Hi neil,
Yes - photons, or more likely cosmic rays from the Big Bang could still be roaming around the edges of our Universe. The tricky part is that for 300,000 years after the big bang spacetime was too hot still to be transparent thus it didn't allow normal photons to travel far. At the edges of the big bang's shock front some photons or cosmic rays probably escaped. Scientists are looking for HUGE
gravity waves that may be the still resonanting aftershock of the Big Bang.
Talking about the edge or centre of the spacetime is also tricky, what do we define is on the other side of the edge that contains our reality, bound by our laws of physics? How many photons or leptons or baryons per cubic light year must there be in an area near or at an edge of the Universe to say well now that volume considered part of our Universe or it is still too dilute yet to be called part of our Universe?
Locating the centre of the Universe where the big bang occured is tricky (probably impossible) because of two limiting factors. The first - the explosion and its aftermath actually created or unfolded our existence. It was not like a grenade going of in an existing room - it was the event that created the room as it went. Secondly and just as mind-bending, space isn't infinite in my estimation - but its 10 times bigger than Newtonian physics would dictate, so it may be 14 billion year old but have a diameter exceeding 80 billion light years - because for the briefest of instances during its creation the four forces we know of today were unified into fewer forces with different characteristics - allowing inflation to occur for a moment at speeds probably 50,000 times lightspeed. Although this was probably exceedingly short lived it permanently disconnected the left hand side of the expanding universe from the right so to speak. Imagine a ball spilt exactly in two and the left half flies away from the right half at 50,000 times c for a millionth of a second and then slows to c instantly after the four forces split apart and the laws of Einstein gain dominance. Well now the left hand side can never see the right hand side or be influenced by it - its too far away for light or any other force carrier to reach and return. Technically its casually disconnected under relativistic physics. Now the Univrse didn't split into two parts - it inflated so fast that at any point in the Universe you are roughly disconnected from 60% of the remainder of Universe (its too far away to ever be seen or reached - not even its gravity can affect you - its propogation wave can never reach you). This phenomenia is called "Hubble Spheres". No occuptant of any Hubble Sphere could tell if the Big Bang orginated in his one - just that it was expanding. You'd need a god or uber-physicists - capable of observing the Universe using more methods permitted by our reality that we don't yet know (but are valid) that supercede relativity to see beyond a Hubble Sphere. This is called hidden variable theory and about 20 years ago a famous mathematican used it to show not even God could break the laws of uncertainty and know both the position and velocity of an electron, regardless of whether he used uber physics or God-powers - it would invalidate creation itself - big call - it implies not even god can see acorss hubble spehere when he acts within the confines of his own creation. Tricky technical theories!
Photons don't have rest mass - they have a momentum potential. So E=mc^2 can be used. A photons energy depends solely on its frequency. If a photon's frequency brought it to an energy level exceeding 120 Giga electron volts it might start altering strong and weak nuclear forces, if it exceeded 10^19 G eV it might suck in electromagentism too, and if it were a million times stronger than that it could re-combine gravity into one unified force again. So in theory you could have a single photon with so much energy it could be a black hole travelling at light speed or if it where far more energetic than this - say 10^50 to 10^ 100 eV and it could be possibly a big bang ready to happen again!
A Solar mass is 10^31 kgs so has energy e= mc^2 around 10^48 Newtons. How many photons would be required to have this energy - well just one really powerful (high enough frequency) one would do! Energy = hf or 6.634 ^ 10 -34 * frequency. So a single photon of frequency 10 ^ 82 hertz would do the job! Of course this is kinda fanciful - because to create such a photon you must have a powersource capable of delivering that kind of energy. Also photons with sufficient energy - and they have been measured up to 10 ^ 20 eV can transform into an electron and positron pair. So while there is no theoretical limit to a pphotons maximum energy - some large practicle impediments arise.
http://www.newton.dep.anl.gov/askasci/phy00/phy00466.htm
Photon have zero rest mass, photons always move at c in any relativistic frame of reference (e.g. outside black holes, worm holes or big bangs).
The sum mass and energy of the Universe may be constant or wavering due to quantum theory - a total vaccuum must theoretically have non-zero energy else it would break Heinsberg's almighty Uncertainity priniple. So as the Universe expands its density goes down - but perhaps its total energy and matter content increases.
Photons always travel in a vaccuum at c - but in other materials their wave front travels slower than c as photons collide with atoms - get absorbed and then re-emitted. A material like diamond might slow light down to less than half its normal vaccuum speed. Electricity travels at c between atoms in a copper wire - but given the effects of electrons being captured and released a moment later you can consider electricity travels at 10% of c thru a normal copper wire at room temperature.
Hope these answers help!