Implications of the branch-cut gravitation
Fecha
2023-12-01Primeiro coorientador
Vasconcellos, César Augusto Zen
Primeiro membro da banca
Radinschi, Irina
Segundo membro da banca
Hess, Peter Otto
Terceiro membro da banca
Mercado, José Alejandro Ayala
Quarto membro da banca
Stefanello, Michel Baptistella
Metadatos
Mostrar el registro completo del ítemResumen
In standard cosmology based on the Friedmann-Lemaître-Robertson-Walker (FLRW) metric the infinitesimal squared pathlength element is given by a time dependent cosmic scale
factor a(t), the coordinates of the proper time dt, the radial dr and the angles dθ, dΦ, and the
curvature parameter k = −1, 0, 1 for negatively, flat or positively curved spacial hypersurfaces, respectively. The interpretation of the metric components as complex differentiable
or holomorphic functions of the spacetime coordinates which are analytically continued to
the complex plane, give a description of a complex metric with the now complex variables
r and t, and a scale factor which is a function of a complex time t. From Einstein’s Field
equations the analytical continued complex Friedmann’s type equations are derived, which
can be combined to one equation, with a complex cosmic scale factor a(t). Applying a shift
function as a variable to the complex cosmic scale factor and integrating with this shift function as bounds over the combined Friedmann equations, a new cosmological scale factor
ln−1
[β(t)] can be identified with a complex time to describe the dynamic of the universe.
The periodicity of the complex logarithm function in the complex plane leads to the interpretation of the concept of multiverses living in different Riemann sheets with the analytical
continuation over the branch cuts as the transition regions. The inverse of the new complex scale factor, i.e. ln[β(t)], represents a linear scaling factor in time, bringing to time a
complex nature, with an imaginary component. In the early universe, at small distances
General Relativity enters the regime of quantum gravity. The branch-cut quantum gravitation describes the transition phase in this early universe by an analytically to the complex
plane continued Wheeler-DeWitt equation which is based on the Horava-Lifshitz gravity theory. The introduction of an energy-dependent effective potential, describing the spacetime
curvature associated with the embedding geometry and its coupling with the cosmological
constant and the matter fields, solutions of the Wheeler-DeWitt equation for the wave function of the Universe are obtained.
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