tholan

I guess I have a lot to learn about it. Thanks.

This is known as Scharnhorst effect. Roughly, the propagation of a photon at the distance scale of quantum electrodynamics in vacuum can be shown to be a series of transformations involving virtual particles (e.g. the photon may be transformed into a virtual electron-positron pair). If one changes the conditions of the vacuum (generating a Casimir vacuum), the propagation of photons is affected.

RyanJ, the text from wikipedia you are quoting refers to dark matter but not to dark energy. In cosmology the content of the universe is modelled as a perfect fluid with an equation of state p = w d relating pressure p and density d. Dark energy is supposed to be something that permeates space homogeneously and exerts a negative pressure acting against gravitation of matter (or energy densities). This means that w < 0. One can see that this may lead to an accelerated expansion of space when inserted in the corresponding Friedmann equation. The WMAP first year data suggest that -1.3 < w < -0.7. If w < -1 then the dark energy is called phantom energy and it violates some energy conditions. If w = -1 and constant in time it is usually refered to it as the cosmological constant.

How is it made sure that the minisuperspace models that result from constraining the degrees of freedom of the geometry can lead to a sensible quantum cosmology if the quantized general relativity is basically a timeless theory?

In a static, spatially infinite and eternal universe with an homogeneous distribution of eternal stars (or a constant homogeneous stellar population) the sum of the flux (the amount of energy that reaches a surface) of all stars at each point of the universe would be infinite. This is known as Olbers’ paradox. Note that stars (or the stellar population) are not eternal since the universe was not eternal in past. This fact suffices to solve Olbers’ paradox. There is, however, another way to solve this paradox without the need of a temporally finite universe (or a finite lifetime of the homogeneous stellar population). If one considers a spatially infinite and eternal universe in which space expands (a de-Sitter model, with constant Hubble parameter leading to a strongly accelerated expansion), Olbers’ paradox is also solved. Any kind of radiation background due to the electromagnetic emission of stars (or whatever; CMB, etc.) would loss enough energy due to the strong redshift. In such a model the integral (sum of the flux due to all stars) would be finite, although there would be an contribution from an infinite number of stars! In other expanding models this is not true. First, they are not eternal (the de-Sitter model is the only one without initial singularity). But, besides of this, one could consider a situation in a very far future in which a (non de-Sitter) universe is very old and the flux of lots of stars is reaching each point (assuming again a constant stellar population). In such a case, expansion is actually reshifting the radiation background, but this is not enough to “dilute” the total flux of energy, which would be increasing with time. This is because the Hubble parameter decreases with time in every model which is not de-Sitter.

Yes, every spacetime is locally flat but you cannot always find a unique set of positive frequency modes that allow you to unequivocally define a representation of the commutation relations. Worst, these representations may not be equivalent. Particles in one reference frame may not be in the other, but, nevertheless, interactions should be invariantly identified by both observers as being caused by the field(s). On the other hand things get also weird in dynamic spacetimes, for example in QFT on a de-Sitter background, in which superhorizon fluctuations take place. How to explain superhorizon fluctuations in terms of particles?

Cosmological redshift would be inexistent, as it is a consequence of the expansion of space. It still would exist redshifts due to Doppler effect (relative peculiar motions) and gravitation (fotons climbing out gravitational wells).

Particles are excitations of quantum fields on flat spacetime, or on some other simple spacetimes. But the point is that excitations are not always particles. This is valid for curved spacetimes in general. It makes no sense to speak about gravitational interaction via gravitons in such cases in which the notion of particle is not well defined.

The notion of particles is given on flat spacetime as well as on other simple geometries. As soon as one wants to set up a theory of matter on a complex or arbitrary geometry, this notion becomes meaningless and is replaced just by the one of excitations of a quantum field. From this point of view I think that the idea of the graviton as the carrier of the gravitational field must be fundamentally wrong. The graviton might be, however, a “low energy” phenomenon of gravitation.

The only way to analyze whether energy is conserved or not is to take a look to what happens within a comoving volume with a definite boundary. We want to know what happens to every of the components of this volume as the volume expands with time. First take a look to matter and radiation. Assume that no matter nor radiation cross the boundaries of our volume. The energy content of matter will remain unchanged (we assume that there are basically no interactions with other components within the volume). The energy content of radiation will decrease, as photons will increase their wavelength. As this increase of wavelength is due to expansion of space we might consider that the energy of the photons goes into gravitational energy of spacetime (the energy of the gravitational field or gravitational potential in Newtonian terms). This is a similar situation as for a photon gravitationally redshifted by a mass. It does also loose electromagnetic energy increasing its potential energy (increasing its distance to the mass). However, the exact notion of energy of the gravitational field is not a well-defined concept in general relativity and this explanation must be taken with care. On the other hand we have also dark energy which we will assume to be a cosmological constant. Since the cosmological constant is a scalar field, its energy density is constant in space and time and, therefore, if the volume increases, the total energy of the dark energy contained within it will increase. Where does this energy come from? Honestly I don’t know. You may solace yourself with the fact that energy conservation in general relativity is not always a well-defined concept.