Cosmological perturbations of unimodular gravity and general relativity are identical

• Published in: General relativity and gravitation Vol. 48; no. 10; pp. 1 - 30
• Main Authors: Basak, Abhishek, Fabre, Ophélia, Shankaranarayanan, S.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2016; Springer Nature B.V
• Subjects: Astronomy; Astrophysics and Cosmology; Big Bang theory; Classical and Quantum Gravitation; Cosmic microwave background; Differential Geometry; Einstein equations; Gravitation; Gravity; Mathematical analysis; Mathematical and Computational Physics; Perturbation methods; Physics; Physics and Astronomy; Quantum Physics; Relativity; Relativity Theory; Research Article; Theoretical; Theory of relativity; Cosmological perturbation theory; CMB; Inflation; Unimodular gravity
• ISSN: 0001-7701; 1572-9532
• DOI: 10.1007/s10714-016-2116-4

Unimodular gravity (UG) is a restricted version of general relativity (GR) in which the variation of the metric determinant is set to zero and the field equations are given by the trace-free part of the full Einstein equations. The background equations in UG and GR are identical. It was recently claimed that the first order contribution in the temperature fluctuations of the Cosmic Microwave Background (CMB) in UG is different from GR. In this work, we calculate the first order perturbation equations in UG and show that the Sachs–Wolfe effect in UG, in terms of gauge invariant variables, is identical to GR. We also show that the second order perturbation equation of Mukhanov–Sasaki variable in UG, is identical to GR. The only difference comes from the gauge choices due the constraint on the metric determinant. Hence, UG and GR are identical and indistinguishable in CMB data on large scales.