Analytic solutions of scalar field cosmology, mathematical structures for early inflation and late time accelerated expansion

Abstract We study the most general cosmological model with real scalar field which is minimally coupled to gravity. Our calculations are based on Friedmann–Lemaitre–Robertson–Walker (FLRW) background metric. Field equations consist of three differential equations. switch independent variable from time scale factor by change $${\dot{a}}/a=H(a)$$ a ˙ / = H ( ) . Thus a new set analytically solvable known methods. formulate Hubble function, field, potential and energy density when one them given in form. ( t ) can be explicitly found as long methods integration techniques available. investigate dynamics universe at early times well late light these formulas. find mathematical machinery turns off accelerated expansion. On other hand expansion explained cosmic domain walls. have compared our results recent observations type Ia supernovae considering tension absolute magnitude tension. Eighty-nine percent present may walls while rest matter.