Modelos cosmológicos aplicados à teoria de Bergmann–Wagoner com condições iniciais naturais

Abstract

Some scalar-tensor theories contain in their action a cosmological term represented by a function λ (ф), that generalizes a cosmological constant. The variation of this function can be used to explain the cosmic inflation during the Primordial Universe and, at the same time, the accelerated expansion observed today. Bergmann-Wagoner’s theory adds to General Relativity a scalar field that can be interpreted, in the frame of Jordan, such as ф (t) = G¯¹, transforming the gravitational “constant"G into a variable. Observations indicate that the state equation for dark energy is w ≈ −1, however, these studies do not rule out the possibility of w ≠ −1, being compatible with the cosmological function in place of the constant. On the other hand, observations indicate that any current variation of the gravitational constant is bounded by the inequality |G˙/G| < 10¯¹³yr¯¹. In the first part of this thesis, a field ф (t) which respects the variation of G observed is generated and generates a cosmological function λ(ф) which has a value “big” next to Big Bang and then decays. This behavior would generate inflation during the Primordial Universe and would also be compatible with the current observations indicate Λ ≈ 10¹²² tp¯² . In the second part, the cosmological function and the Hubble parameter were modeled so that λ(t) α t¯² e H(t) α t¯¹, and the behavior of the cosmological parameters and the possible consequences for the evolution of the Universe were studied in these models. We found the general solutions for the cases with no matter and spatially flat, and implemented integrators to solve the equations differences in presence of matter and curvature. The initial conditions used were defined so that the cosmological parameters have “natural” close to Big Bang.