Abstract
An exact scalar field cosmological model is constructed from the exact solution of the field equations. The solutions are exact and no approximation like slow roll is used. The model gives inflation, solves horizon and flatness problems. The model also gives a satisfactory estimate of present vacuum energy density as well as vacuum energy density at Planck epoch and solves cosmological constant problem of 120 orders of magnitude discrepancy of vacuum energy density. Further, this model predicts existence of dark matter/energy and gives an extremely accurate estimate of present energy density of dark matter and energy. Along with explanations of graceful exit, radiation era, matter domination, this model also indicates the reason for present accelerated state of the universe. In this work a method is shown following which one can construct an infinite number of exact scalar field inflationary cosmological models.
Highlights
Inflation was proposed by Alan Guth [1] the idea of an exponential type expansion was due to Starobinsky and others [2,3,4]
An exact scalar field cosmological model is constructed from the exact solution of the field equations
The model gives a satisfactory estimate of present vacuum energy density as well as vacuum energy density at Planck epoch and solves cosmological constant problem of 120 orders of magnitude discrepancy of vacuum energy density
Summary
Inflation was proposed by Alan Guth [1] the idea of an exponential type expansion was due to Starobinsky and others [2,3,4]. Most of the modern models depend on the idea of chaotic inflation due to Linde In these models the initial value of the inflaton field is set chaotically when the universe exits from Planck era. The above problems namely Flatness problem and Horizon problem are problems of Standard Big Bang theory are solved by assuming an accelerated expansion in early universe for a very short duration. In some models a kind of approximation is used to solve the difficult equations This approximation is known as slow roll approximation which assumes that the field rolls very slowly. All the above models explain the mechanism of inflation and solve Horizon and Flatness problems. Ai and a f are values of scale factor when inflation starts and ends respectively These above models fail to explain cosmological constant problem [13] and dark matter problem. It is shown that this idea fitted in an exact mathematical framework essentially solves all problems of standard cosmology
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