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Register a new userBehavior of Friedmann-Lemaitre-Robertson-Walker Singularities
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Added by
Leonardo Fernandez-Jambrina
Publication date
2016
fields
Physics
and research's language is
English
Authors
L. Fernandez-Jambrina
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A regularization procedure has been recently suggested for regularizing Big Bang singularities in Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes. We argue that this procedure is only appliable to one case of Big Bang singularities and does not affect other types of singularities.
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We completely classify Friedmann-Lema^{i}tre-Robertson-Walker solutions with spatial curvature $K=0,pm 1$ and equation of state $p=wrho$, according to their conformal structure, singularities and trapping horizons. We do not assume any energy conditions and allow $rho < 0$, thereby going beyond the usual well-known solutions. For each spatial curvature, there is an initial spacelike big-bang singularity for $w>-1/3$ and $rho>0$, while no big-bang singularity for $w<-1$ and $rho>0$. For $K=0$ or $-1$, $-1<w<-1/3$ and $rho>0$, there is an initial null big-bang singularity. For each spatial curvature, there is a final spacelike future big-rip singularity for $w<-1$ and $rho>0$, with null geodesics being future complete for $-5/3le w<-1$ but incomplete for $w<-5/3$. For $w=-1/3$, the expansion speed is constant. For $-1<w<-1/3$ and $K=1$, the universe contracts from infinity, then bounces and expands back to infinity. For $K=0$, the past boundary consists of timelike infinity and a regular null hypersurface for $-5/3<w<-1$, while it consists of past timelike and past null infinities for $wle -5/3$. For $w<-1$ and $K=1$, the spacetime contracts from an initial spacelike past big-rip singularity, then bounces and blows up at a final spacelike future big-rip singularity. For $w<-1$ and $K=-1$, the past boundary consists of a regular null hypersurface. The trapping horizons are timelike, null and spacelike for $win (-1,1/3)$, $win {1/3, -1}$ and $win (-infty,-1)cup (1/3,infty)$, respectively. A negative energy density ($rho <0$) is possible only for $K=-1$. In this case, for $w>-1/3$, the universe contracts from infinity, then bounces and expands to infinity; for $-1<w<-1/3$, it starts from a big-bang singularity and contracts to a big-crunch singularity; for $w<-1$, it expands from a regular null hypersurface and contracts to another regular null hypersurface.
In a recent paper [arXiv:1206.4916] by T. Padmanabhan, it was argued that our universe provides an ideal setup to stress the issue that cosmic space is emergent as cosmic time progresses and that the expansion of the universe is due to the difference between the number of degrees of freedom on a holographic surface and the one in the emerged bulk. In this note following this proposal we obtain the Friedmann equation of a higher dimensional Friedmann-Robertson-Walker universe. By properly modifying the volume increase and the number of degrees of freedom on the holographic surface from the entropy formulas of black hole in the Gauss-Bonnet gravity and more general Lovelock gravity, we also get corresponding dynamical equations of the universe in those gravity theories.
Scalar field cosmologies with a generalized harmonic potential and matter with energy density $rho_m$, pressure $p_m$, and barotropic equation of state (EoS) $p_m=(gamma-1)rho_m, ; gammain[0,2]$ in Kantowski-Sachs (KS) and closed Friedmann--Lema^itre--Robertson--Walker (FLRW) metrics are investigated. We use methods from non--linear dynamical systems theory and averaging theory considering a time--dependent perturbation function $D$. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late--time attractors of full and time--averaged systems are two anisotropic contracting solutions, which are non--flat locally rotationally symmetric (LRS) Kasner and Taub (flat LRS Kasner) for $0leq gamma leq 2$, and flat FLRW matter--dominated universe if $0leq gamma leq frac{2}{3}$. For closed FLRW metric late--time attractors of full and averaged systems are a flat matter--dominated FLRW universe for $0leq gamma leq frac{2}{3}$ as in KS and Einstein-de Sitter solution for $0leqgamma<1$. Therefore, time--averaged system determines future asymptotics of full system. Also, oscillations entering the system through Klein-Gordon (KG) equation can be controlled and smoothed out when $D$ goes monotonically to zero, and incidentally for the whole $D$-range for KS and for closed FLRW (if $0leq gamma< 1$) too. However, for $gammageq 1$ closed FLRW solutions of the full system depart from the solutions of the averaged system as $D$ is large. Our results are supported by numerical simulations.
It is shown that only the maximally-symmetric spacetimes can be expressed in both the Robertson-Walker form and in static form - there are no other static forms of the Robertson-Walker spacetimes. All possible static forms of the metric of the maximally-symmetric spacetimes are presented as a table. The findings are generalized to apply to functionally more general spacetimes: it is shown that the maximally symmetric spacetimes are also the only spacetimes that can be written in both orthogonal-time isotropic form and in static form.
This paper presents a compelling argument for the physical light speed in the homogeneous and isotropic Friedman-Lemaitre-Robertson-Walker (FLRW) universe to vary with the cosmic time coordinate t of FLRW. It will be variable when the radial co-moving differential coordinate of FLRW is interpreted as physical and therefor transformable by a Lorentz transform locally to differentials of stationary physical coordinates. Because the FLRW differential radial distance has a time varying coefficient a(t), in the limit of a zero radial distance the light speed c(t) becomes time varying, proportional to the square root of the derivative of a(t) Since we assume homogeneity of space, this derived c(t) is the physical light speed for all events in the FLRW universe. This impacts the interpretation of astronomical observations of distant phenomena that are sensitive to light speed. A transform from FLRW is shown to have a physical radius out to all radial events in the visible universe. This shows a finite horizon beyond which there are no galaxies and no space. The general relativity (GR) field equation to determine a(t) and c(t) is maintained by using a variable gravitational constant and rest mass that keeps constant the gravitational and particle rest energies. This keeps constant the proportionality constant between the GR tensors of the field equation and conserves the stress-energy tensor of the ideal fluid used in the FLRW GR field equation. In the same way all of special and general relativity can be extended to include a variable light speed.
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