Complete perturbation theory for modified mass-to-horizon cosmology

Develop a complete cosmological perturbation theory for generalized mass-to-horizon (MHR) cosmology by deriving the scalar and tensor mode equations directly within the modified framework, so that the primordial spectra, their normalization, and their scale dependence can be determined self-consistently and the persistence of the background-level sensitivity to the MHR deformation can be tested.

Background

The paper derives modified Friedmann equations and inflationary background observables for the generalized mass-to-horizon relation M = γc²Lⁿ/G, but it evaluates the tensor-to-scalar ratio, scalar spectral index, and scalar amplitude using standard canonical slow-roll formulas as a phenomenological prescription. The authors explicitly identify the absence of a perturbation theory formulated within MHR cosmology as an open direction. A complete treatment would establish the appropriate scalar and tensor mode equations and determine the primordial spectra and their normalization without relying on standard-gravity expressions, thereby testing whether the strong sensitivity of the scalar power-spectrum amplitude to deviations from n = 1 survives at the perturbative level.