If you put a wall, the photons cannot cross it. The wall may not move, because the photons on both sides exert the same force on it. But that does not mean that there is no pressure. It just means that there is equilibrium between the pressures on both sides. To calculate whether there is pressure or not, you have to consider only whether there is a net force on a wall from one side.

Now as to your remark that the pressure counteracts universe expansion, that is not so clear. Superficially, it may look like that, because the pressure appears with negative sign in an equation sporting the second derivative of the expansion scalar on the other side of the equality. But if you actually solve the pair of Friedmann-Lemaître equations for a dust universe and for a radiation-dominated universe, the latter expands faster at the beginning (i.e. for small time t), the expansion goes as t2/3 in the dust case (zero pressure) and as t1/2 in the radiation case. Of course, at large times, this means that the radiation-dominated universe expands more slowly than the pressure-less one (at least, if the cosmological constant is zero).

If you put a wall, the photons cannot cross it. The wall may not move, because the photons on both sides exert the same force on it. But that does not mean that there is no pressure. It just means that there is equilibrium between the pressures on both sides. To calculate whether there is pressure or not, you have to consider only whether there is a net force on a wall from one side.

Now as to your remark that the pressure counteracts universe expansion, that is not so clear. Superficially, it may look like that, because the pressure appears with negative sign in an equation sporting the second derivative of the expansion scalar on the other side of the equality. But if you actually solve the pair of Friedmann-Lemaître equations for a dust universe and for a radiation-dominated universe, the latter expands faster at the beginning (i.e. for small time t), the expansion goes as t2/3 in the dust case (zero pressure) and as t1/2 in the radiation case. Of course, at large times, this means that the radiation-dominated universe expands more slowly than the pressure-less one (at least, if the cosmological constant is zero).

The pressure term in Friedman's equation comes from the energy-stress tensor, but depends on the equation of state for a photon gas. As i can show, this equation of state can be obtained by having photons confined to a box with perfectly reflecting walls (not going through the walls as i misspoke in my first entry).  The equation of state is then (1/3)c2(mass density of the photons). How the equation of state arises in the GR calculation, however, is to assume, in constructing the stress-energy tensor, that the time average of the square of the electric field is the same for x, y, and z.  That is, Ex2 = Ey2 = Ez2.  This means there is a value for E2 and thus the electric field must have a specific direction.  But this seems to contradict the assumption of isotropy for the universe. This is what puzzles me and makes me question the reality of the photon pressure.

Let me add that certainly there is pressure on the walls of a container of photon gas, but the universe does not constitute such a container.

I think the electric field does have meaning but averages to zero on some "coarse graining" view of things.  I have always been bothered by the photon gas model since it requires mass for the photons to interact and equilibrate to some state.  Interesting question.  

Let me correct my previous entry as follows. The universe is not necessarily globally isotropic, but should be "locally" isotropic.

But isn't the Friedman model globally isotropic by definition?  Local anisotropy can average to such a large scale situation.  Am I missing something? 

The example Wolfgang Rindler gives is that of a cone.  The surface of a cone is homogenous everywhere but not isotropic due to the tip of the cone. I think topology comes into play here. GR metrics only define the local geometry. You extend this geometry by using the metrics to come up with the field equations. However, then you can come up with various topologies such as the flat universe as a hypertorus that are homogeneous but not isotropic.

Photons always exert a pressure, although it may be balanced by some other force. In cosmology and stellar physics photons support expansion that is counteracted by gravity. A small excess of radiation energy over gravity potential in distant space can explain large scale acceleration of galaxies and clusters.

Friedman models give a different view of photons in which they contribute stress energy to increase gravitational curvature. This is the main reason dark matter is included in calculations.

Other metrics of the type containing central mass and charge are not in agreement with Friedman about how photons and EM are applied to stress energy. In other threads I have recommended a revision to FLRW allowing photons to weaken gravity. Other researchers have given strong opposition.

Photons can't exert pressure on space, only on material surfaces. They travel through space, for crying out loud!  Dark matter has nothing to do with radiation. and models other than Friedman's would still have radiation pressure contributing to positive curvature. The inference of dark matter is the result of gravitational studies of galaxies and galaxy clusters, not some aspect of photons.

Please send me the questions relating to m field of activity.R.G.Rastogi