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 \(t < t_\mathrm{rec}\), where \(t_\mathrm{rec}\) 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 \(t > t_\mathrm{rec}\) 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.

修改后的引力理论解释了早期宇宙和晚期宇宙学，星系和星系团的动力学。修正重力（MOG）理论将广义相对论（GR）扩展了三个额外的自由度：标量场G，增强了牛顿重力常数\（G_N \）的强度，重力自旋1矢量引力场\（\ phi _ \ mu \）和超轻旋转1引力子的有效质量\（\ mu \）。对于\（t <t_ \ mathrm {rec} \），其中\（t_ \ mathrm {rec} \）表示重组和重新电离的时间，矢量引力子的密度\（\ rho _ \ phi> \ rho _b \），其中\（\ rho _b \）是重子的密度，而对于\（t> t_ \ mathrm {rec} \），我们有\（\ rho _b> \ rho _ \ phi \）。物质密度由\（\ Omega _M = \ Omega _b + \ Omega _ \ phi + \ Omega _r \）进行参数化，其中\（\ Omega _r = \ Omega _ \ gamma + \ Omega _ \ nu \）。对于通过普朗克协作获得的宇宙学参数值，可以按照\（\ Lambda \） CDM模型来拟合CMB声波振荡功率谱，极化和透镜数据。当重子密度\（\ rho _b \）占据了晚期宇宙时，MOG解释了星系旋转曲线，星系团，星系透镜和星系团的动力学与功率谱有关，而没有占优势的暗物质。