Using Cosmological Perturbation Theory to Distinguish between GR and Unimodular Gravity

Unimodular gravity is one of the oldest geometric theories and alternatives to general relativity. Essentially, it based on Einstein–Hilbert Lagrangian with an additional constraint determinant metric. It can be explicitly shown that unimodular recast as relativity in presence a cosmological constant. This fact has led many discussions equivalence both at classical quantum levels. Here, we present analysis focused scalar perturbations around background. We focus unusual situation which typical conservation laws are not adopted. The discussion extended case where non-minimal coupled field introduced. also gauge-invariant showing display instabilities. Our results reinforce verified completely perturbative level.