Cosmological term

This procedure leads to the Einstein gravitational field equations, one form of which, without cosmological term, is... 

Introduction of the cosmological term therefore results in an empty universe with a time-dependent metric exactly the opposite of Einstein s intention to produce a matter dominated static universe. 

A planet in orbit therefore looses energy, and like a classical orbiting electron (section 3.4.2), spirals in towards the nucleus of the system. In the case of an atom this is prevented by the quantum potential and there is no reason why a cosmological quantum effect could not be responsible for the stabilization of satellite orbits. In fact, there is the evidence of planets and moons in the solar system on orbits characterized by integers, as discussed in section 5.3.1. The cosmological term. A, which Einstein included in the gravitational field equations (6.4) describes exactly such an effect. 

In the conventional view, (1) is logically prior to (2) however, it is perfectly possible to reverse the logical priority of (1) and (2) so that, in effect, we can choose to define the radial measure in terms of (2) rather than assume that it is known by some independent means. If this is done, then, we have immediately, made it impossible to conceive of radial measure in the absence of material. With this as a starting point, we are able to construct a completely Machian cosmology in a way outlined in the following sections. 

The term k in this metric is a constant that determines the spacial curvature of the cosmology. For k = 1 the cosmology is a closed spherical universe, for k = 0 the cosmology is flat, and for k - — 1 the cosmology is open. The Einstein field equations give a constraint equation and a dynamical equation for the rate the radius changes with time. If we define a velocity as v = (R/R)H(t)r, where H (t) is the Hubble parameter, a constant locally, the constraint equations is... 

Here, we shall discuss the implications of cosmological expansion for the searches of a quantum-gravity-induced refractive index and a stochastic effect. We will consider Friedman-Robertson-Walker (FRW) metrics as an appropriate candidate for standard homogeneous and isotropic cosmology. Let R be the FRW scale factor, and a subscript 0 will denote the value at the present era. Ho is the present Hubble expansion parameter, and the deceleration parameter qo is defined in terms of the curvature k of the FRW metric by k ( 2[Pg.588]

Such a term is called the cosmological constant, and has been historically introduced by Einstein, as a modification of his original theory. We have then... 

As we have seen during the course on inflation, a scalar field can behave as a cosmological constant when its kinetic term becomes negligible in front of its potential term. However, the features of the scalar field we are interested in differ significantly from an inflationary scalar field in the former case, we want a field that is negligible at early times and which dominates afterwards, whereas in the latter case, it is the contrary. Historically, the first scalar field dark energy model was aimed to address the possibility to have some components with a constant equation of state parameter w other than 0 (matter), 1/3 (radiation), —1/3 (curvature) and —1 (cosmological constant) (Ratra Peebles 1988). 

And the source term of the deflexion is the gravitational potential, , which in a cosmological context is given by a slightly modified Poisson equation,... 

In the following years main attention was devoted to detailed elaboration of the concept of the cold dark matter dominated Universe. Here a central issue was the amount of dark matter. Initially opinions varied from a moderate density of the order of 0.2 critical density up to the critical density. Only a few years ago it was clarified that dark matter constitutes only 0.25 of the critical density, and the rest is mostly dark energy, characterized by the cosmological constant or the U A-term. 

As we have seen a number of times already, in his articles on Steam and the Steam Engine in the 1797, third, edition of the Encyclopaedia Britannica, Watt s close friend John Robison wrote about steam in terms that were still significantly faithful to the original ideas with which Black and Watt had worked. Reading those articles is to see an earlier cosmology preserved as if in amber. Robison depicted steam as a compound of water with latent heat. Writing about a steam bubble formed in boiling water, he stated ... 

For matter (non-relativistic matter often called dust ), p p, so that p/po = (ao/a)3. In contrast, for radiation (relativistic particles) p = pi3, so that p/po = (ao/a)4. Another interesting case is that of the energy density and pressure associated with the vacuum (the quantum mechanical vacuum is not empty ). In this case p = —p, so that p = po- This provides a term in the Friedmann equation entirely equivalent to Einstein s cosmological constant A. More generally, for p = wp, p/po = (ao/a)3(1+w Allowing for these three contributions to the total energy density, eq. 2.9 may be rewritten in a convenient dimensionless form... 

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