Primordial Power Spectra of Cosmological Fluctuations with Generalized Uncertainty Principle and Maximum Length Quantum Mechanics

Understand

The existence of the cosmological particle horizon as the maximum measurable length $l_{max}$ in the universe leads to a generalization of the quantum uncertainty principle (GUP) to the form $\Delta x \Delta p \geq \frac{\hbar}{2}\frac{1}{1-\alpha\Delta x^2} $, where $\alpha\equiv l_{max}^{-2}$.

• The effects of this GUP on simple quantum mechanical systems has been shown recently by one of the authors\cite{Perivolaropoulos:2017rgq} to be extremely small (beyond current measurements) due to the extremely large scale of the current particle horizon.
• This is not the case in the Early Universe during the quantum generation of the inflationary primordial fluctuation spectrum.
• We estimate the effects of such GUP on the primordial fluctuation spectrum and on the corresponding spectral index.