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. We switch independent variable from time to scale factor by change of variable ȧ/a = H(a). Thus a new set of differential equations are analytically solvable with known methods. We formulate Hubble function, the scalar field, potential and energy density when one of them is given in the most general form. a(t) can be explicitly found as long as methods of integration techniques are available. We investigate the dynamics of the universe at early times as well as at late times in light of these formulas. We find mathematical machinery which turns on and turns off early accelerated expansion. On the other hand late time accelerated expansion is explained by cosmic domain walls. We have compared our results with recent observations of type Ia supernovae by considering the Hubble tension and absolute magnitude tension. Eighty-nine percent of present universe may consist of domain walls while rest is matter.

Analytic Solutions of Brans-Dicke Cosmology: Early Inflation and Late Time Accelerated Expansion

“…Most probably φ 2 term in the potential is responsible for late time accelerated expansion. This formula is simpler than the corresponding formula V (φ) in our previous study [55].…”

“…We have already compared this model with observation of type Ia supernovae data in [55]. In our previous study we have obtained H 0 = 71.80 ± 0.22, Ω Λ,0 = 0.715 ± 0.012, Ω m = 0.285 ± 0.012 and χ 2 /ν = 0.990 for absolute magnitude M = −19.30.…”

“…We have shown that universe has an accelerated expansion when one introduces cosmic domain walls with matter in the energy density in section 9.2. We had studied this case with Friedmann cosmology in [55], and we have compared our model with the latest supernovae data. It is seen that both dark energy dominated and domain wall dominated universe have perfect fit with data.…”

“…First one makes Brans-Dicke cosmology equivalent to Einstein cosmology which have been studied in [55]. The second one implies…”

“…Then the distance modulus is defined as µ = m − M . Now we borrow one of our plots from our previous work [55]. In our previous study we have already performed curve fitting with type Ia supernovae data.…”