1,396 research outputs found
Finite-time Singularities in Swampland-related Dark Energy Models
In this work we shall investigate the singularity structure of the phase
space corresponding to an exponential quintessence dark energy model recently
related to swampland models. The dynamical system corresponding to the
cosmological system is an autonomous polynomial dynamical system, and by using
a mathematical theorem we shall investigate whether finite-time singularities
can occur in the dynamical system variables. As we demonstrate, the solutions
of the dynamical system are non-singular for all cosmic times and this result
is general, meaning that the initial conditions corresponding to the regular
solutions, belong to a general set of initial conditions and not to a limited
set of initial conditions. As we explain, a dynamical system singularity is not
directly related to a physical finite-time singularity. Then, by assuming that
the Hubble rate with functional form , is a
solution of the dynamical system, we investigate the implications of the
absence of finite-time singularities in the dynamical system variables. As we
demonstrate, Big Rip and a Type IV singularities can always occur if
respectively. However, Type II and Type III
singularities cannot occur in the cosmological system, if the Hubble rate we
quoted is considered a solution of the cosmological system.Comment: EPL Accepte
Effects of Spatial Curvature on the Gravity Phase Space: no Inflationary Attractor?
In this paper we study the effects of spatial curvature of the metric on the
phase space of vacuum gravity. Particularly, we appropriately choose the
variables of the dynamical system, in order for this to be autonomous, and we
study the phase space of the resulting theory, focusing on de Sitter, matter
and radiation domination fixed points. Our analysis indicates that the effect
of spatial curvature on the phase space is radical, since it destabilizes all
the stable de Sitter vacua of the flat spacetime vacuum gravity phase
space, making the phase space having non-trivial unstable submanifolds. This
instability occurs regardless if the spacetime has elliptic or hyperbolic
spatial sections, and it is also robust towards the choice of initial
conditions. We investigate the source of the instability in the system, and
also we discuss the stability of the matter and radiation domination vacua,
which, as we demonstrate, are also highly unstable. Our results for de Sitter
attractors indicate that the stable de Sitter attractors of the vacuum
gravity theory for a flat Universe, are destabilized by the presence of
curvature, and this shows that inflation for vacuum gravity in non-flat
spacetime is problematic, at least at the phase space level. This result holds
true for both elliptic and hyperbolic spacetimes.Comment: CQG Accepte
Dynamical Systems Perspective of Cosmological Finite-time Singularities in Gravity and Interacting Multifluid Cosmology
In this work we shall investigate the occurrence of future cosmological
finite-time singularities in the dynamical system corresponding to two
cosmological theories, namely that of vacuum gravity and that of three
fluids. The vacuum gravity is an example for which the variables we will
choose to quantify the phase space dynamics, do not necessarily blow-up near a
cosmological singularity. After appropriately choosing the variables, we shall
investigate the behavior of the corresponding dynamical system near some types
of cosmological finite-time singularities, for some limiting cases in which we
can produce analytic solutions for the dynamical variables. The most
interesting case from both a mathematical and physical point of view, is the
Big Rip case, and particularly in the limiting case of a very strong
singularity. The physically appealing outcome is that the resulting
non-autonomous dynamical system is attracted asymptotically to an accelerating
attractor solution, with equation of state parameter . Our analytic
results, show that an extremely strong Big Rip singularity in vacuum
gravity theories is always related to an accelerating solution, or tends to
acceleration. The converse statement though may not be true. The second
cosmology we shall study is a multifluid cosmology, consisting of three fluids,
the interacting dark matter and dark energy fluids, and the baryonic fluid. By
appropriately choosing the variables, we will show that the dynamical system
can become an autonomous polynomial dynamical system, in which case, by using a
dominant balance analysis, we shall investigate the occurrence of finite-time
singularities in this system.Comment: PRD Accepte
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