Gravitational Theory of Cosmology, Galaxies and Galaxy Clusters

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 the 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 $\Omega_r=\Omega_\gamma+\Omega_\nu$. 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.