Scalar–Tensor–Vector Modified Gravity in Light of the Planck 2018 Data

John W Moffat,Viktor Toth

doi:10.3390/universe7100358

Abstract

The recent data release by the Planck satellite collaboration presents a renewed challenge for modified theories of gravitation. Such theories must be capable of reproducing the observed angular power spectrum of the cosmic microwave background radiation. For modified theories of gravity, an added challenge lies in the fact that standard computational tools do not readily accommodate the features of a theory with a variable gravitational coupling coefficient. An alternative is to use less accurate but more easily modifiable semianalytical approximations to reproduce at least the qualitative features of the angular power spectrum. We extend a calculation that was used previously to demonstrate compatibility between the Scalar–Tensor–Vector–Gravity (STVG) theory, also known by the acronym MOG, and data from the Wilkinson Microwave Anisotropy Probe (WMAP) to show the consistency between the theory and the newly released Planck 2018 data. We find that within the limits of this approximation, the theory accurately reproduces the features of the angular power spectrum.

Highlights

Though highly isotropic, the cosmic microwave background (CMB) shows small temperature fluctuations as a function of the sky direction
The cosmic microwave background (CMB) shows small temperature fluctuations as a function of the sky direction. The magnitude of these fluctuations depends on the angular size. This location and size of these peaks is an important prediction of the standard model of cosmology, which has been confirmed by increasingly accurate experiments, such as the Boomerang experiment [1], the Wilkinson Microwave
Without access to a standard suite of computer programs that can reliably and provably deal with a variable-G modified theory of gravity, we opted for another approach: use a semianalytical approximation that is sufficiently accurate to reproduce the key qualitative features of the CMB angular power spectrum and perhaps even allow us to make some cautious predictions

Summary

The MOG Theory

Our MOG modified gravity theory, known as Scalar–Tensor–Vector–Gravity (STVG [5]), is a relativistic theory of gravitation based on an action principle. Without access to a standard suite of computer programs that can reliably and provably deal with a variable-G modified theory of gravity, we opted for another approach: use a semianalytical approximation that is sufficiently accurate to reproduce the key qualitative features of the CMB angular power spectrum and perhaps even allow us to make some cautious predictions. Such an approximation method was published by Mukhanov [6]. In light of the recent release of Planck 2018 data, we found it imperative to revisit and, if necessary, refine this calculation and compare the Planck results against the MOG predictions

Semi-Analytical Estimation of CMB Anisotropies

The MOG CMB Spectrum

Conclusions