1,721,026 research outputs found
Mapping solutions in nonmetricity gravity: Investigating cosmological dynamics in conformal equivalent theories
No full textWe investigate the impact of conformal transformations on the physical properties of solution trajectories in nonmetricity gravity. Specifically, we explore the phase space and reconstruct the cosmological history of a spatially flat Friedmann–Lemaître–Robertson–Walker universe within scalar-nonmetricity theory in both the Jordan and Einstein frames. A detailed analysis is conducted for three connections defined in the coincident and non-coincident gauges. Our findings reveal the existence of a unique one-to-one correspondence for equilibrium points in the two frames. Furthermore, we demonstrate that solutions describing accelerated universes remain invariant under the transformation that relates these conformally equivalent theories
Nonzero Spatial Curvature in Symmetric Teleparallel Cosmology
Full text linkWe consider the symmetric teleparallel -gravity in
Friedmann--Lema\^{\i}tre--Robertson--Walker cosmology with nonzero spatial
curvature. For a nonlinear model there exist always the
limit of General\ Relativity with or without the cosmological constant term.
The de Sitter solution is always provided by the theory and for the specific
models f_{A}\left( Q\right) \simeq Q^{\frac{\alpha}{\alpha-1}}% ~,~f_{B}\left(
Q\right) \simeq Q+f_{1}Q^{\frac{\alpha}{\alpha-1}} and it was found to be the unique attractor. Consequently
small deviations from STGR can solve the flatness problem and lead to a de
Sitter expansion without introduce a cosmological constant term. This result is
different from that given by the power-law theories for the other two scalar of
the trinity of General Relativity. What makes the nonlinear symmetric
teleparallel theory to stand out are the new degree of freedom provided by the
connection defined in the non-coincidence frame which describes the nonzero
spatial curvature.Comment: 23 pages, 3 figures, to appear in Physics of the Dark Univers
Semi-Classical limit and quantum corrections in noncoincidence power-law -Cosmology
Full text linkWithin the framework of symmetric teleparallel -gravity for a connection defined in the non-coincidence gauge we derive the Wheeler-DeWitt equation of quantum cosmology. Because the gravitational field equation in -gravity admits a minisuperspace description the Wheeler-DeWitt equation is a single inhomogeneous partial differential equations. We assume the power-law model and with the application of linear quantum observables we calculate the wavefunction of the universe. Finally, we investigate the effects of the quantum correction terms in the semi-classical limit.31 pages, no figure
Dynamical analysis of -cosmology
Full text linkWe study the evolution of the physical variables in -gravity for two families of symmetric and flat connections in a spatially
flat Friedmann--Lema\^{\i}tre--Robertson--Walker geometry where the equation of
motion for the nonmetricity scalar is not trivially identity. From the analysis
of dynamics we found that the de Sitter universe is always an attractor while
the cosmological models admit scaling solutions which can describe the early
acceleration phase of our universe or the matter and the radiation epochs.Comment: 21 pages; 7 figures, 1 table, to appear in Physics of the Dark
Univers
Linearization of newton’s second law
No full textThe geometric linearization of nonlinear differential equation is a robust method for the
construction of analytic solutions. The method is related to the existence of Lie symmetries
which can be used to determine point transformations such that to write the given differential
equation in a linear form. In this study we employ another geometric approach and we utilize
the Eisenhart lift to geometric linearize the Newtonian system describing the motion of a
particle in a line under the application of an autonomous force. Our findings reveal that
for the oscillator, the Ermakov potential with or without the oscillator term, and the Morse
potential, Newton’s second law can be globally expressed in the form of that of a free particle.
This study open new directions for the geometric linearization of differential equations via
equivalent dynamical system
Cosmological Constant from Equivalent Transformation in Quantum Cosmology
Full text linkWe explore the introduction of the cosmological constant via equivalent
transformations in cosmology. We consider the Wheeler-DeWitt equation for the
CDM universe and we construct the Hamilton-Jacobi action for the CDM
model. We discuss how this approach allows us to relate different physical
systems, providing insights into the role of the cosmological constant in
cosmology.Comment: 10 pages, no figure
Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations
No full textWe apply the theory of innitesimal transformations for the study of a family of 1+1 fth-order partial dierential equations which have been proposed before for the description of multiple kink solutions. In this analysis we perform a complete classication of the Lie symmetries and of the one-dimensional optimal system. The results are applied for the derivation of similarity solutions and in particular we nd travel-wave and scaling solutions. We show that the kink-solution of these equations can be recovered by the use of the Lie symmetries, while new solutions are also derived
Dynamical analysis in Chameleon dark energy
Full text linkWe present a detailed analysis of the phase-space for the field equations in
scalar field cosmology with a chameleon cosmology in a spatially flat
Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. For the matter source we
assume that it is an ideal gas with a constant equation of state parameter,
while for the scalar field potential and the coupling function of the chameleon
mechanism we consider four different sets which provide four different models.
We consider the -normalization approach and we write the field equations
with the help of dimensionless variables. The asymptotic solutions are
determined from where we find that the theory can describe the main eras of
cosmological history and evolution. Future attractors which describe
acceleration exist, however we found past acceleration solutions related to the
inflationary era, as also the radiation epoch and the matter dominated eras are
provided by the dynamics. We conclude that the Chameleon dark energy model can
be used as a unified model for the elements which contribute to the dark sector
of the universe.Comment: 34 pages, 13 figures, to appear in Fortschritte der Physik (Progress
of Physics
Classical and Quantum solutions in Scalar field cosmology via the Eisenhart lift and linearization
Full text linkThis study introduces a novel approach for solving the cosmological field
equations within scalar field theory by employing the Eisenhart lift. The field
equations are reformulated as a system of geodesic equations for the Eisenhart
metric. In the case of an exponential potential, the Eisenhart metric is shown
to be conformally flat. By applying basic geometric principles, a new set of
dynamical variables is identified, allowing for the linearization of the field
equations and the derivation of classical cosmological solutions. However, the
quantization of the Eisenhart system reveals a distinct set of solutions for
the wavefunction, particularly in the presence of symmetry breaking at the
quantum level.Comment: 18 pages, no figure
Symmetric teleparallel cosmology with boundary corrections
Full text linkWe investigate the geometrodynamical effects of introducing the boundary term
in symmetric teleparallel gravity. Specifically, we consider a homogeneous and
isotropic universe in , where is the non-metricity
scalar, and is the boundary term that relates the non-metricity and Ricci
scalars. For the connection in the coincidence gauge, we find that the field
equations are of fourth-order, and the fluid components introduced by the
boundary are attributed to a scalar field. In the coincidence gauge, the
cosmological field equations are equivalent to those of teleparallelism with a
boundary term. Nevertheless, for the connection defined in the non-coincidence
gauge, the geometrodynamical fluid consists of three scalar fields. We focus on
the special case of theory, and
we determine a new analytic cosmological solution that can explain the
late-time acceleration of the universe and provide a geometric mechanism for
the unification of dark energy with dark matter.Comment: 24 pages, 2 figure
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