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Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar

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arxiv 1902.07876 v2 pith:JY5YPYPJ submitted 2019-02-21 hep-th gr-qchep-ph

Ariel Edery , Yu Nakayama This is my paper · ORCID
classification hep-thgr-qchep-ph
keywords gravityscalarfieldmasslesseinsteinpalatinipureconstant
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abstract

Pure $R^2$ gravity has been shown to be equivalent to Einstein gravity with non-zero cosmological constant and a massless scalar field. We show that the Palatini formulation of pure $R^2$ gravity is equivalent to Einstein gravity with non-zero cosmological constant as before but with no massless scalar field. This is an important new development because the massless scalar field is not readily identifiable with any known particle in nature or unknown particles like cold dark matter which are expected to be massive. We then include a non-minimally coupled Higgs field as well as fermions to discuss how the rest of the standard model fields fit into this paradigm. With Higgs field, Weyl invariance is maintained by using a hybrid formalism that includes both the Palatini curvature scalar $\mathcal{R}$ and the usual Ricci scalar $R$

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Critical gravity from four dimensional scale invariant gravity

    hep-th 2019-08 accept novelty 6.0 of 10

    A purely quadratic, scale-invariant gravity action becomes critical when beta equals 6 alpha, turning its massive spin-two ghost into a massless graviton.

  2. Cosmological phase space of generalized hybrid metric-Palatini theories of gravity

    gr-qc 2019-08 conditional novelty 6.0 of 10

    A dynamical-systems analysis of f(R,ℛ) hybrid metric-Palatini gravity shows no global attractors in the cosmological phase space and only two classes of fixed-point scale factors, one of which predicts a jerk paramete...

  3. Inflationary assessment of $F(\mathcal{R},\tilde{\mathcal{R}})$ Einstein-Cartan models

    gr-qc 2025-12 conditional novelty 5.0 of 10

    Adding cubic Holst-invariant terms to F(R,R̃) Einstein-Cartan inflation models systematically lowers the predicted spectral index n_s and tensor-to-scalar ratio r, restoring data compatibility in parameter regions whe...

  4. Spacetime and Planck mass generation from scale-invariant degenerate gravity

    hep-th 2024-11 reject novelty 5.0 of 10

    The paper computes a one-loop effective potential that can produce a Planck mass from a scalar vacuum, but the curvature that seeds it is assumed by hand and the vierbein scale factor runs away.

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