Chern-Simons modification of general relativity

Abstract

General relativity is extended by promoting the three-dimensional gravitational Chern-Simons term to four dimensions. This entails choosing an embedding coordinate v µ -an external quantity, which we fix to be a non-vanishing constant in its time component. The theory is identical to one in which the embedding coordinate is itself a dynamical variable, rather than a fixed, external quantity. Consequently diffeomorphism symmetry breaking is hidden in the modified theory: the Schwarzschild metric is a solution; gravitational waves possess two polarizations, each traveling at the velocity of light; a conserved energy-momentum (pseudo-) tensor can be constructed. The modification is visible in the intensity of gravitational radiation: the two polarizations of a gravity wave carry intensities that are suppressed/enchanced by the extension. *

Non‐linear Realizations and Higher Curvature Supergravity

“…Further properties of the theories with the bosonic sector (111) can be found in [40]. Notice that we did not have to impose the constraints (28) and (32) to eliminate any ghosts, we only impose them such that the theory becomes simpler and the L 0 sector takes the form it has in the previous subsection 3.1.…”

“…This is the action for chiral gravity which has been discussed in [40] and in a cosmological setup in [41,42]. In the opposite case in which Reh(φ) = 0, we are left with…”

“…Notice that this coupling Imf (φ) R 2 HP will lead to violation of CP conservation [40]. In a cosmological framework, parity violating terms appear in the effective theory of inflation [41].…”

“…For example, on cosmological backgrounds C mn contributes only with second time derivatives. In particular, if we have the coupling with a scalar profile of the form φ = φ(t), then the theory will not develop instabilities around a Minkowski background 3 [40].…”

Dynamical Chern–Simons modified gravity, Gödel Universe and variable cosmological constant

“…Among a great number of possible Lorentz-CPT breaking modification of gravity [1], the four-dimensional gravitational Chern-Simons term originally introduced in [2] is certainly the most popular one. The main reasons for it are its relatively simple form, evident gauge symmetry and straightforward analogies with the three-dimensional gravitational ChernSimons term [3].…”