Abstract
We calculate six invariant terms of a gravitational field theory that nonlinearly realizes the Conformal/Poincar\'e quotient, and reduce to the known conformal Galileons in the limit when only the conformal mode is kept. Five of the six terms are regular coset terms, while the sixth is a Wess-Zumino (WZ) term that gives the well-known gravitational action for the trace anomaly. The obtained terms can be embedded in a quantum effective field theory (EFT) without spoiling their key features, although at a cost of certain fine tunings. The additional massive modes that appear in the EFT would have been troublesome, however, for sub-Planckian curvatures their masses are (super)-Planckian and therefore the respective states are outside of the EFT regime. We discuss certain novel cosmological solution of this theory and their validity within the EFT. Furthermore, we show that the obtained 4D terms, except the WZ term, can also be derived from higher dimensional Lovelock terms by reducing the latter to the genuinely four dimensional terms according to a well-defined algorithm.
Highlights
If one were to start with a Galileon as a stand-alone scalar field theory without gravity, we know that massive gravity would provide gravitational dressing of the Galileon
It seems natural to ask [22] whether there exists a gravitational field theory where the conformal Gallileon would be a NG mode, like the ordinary Galileon is in massive gravity
This led to the well-known action of New Massive Gravity (NMG) [24] and its generalization [25], both obtained in a local Weyl invariant form
Summary
Theories that modify gravity in the infrared, such as brane-induced gravity [1] or massive gravity [2,3], exhibit interesting ultraviolet properties as quantum effective field theories: the terms that amend the Einstein-Hilbert (EH) action in these theories—e.g., the covariant graviton mass term—turn out to contain special higher dimensional (irrelevant) operators at a scale much below the Planck mass; while the emergence of this strong interaction scale is not unlike in massive non-Abelian gauge theories [4], both the dynamics and open questions due to these higher dimensional operators in massive gravity are considerably richer, see, e.g., [5,6,7,8,9,10,11,12,13,14,15]. It seems natural to ask [22] whether there exists a gravitational field theory where the conformal Gallileon would be a NG mode (gauge mode), like the ordinary Galileon is in massive gravity. This question was addressed in [22] in 3D. To obtain the gravitationally dressed conformal Galileons we considered a full gravitational conformal/Poincarecoset in 3D This led to the well-known action of New Massive Gravity (NMG) [24] and its generalization [25], both obtained in a local Weyl invariant form. Since 1⁄2Ka; Pb ∝ −2ηabD not all the NG fields of the coset are independent; the inverse Higgs constraint (IHC) [32] will enable us to eliminate the NG’s related to broken Ka’s in favor of the NG related to broken D
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