Axiverse cosmology and the energy scale of inflation

Ultra-light axions ($m_a\lesssim 10^{-18}$eV), motivated by string theory, can be a powerful probe of the energy scale of inflation. In contrast to heavier axions the isocurvature modes in the ultra-light axions can coexist with observable gravitational waves. Here it is shown that large scale structure constraints severely limit the parameter space for axion mass, density fraction and isocurvature amplitude. It is also shown that radically different CMB observables for the ultra-light axion isocurvature mode additionally reduce this space. The results of a new, accurate and efficient method to calculate this isocurvature power spectrum are presented, and can be used to constrain ultra-light axions and inflation.