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Dynamically induced spin-2 mass in a Weyl-invariant framework

Ioannis D. Gialamas, Kyriakos Tamvakis

Abstract

We combine the ghost-free bimetric theory of gravity with the concept of local Weyl invariance, realized in the framework of Einstein-Cartan gravity. The gravitational sector, characterized by two independent metrics and two independent connections, is coupled to a scalar field that can in principle develop a non-vanishing expectation value through radiative corrections. The spectrum of the model, apart from the massless standard graviton and a pair of axion-like pseudoscalars, associated with the presence of the Holst invariants in the action, includes an additional spin-$2$ state of a non-vanishing Fierz-Pauli mass proportional to the scalar field vacuum expectation value. We analyze the phenomenology of the model and specify the conditions under which the massive spin-$2$ state could be a primary dark matter candidate.

Dynamically induced spin-2 mass in a Weyl-invariant framework

Abstract

We combine the ghost-free bimetric theory of gravity with the concept of local Weyl invariance, realized in the framework of Einstein-Cartan gravity. The gravitational sector, characterized by two independent metrics and two independent connections, is coupled to a scalar field that can in principle develop a non-vanishing expectation value through radiative corrections. The spectrum of the model, apart from the massless standard graviton and a pair of axion-like pseudoscalars, associated with the presence of the Holst invariants in the action, includes an additional spin- state of a non-vanishing Fierz-Pauli mass proportional to the scalar field vacuum expectation value. We analyze the phenomenology of the model and specify the conditions under which the massive spin- state could be a primary dark matter candidate.

Paper Structure

This paper contains 9 sections, 57 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Framework
  3. The model
  4. Equations of motion
  5. Background solutions and particle spectrum
  6. Proportional solutions
  7. Linearization
  8. Massive spin-2 phenomenology
  9. Summary and Conclusions

Figures (1)

  • Figure 1: The Fierz-Pauli mass, $m_{\rm FP}$, as function of the $v_\Phi$ (left) and $\bar{\alpha}$ (right), with parameters $\beta_1=-1=-\beta_4$. The cyan and red shaded regions indicate the constraints on $m_{\rm FP}$ and $\bar{\alpha}$ derived in Babichev:2016bxi, under the assumption that the massive spin-2 particle constitutes DM.