effective semiclassical description of this state, she can do so by ignoring the entropy. This leads to a partially equivalent description in which the pressure appears to be negative and equal in magnitude to the energy density, as if the energy-momentum tensor was that of a cosmological constant. From this effective perspective, the state describes a period of string-scale inflation of minimal duration. The stringy state ultimately decays, possibly by a process akin to Hawking radiation, and undergoes a transition into a phase of hot radiation. But, from the effective perspective, the same decay corresponds to the heating of the Universe at the end of inflation. Small quantum mechanical fluctuations in the initial state lead to a scale-invariant temperature anisotropies in the hot radiation. The temperature anisotropies are interpreted in the effective description as arising from quantum fluctuations of the curvature and an effective inflaton field. The stringy microscopic description determines the parameters of the model of inflation, as well as the cosmological observables, in terms of the string length scale and coupling strength. In particular, it describes a high-scale model of inflation with a large scalar-to-tensor ratio which is qualitatively compatible with the cosmological observations. Our framework is similar, conceptually, to a recent description of black holes in terms of a maximal entropy state of strings in the Hagedorn phase.

Original languageEnglish
Article number123502
JournalPhysical Review D
Issue number12
StatePublished - 15 Jun 2020

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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