Scalar field cosmology in Lyra's geometry

Abstract

<p>The new classes of homogeneous cosmological models for the scalar fields are build in the context of Lyra’s geometry. The different types of exact solution for the model are obtained by applying two procedures, viz the generating function method and the first order formalism.</p>

Exact Cosmological Models with Yang–Mills Fields on Lyra Manifold

“…which follows from the conservation equation, T k i;k = 0, and (7). Taking into account equations (20) and (27), the continuity equation (26) becomeṡ Λ + 2ββ + 6Hβ 2 = 0.…”

“…where β = β(t) is a function of time only, and the factor 2/ √ 3 is used in order to simplify the writing of all the following equations. Given the line element (2) and taking the total EMT as a sum of ( 7) and (20), one can reduce the main equations of the model (1) to the following set of equations:…”

Geometric standing wave braneworld and field localization in Lyra manifold

“…( 15) were derived in [26] for the case N = 4. Several solutions in four dimensional space-time were obtained where different possible interpretations for the Lyra displacement vector were given [28][29][30][31][32][33]. Solutions in higer dimensional theory were considered in recent years in different contexts [34,35].…”

Vacuum expansion in arbitrary–gauge Lyra geometry

“…On the other hand, combination of (19) and (20) together with (26) allows one to obtain ä a ϭ qe Ϫ2⌽ (29) which clearly shows an accelerating universe for positive timedependent cosmological term (i.e., for q > 0). The Hubble parameter can be determined by solving (29), this gives…”

“…And a time-dependent vector field can be thought of as a variable cosmological-type term [17]. However, as it was pointed out, the vector field alone cannot be considered as a cosmological term (with cc = -1), but rather a stiff matter, because having a constant equation of state, = +1 [29]. But, the vector field can be identified with the cosmological term if it is considered as a component of the total conservative energy of the universe [30].…”