Unimodular $f(R,T)$ Gravity

Understand

We extend the idea of unimodular gravity to the modified $f(R,T)$ theories.

• A new class of cosmological solutions, that the unimodular constraint on the metric imposes on the $f(R,T)$ theories, are studied.
• This extension is done in both Jordan and Einstein frames.
• We show that while the Lagrange multiplier (that imposes the unimodular constraint on the action) depends on the cosmic time in Jordan frame and therefore, can act as an evolving scalar field in the universe history, in the Einstein frame it acts as a cosmological constant.