CMB Polarization and Theories of Gravitation with Massive Gravitons

Abstract

We study in this paper three different theories of gravitation with massive gravitons - the modified Fierz-Pauli (FP) model, Massive Gravity and the bimetric theory proposed by Visser - in linear perturbation theory around a Minkowski and a flat FRW background. For the TT tensor perturbations we show that the three theories give rise to the same dynamical equations and to the same form of the Boltzmann equations for the radiative transfer in General Relativity (GR). We then analyze vector perturbations in these theories and show that they do not give the same results as in the previous case. We first show that vector perturbations in Massive Gravity present the same form as found in General Relativity, whereas in the modified FP theory the vector gravitational-wave (GW) polarization modes (${\Psi }_3$ amplitudes in the Newman-Penrose (NP) formalism) do not decay too fast as it happens in the former case. Rather, we show that such ${\Psi }_3$ polarization modes give rise to an unusual vector Sachs-Wolfe effect, leaving a signature in the quadrupole form $Y_{2,\pm 1}(\theta ,\phi )$ on the CMB polarization. We then derive the details for the Thomson scattering of CMB photons for these ${\Psi }_3$ modes, and then construct the correspondent Boltzmann equations. Based upon these results we then qualitatively show that ${\Psi }_3$-mode vector signatures - if they do exist - could clearly be distinguished on the CMB polarization from the usual ${\Psi }_4$ tensor modes.

arXiv commentTo appear in Classical and Quantum Gravity

References in corpus (11)

• Phases of massive gravity
• Gravitational wave astronomy
• Bounding the mass of the graviton using binary pulsar observations
• Mass for the graviton
• Limits on the detectability of the CMB B-mode polarization imposed by foregrounds
• Graviton Mass or Cosmological Constant?
• Cosmological attractors in massive gravity
• Theoretical tools for CMB physics
• Polarization states of gravitational waves with a massive graviton
• Massive gravity and structure formation
• The First Space-Based Gravitational-Wave Detectors

Cited by in corpus (15)

• Theoretical Aspects of Massive Gravity
• Lorentz Breaking Massive Gravity in Curved Space
• Weak Field Limit and Gravitational Waves in $f(T,B)$ Teleparallel Gravity
• Graviton mass bounds from space-based gravitational-wave observations of massive black hole populations
• Massive relic gravitational waves from f(R) theories of gravity: production and potential detection
• Gravitational waves in non-local gravity
• Extra polarization states of cosmological gravitational waves in alternative theories of gravity
• Gravitational Waves in Higher Order Teleparallel Gravity
• The Exact Amplitudes of Six Polarization Modes for Gravitational Waves
• Linearized physics and gravitational-waves polarizations in the Palatini formalism of GBD theory
• CMB anisotropies induced by tensor modes in Massive Gravity
• Observational Constraints on Visser's Cosmological Model
• Gravitational waves in massive gravity: Waveforms generated by a particle plunging into a black hole and the excitation of quasinormal modes and quasibound states
• Massive gravitational waves from the Cosmic Defect theory
• BB mode angular power spectrum of CMB from massive gravity