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Register a new userDynamical system perspective of cosmological models minimally coupled with scalar field
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Added by
Sanasam Surendra Singh
Publication date
2019
fields
Physics
and research's language is
English
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The stability criteria for spatially flat homogeneous and isotropic cosmological dynamical system is investigated with the interaction of a scalar field endowed with a perfect fluid.In this paper, we depict the dynamical system perspective to study, qualitatively, the scalar field cosmology under two special cases, with and without potential. For analysis with potential we use simple exponential potential form, $V_{o}e^{-lambda phi}$. We generate, by introducing new dimensionless variables, an autonomous system of ordinary differential equations $(ASODE)$ for each case and obtain respective fixed points. We also analyse the type of fixed points, nature and stability of the fixed points and how their nature and behavior reflect towards the cosmic scenarios. Throughout the whole work, the investigation of this model has shown us the deep connection between these theories and cosmic acceleration phenomena. The phase plots of the system at different conditions and different values of $gamma$ have been analyzed in detail and their interpretations have been worked out.The perturbation plots of the dynamical system have also been studied and analyzed which emphasize our analytical findings.
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We show that the combined minimal and non minimal interaction with the gravitational field may produce the generation of a cosmological constant without self-interaction of the scalar field. In the same vein we analyze the existence of states of a scalar field that by a combined interaction of minimal and non minimal coupling with the gravitational field can exhibit an unexpected property, to wit, they are acted on by the gravitational field but do not generate gravitational field. In other words, states that seems to violate the action-reaction principle. We present explicit examples of this situation in the framework of a spatially isotropic and homogeneous universe.
We investigate the dynamical behavior of a scalar field non-minimally coupled to Einsteins tensor and Ricci scalar in geometries of asymptotically de Sitter spacetimes. We show that the quasinormal modes remain unaffected if the scalar field is massless and the black hole is electrically chargeless. In the massive case, the coupling of both parameters produces a region of instability in the spacetime determined by the geometry and field parameters. In the Schwarzschild case, every solution for the equations of motion with $ell>0$ has a range of values of the coupling constant that produces unstable modes. The case $ell=0$ is the most unstable one, with a threshold value for stability in the coupling. For the charged black hole, the existence of a range of instability in $eta$ is strongly related to geometry parameters presenting a region of stability independent of the chosen parameter.
We study dynamics of non-minimally coupled scalar field cosmological models with Higgs-like potentials and a negative cosmological constant. In these models the inflationary stage of the Universe evolution changes into a quasi-cyclic stage of the Universe evolution with oscillation behaviour of the Hubble parameter from positive to negative values. Depending on the initial conditions the Hubble parameter can perform either one or several cycles before to become negative forever.
In this paper we discuss local averages of the energy density for the non-minimally coupled scalar quantum field, extending a previous investigation of the classical field. By an explicit example, we show that such averages are unbounded from below on the class of Hadamard states. This contrasts with the minimally coupled field, which obeys a state-independent lower bound known as a Quantum Energy Inequality (QEI). Nonetheless, we derive a generalised QEI for the non-minimally coupled scalar field, in which the lower bound is permitted to be state-dependent. This result applies to general globally hyperbolic curved spacetimes for coupling constants in the range $0<xileq 1/4$. We analyse the state-dependence of our QEI in four-dimensional Minkowski space and show that it is a nontrivial restriction on the averaged energy density in the sense that the lower bound is of lower order, in energetic terms, than the averaged energy density itself.
Solution generating techniques for general relativity with a conformally (and minimally) coupled scalar field are pushed forward to build a wide class of asymptotically flat, axisymmetric and stationary spacetimes continuously connected to Kerr. This family contains, amongst other things, rotating extensions of the Bekenstein black hole and also its angular and mass multipolar generalisations. Further addition of NUT charge is also discussed.
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