Analyzing modified unimodular gravity via Lagrange multipliers

Abstract

The so-called unimodular version of General Relativity is revisited. Unimodular gravity is constructed by fixing the determinant of the metric, what leads to the trace-free part of the equations instead of the usual Einstein field equations. Then, a cosmological constant naturally arises as an integration constant. While unimodular gravity turns out equivalent to General Relativity (GR) at the classical level, it provides important differences at the quantum level. Here we extend the unimodular constraint to some extensions of General Relativity that have drawn a lot of attention over the last years, as $f(R)$ gravity (or its scalar-tensor picture) and Gauss-Bonnet gravity. The corresponding unimodular version of such theories is constructed as well as the conformal transformation that relates the Einstein and Jordan frames for these non-minimally coupled theories. From the classical point of view, the unimodular versions of such extensions are completely equivalent to their originals, but an effective cosmological constant arises naturally, what may provide a richer description of the universe evolution. Here we analyze the case of Starobisnky inflation and compared with the original one.

8 pages. Title changed, some comments added, conclusions unchanged. Version published in PRD

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• Lorenz Gauge Fixing of $f(T)$ Teleparallel Cosmology
• Weyl relativity: A novel approach to Weyl's ideas
• Reheating and particle creation in unimodular f(R, T) gravity
• Nonconservative traceless type gravity
• Effects of Rastall parameter on perturbation of dark sectors of the Universe
• First order formalism for thick branes in modified gravity with Lagrange multiplier
• Quartet-metric/multi-component gravity: scalar graviton as emergent dark substance
• Cosmological Inflation in a Generalized Unimodular Gravity
• Non-minimal Unimodular Inflation
• Higgs Inflation in Unimodular Gravity
• $\Lambda CDM$ periodic cosmology
• Resolution of the cosmological constant problem by unimodular gravity and signature reversal symmetry