Can cosmic inflation be explained by matter antimatter reactions? The big bang theory proposes that equal amounts of matter and antimatter were created in the beginning. Shortly afterwards most of it annihilated. Could that have produced enough energy to drive cosmic inflation?   
 A: Matter antimatter annihilation doesn't produce inflation, because the stress tensor of hot fermions doesn't lead to a cosmological constant. The main property of inflation is that at early times, the universe was dominated by a large positive cosmological constant, and this can be due to a scalar field, it violates the energy condition that the pressure is less than 1/3 the energy density.
For a photon gas, the pressure is exactly 1/3 the energy density. For any massive particle, in the limit of extremely high temperature, the pressure is 1/3 the energy density also, but slightly less because the mass breaks the scale symmetry. When you have scale invariance, the trace of the stress tensor is zero, so the energy component minus 3 times the pressure component must be zero, which explains this universal result.
The only relativistically invariant system that violates this pressure bound is a scalar condensate with a potential. In this case, you can see that a scalar field expectation value can't pick out a rest frame, so the stress tensor must be proportional to the metric tensor, and the pressure is equal to the energy density. This is a gross violation of the dominant energy condition, and it leads to runaway inflation. It is only such a system that can lead to inflation.
Further, the initial conditions of the universe in inflation are not hot at all, they are cold--- the field has an expectation value, which drive the universe to deSitter, and in a causal patch, the deSitter space is otherwise empty. This is a low-entropy initial condition (a cold initial condition), and one way of interpreting this is that the deSitter horizon is too small to allow any large entropy inside the causal patch.
A: Thermodynamic Aspects
Just to expand more on Karsus Ren's point:
In the early universe we generally like to assume thermal and chemical equilibrium. What this equates to is that reactions are equally likely to happen each way. Matter-Antimatter annihilation is relatively symmetric process. Lets just look at electrons/positron annihilations. This have the form of:
$e^++e^-=>2\gamma$
But we can also have two photons collide to form an electron positron pair.
$2\gamma => e^++e^-$
These two processes have the same amount of energy involved. So if we are in the pre-inflationary universe, with energies up in $10^{27}K = 9\times 10^{16} MeV$, we have photons travelling around with such high energies that the issue resolves somewhat simply. We can actually calculate the number density of fermions (both particles and antiparticles) fairly easily since $m_e=0.5 MeV <<T$.
$n_i=g_i e^{\mu/T} \int \frac{d^3p}{2\pi^3}e^{-E_i/T} = g_i \frac{T^3}{\pi^2}e^{\mu/T}$ (for $m_e<<T$)
Where $g_i$ is a constant determined by the number of spin states of species. We can also get from this calculation that even if there is some small chemical potential (found in the $\mu$ term), it is hugely overshadowed by the $T$ term, so we can easily assume number density equilibrium, so no annihilations.
Cosmological Aspects
In addition, there if there were high energy annihilation events in the hyper-early universe it couldn't cause an inflationary scenario. The expansion rate of the universe is determined by the Friedmann equations in terms of the scale factor which time-evolution is determined by the total energy in radiation, matter, and cosmological constant. Annihilation events would move more fraction of the universe's "inventory" from matter to radiation, making the universe scale factor change from more $a(t)=a_ot^{2/3}$ to $a(t)=a_ot^{1/2}$ (see friedmann equations). Although this means that it would slightly increase expansion speed, it wouldn't create the $a(t)=a_oe^{Ht}$ type behavior seen in the inflationary epoch.
A: No.
In the Big Bang model of the creation of the universe  all the energy  comes from the initial singularity from which space and time expand. The energies you describe are already created then, at 0,0,0,0  ,though it is an energy momentum tensor that is generated which obeys the equations of General Relativity. A simple minded energy conservation will not work.
It is worth noting that all points in our present space time started at that space time point, back in 0,0,0,0.
A: What about interaction graviton/antigraviton to prevent matter-antimatter anhilitaion as a repulsive aspect of gravity?
