in the Friedmann model, the pressure p is negative. But the dimensions of p are force/r^2 (1) where r^2 is a twodimensional surface. If our universe is threedimensional, the pressure would write force/r^3 (2) where r^3 is the hypersurface of our universe (which corresponds to the universe at time t). to obtain (1), one has to integrate (2) over r, which leads to a negative pressure...where is my mistake?
Nobody knows whether there is an error in my reasoning? If there is no error this would explain the paradox that the expansion of the universe accelerates with a negative pressure with is only an artifact...
The dimension of pressure are force/r^2 just because the correct definition of pressure involves the ratio between a force and a two-dimensional surface, in a three-dimensional space. The other definition you give (force/r^3) do not correspond to a pressure, but to something like a force density. But I'm not completely sure to understand your argument.
I understand that the definition of pressure is force/r^2. But, in order to inflate a threedimensional space you need what you call a force density (force/r^3).
with a pressure (f/r^2) yu can nly deform a twodimensional space (like a balloon) and to account for the inflation of the universe you have to use a force density (f/r^3).
The "pressure" in the Friedmann model---which also applies to the inflationary scenario---is anything but a pressure. It is well-known that negative pressures cause implosion---not explosion (cf Landau & Lifshitz, Statistical Physics). In the de Sitter model it is the cosmological constant that causes the universe to expand. To quote de Sitter "What makes the universe expand or swell up? That is done by Lambda. Another answer cannot be given." How can a pure constant make the universe expand? All this points to the incorrectness of the cosmological models based on Einstein's equations.
Bernard, I agree with your comment. But, dark energy is supposed to be the 'fluid' which has a negative 'pressure' and accelerates the expansion of the universe. My hypotesis is that there is no need of a dark energy to have a negative pressure, it is only a question of geometry (and dimensions).
Nathalie, there is growing contention [Arp and colleagues that most of the extragalactic redshifts are "intrinsic" and are not velocity dependent. I, personally, do not know what an intrinsic redshift is, as all frequency shifts that I know are due to velocity. In fact, I have used the longitudinal Doppler effect to define hyperbolic distance as its logarithm [A New Perspective on Relativity, World Scientific, 2011]. But, if true, it would eliminate the need of "dark matter". If large redshifts are not due to large recession velocities is the universe really expanding? Be that as it may, negative pressures cause implosion: Entropy increases with volume, or the pressure is positive. If pressure were negative, volume contraction would be necessary so that the entropy would increase. Never would expansion result from a negative pressure for that would cause entropy to spontaneously decrease.
I partly agree with you (except for the pressure, just a question of dimensions)...maybe our point of views converge (it would be too long to explain my theory: I take time as the logarithm of distances). If you want, you may, take a look at my articles (those dealing with cosmology): they are on RG with fulltexts.
I will not attempt to answer all of your questions, only the one about the relationship between force and pressure in a 3D space. In that space, a force is a vector (3 components) with a direction. Perpendicular to that direction, there is a plane that is a 2D entity and it is the surface on which acts the force. This is the surface that appears in the definition of the pressure. A pressure is measured on a surface and is due only to forces normal (perpendicular) to that surface. People, please do not bring Bernouilli's principle in this discussion, because it is a kinematic effect.
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