Variation of the Gravitational Constant as Well as Cosmology from the Early Inflation to Late Acceleration and Future Universe

Here, cosmology is obtained from the variable gravitational constant G ∝ φ with φ(x) being a scalar and its fluctuations around the ground state. The gravitational action contains Einstein-Hilbert like term with variable G, kinetic energy and self-interaction potential for φ(x). Two phase transitions take place in this model. The first one takes place at the GUT (grand unified theory) scale ∼ 2.45×1014GeV, when the early universe exits the inflationay phase and the second one at the electro-weak scale. Spontaneous symmetry breaking takes place around this scale As a consequence, variable G acquires constant value GN (the Newtonian gravitational constant).The standard model of cosmology is obtained in the post-second phase transition era. Interestingly, the dark matter and quintessence dark energy are created from the gravitational sector as a combined effect of the linear term of scalar curvature and φ(x) without using non-linear terms of curvature or any 1