String length constraining from the stochastic gravitational waves background

TL;DR

This paper derives an exact spectrum of stochastic gravitational waves from string gas cosmology, revealing constraints on string length and ruling out certain phases based on current CMB observations.

Contribution

It provides a novel exact spectrum derivation using Lambert W function and constrains string length to below seven orders of magnitude of Planck scale.

Findings

Non-Hagedorn phase ruled out by current B-mode polarization

Unique spectrum from Hagedorn phase with logarithmic term

String length constrained to less than 7 orders of magnitude of Planck scale

Abstract

We study the stochastic gravitational waves from string gas cosmology. With the help of the Lambert W function, we derive the exact energy density spectrum of the stochastic gravitational waves in term of tensor-to-scalar. New feathers with the spectrum are found. First, the non-Hagedorn phase can be ruled out by the current B-mode polarization in the cosmic microwave background. Second, the exact spectrum from the Hagedorn phase with a logarithmic term is shown to be unique in the measurable frequency range. Third, which is the most important, we find the string length can be constrained to be lower than 7 $\sim$ orders of that Planck scale.