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Register a new userDynamics in Varying vacuum Finsler-Randers Cosmology
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Added by
Giannis Papagiannopoulos
Publication date
2020
fields
Physics
and research's language is
English
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In the context of Finsler-Randers theory we consider, for a first time, the cosmological scenario of the varying vacuum. In particular, we assume the existence of a cosmological fluid source described by an ideal fluid and the varying vacuum terms. We determine the cosmological history of this model by performing a detailed study on the dynamics of the field equations. We determine the limit of General Relativity, while we find new eras in the cosmological history provided by the geometrodynamical terms provided by the Finsler-Randers theory.
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We study for the first time the dynamical properties and the growth index of linear matter perturbations of the Finsler-Randers (FR) cosmological model, for which we consider that the cosmic fluid contains matter, radiation and a scalar field. Initially, for various FR scenarios we implement a critical point analysis and we find solutions which provide cosmic acceleration and under certain circumstances we can have de-Sitter points as stable late-time attractors. Then we derive the growth index of matter fluctuations in various Finsler-Randers cosmologies. Considering cold dark matter and neglecting the scalar field component from the perturbation analysis we find that the asymptotic value of the growth index is $gamma_{infty}^{(FR)}approxfrac {9}{16}$, which is close to that of the concordance $Lambda$ cosmology, $gamma^{(Lambda)} approxfrac{6}{11}$. In this context, we show that the current FR model provides the same Hubble expansion with that of Dvali, Gabadadze and Porrati (DGP) gravity model. However, the two models can be distinguished at the perturbation level since the growth index of FR model is $sim18.2%$ lower than that of the DPG gravity $gamma^{(DGP)} approx frac{11}{16}$. If we allow pressure in the matter fluid then we obtain $gamma_{infty}^{(FR)}approxfrac{9(1+w_{m})(1+2w_{m})}{2[8+3w_{m}% (5+3w_{m})]}$, where $w_{m}$ is the matter equation of state parameter. Finally, we extend the growth index analysis by using the scalar field and we find that the evolution of the growth index in FR cosmologies is affected by the presence of scalar field.
We study the dynamical properties of a large body of varying vacuum cosmologies for which dark matter interacts with vacuum. In particular, performing the critical point analysis we investigate the existence and the stability of cosmological solutions which describe de-Sitter, radiation and matter dominated eras. We find several cases of varying vacuum models that admit stable critical points, hence they can be used in describing the cosmic history.
In this paper we return to the subject of Jacobi metrics for timelike and null geodsics in stationary spactimes, correcting some previous misconceptions. We show that not only null geodesics, but also timelike geodesics are governed by a Jacobi-Maupertuis type variational principle and a Randers-Finsler metric for which we give explicit formulae. The cases of the Taub-NUT and Kerr spacetimes are discussed in detail. Finally we show how our Jacobi-Maupertuis Randers-Finsler metric may be expressed in terms of the effective medium describing the behaviour of Maxwells equations in the curved spacetime. In particular, we see in very concrete terms how the magnetolectric susceptibility enters the Jacobi-Maupertuis-Randers-Finsler function.
In this work the exact Friedmann-Robertson-Walker equations for an Elko spinor field coupled to gravity in an Einstein-Cartan framework are presented. The torsion functions coupling the Elko field spin-connection to gravity can be exactly solved and the FRW equations for the system assume a relatively simple form. In the limit of a slowly varying Elko spinor field there is a relevant contribution to the field equations acting exactly as a time varying cosmological model $Lambda(t)=Lambda_*+3beta H^2$, where $Lambda_*$ and $beta$ are constants. Observational data using distance luminosity from magnitudes of supernovae constraint the parameters $Omega_m$ and $beta$, which leads to a lower limit to the Elko mass. Such model mimics, then, the effects of a dark energy fluid, here sourced by the Elko spinor field. The density perturbations in the linear regime were also studied in the pseudo-Newtonian formalism.
Properties of unstable false vacuum states are analyzed from the point of view of the quantum theory of unstable states. Some of false vacuum states survive up to times when their survival probability has a non-exponential form. At times much latter than the transition time, when contributions to the survival probability of its exponential and non-exponential parts are comparable, the survival probability as a function of time t has an inverse power-like form. We show that at this time region the instantaneous energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t to infty$.
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