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 radia
tion. For modified theories of gravity, an added challenge lies with 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 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.
Renormalization group methods are applied to a scalar field within a finite, nonlocal quantum field theory formulated perturbatively in Euclidean momentum space. It is demonstrated that the triviality problem in scalar field theory, the Higgs boson m
ass hierarchy problem and the stability of the vacuum do not arise as issues in the theory. The scalar Higgs field has no Landau pole.
The formation, accretion and growth of supermassive black holes in the early universe are investigated. The accretion rate ${dot M}$ is calculated using the Bondi accretion rate onto black holes. Starting with initial seed black holes with masses $M_
{rm BH}sim 10^2-10^3M_{odot}$, the Bondi accretion rate can evolve into a supermassive black hole with masses $M_{rm BH}sim 10^9-10^{10}M_{odot}$ and with a young quasar lifetime $sim 10^5-10^6$ years by super-Eddington accretion.
The boson and fermion particle masses are calculated in a finite quantum field theory. The field theory satisfies Poincare invariance, unitarity and microscopic causality, and all loop graphs are finite to all orders of perturbation theory. The infin
ite derivative nonlocal field interactions are regularized with a mass (length) scale parameter $Lambda_i$. The $W$, $Z$ and Higgs boson masses are calculated from finite one-loop self-energy graphs. The $W^{pm}$ mass is predicted to be $M_W=80.05$ GeV, and the higher order radiative corrections to the Higgs boson mass $m_H=125$ GeV are damped out above the regulating mass scale parameter $Lambda_H=1.57$ TeV. The three generations of quark and lepton masses are calculated from finite one-loop self-interactions, and there is an exponential spacing in mass between the quarks and leptons.
A consequence of adopting a modified gravitational theory (MOG) for the aLIGO GW190521 gravitational wave detection involving binary black hole sources is to fit the aLIGO strain and chirp data with lower mass, compact coalescing binary systems such
as neutron star-neutron star (NS-NS), black hole - neutron star (BH-NS), and black hole-black hole (BH-BH) systems. In MOG BH - BH component masses can be smaller than the component masses $m_1=85M_odot$ and $m_2=66M_odot$ inferred from the aLIGO GW190521 gravitational wave event. This reduces the mass of the final remnant mass $M_f=150M_odot$ and allows the primary, secondary and final remnant masses of the black holes to be formed by conventional stellar collapse models.
The modified gravity (MOG) theory is applied to the gravitational wave binary merger GW190814 to demonstrate that the modified Tolman-Oppenheimer-Volkoff equation for a neutron star can produce a mass $M=2.6 -2.7 M_odot$, allowing for the binary seco
ndary component to be identified as a heavy neutron star in the hypothesized mass gap $2.5 - 5 M_odot$.
The lensing and Einstein ring at the core of the galaxy cluster Abell 3827 are reproduced in the modified gravity theory MOG. The estimated effective lensing mass $M_L=(1+alpha)M_b=5.2times 10^{12} M_odot$ within $R=18.3$~kpc for a baryon mass $M_b=1
.0times 10^{12} M_odot$ within the same radius produces the observed Einstein ring angular radius $theta_E=10$. A detailed derivation of the total lensing mass is based on modeling of the cluster configuration of galaxies, intracluster light and X-ray emission. The MOG can fit the lensing and Einstein ring in Abell 3827 without dark matter as well as General Relativity with dark matter.
A covariant modified gravity (MOG) is formulated by adding to general relativity two new degrees of freedom, a scalar field gravitational coupling strength $G= 1/chi$ and a gravitational spin 1 vector field $phi_mu$. The $G$ is written as $G=G_N(1+al
pha)$ where $G_N$ is Newtons constant, and the gravitational source charge for the vector field is $Q_g=sqrt{alpha G_N}M$, where $M$ is the mass of a body. Cosmological solutions of the theory are derived in a homogeneous and isotropic cosmology. Black holes in MOG are stationary as the end product of gravitational collapse and are axisymmetric solutions with spherical topology. It is shown that the scalar field $chi$ is constant everywhere for an isolated black hole with asymptotic flat boundary condition. A consequence of this is that the scalar field loses its monopole moment radiation.
A modified gravitational theory explains early universe and late time cosmology, galaxy and galaxy cluster dynamics. The modified gravity (MOG) theory extends general relativity (GR) by three extra degrees of freedom: a scalar field $G$, enhancing th
e strength of the Newtonian gravitational constant $G_N$, a gravitational, spin 1 vector graviton field $phi_mu$, and the effective mass $mu$ of the ultralight spin 1 graviton. For $t < t_{rm rec}$, where $t_{rm rec}$ denotes the time of recombination and re-ionization, the density of the vector graviton $rho_phi > rho_b$, where $rho_b$ is the density of baryons, while for $t > t_{rm rec}$ we have $rho_b > rho_phi$. The matter density is parameterized by $Omega_M=Omega_b+Omega_phi+Omega_r$ where $Omega_r=Omega_gamma+Omega_ u$. For the cosmological parameter values obtained by the Planck Collaboration, the CMB acoustical oscillation power spectrum, polarization and lensing data can be fitted as in the $Lambda$CDM model. When the baryon density $rho_b$ dominates the late time universe, MOG explains galaxy rotation curves, the dynamics of galaxy clusters, galaxy lensing and the galaxy clusters matter power spectrum without dominant dark matter.
The equation of motion in the generally covariant modified gravity (MOG) theory leads, for weak gravitational fields and non-relativistic motion, to a modification of Newtons gravitational acceleration law. In addition to the metric $g_{mu u}$, MOG h
as a vector field $phi_mu$ that couples with gravitational strength to all baryonic matter. The gravitational coupling strength is determined by the MOG parameter $alpha$, while parameter $mu$ is the small effective mass of $phi_mu$. The MOG acceleration law has been demonstrated to fit a wide range of galaxies, galaxy clusters and the Bullet Cluster and Train Wreck Cluster mergers. For the SPARC sample of rotationally supported spiral and irregular galaxies, McGaugh et al. [24] (MLS) have found a radial acceleration relation (RAR) that relates accelerations derived from galaxy rotation curves to Newtonian accelerations derived from galaxy mass models. Using the same SPARC galaxy data, mass models independently derived from that data, and MOG parameters $alpha$ and $mu$ that run with galaxy mass, we demonstrate that adjusting galaxy parameters within $pm 1$-sigma bounds can yield MOG predictions consistent with the given rotational velocity data. Moreover, the same adjusted parameters yield a good fit to the RAR of MLS, with the RAR parameter $a_0=(5.4pm .3)times 10^{-11},{rm m/s^2}$.
