Attractive gravity has negative energy, what about repulsive gravity in the inflation phase? Alan Guth's cosmic inflation theory posits that about 10^-38 second before the Big Bang which led to our particular universe, a tiny patch of space doubled in size more than 100 times, from sub-atomic size to about 1cm. This "inflation" now ends, the potential energy of the scalar field in this pebble-sized infant universe converts to a hot soup of particles and radiation, and what we call the Big Bang is this hot soup expanding. 
The theory explains the start and the end of inflation thus: Permeating that tiny patch was a scalar field, the potential energy curve of which happened to have a peculiar shape which caused negative pressure, and negative pressure caused gravity to be repulsive rather than attractive, hence the inflation. Like a ball perched on a hilltop, that potential energy is not stable, and at some point it would roll down the curve, this potential energy loss turns into matter and radiation, ending the inflation phase. 
Now, during the inflation phase, space expanded at a constant energy density, therefore energy appears to be macically created, potentially violating energy conservation. In videos of his talks about inflation, professor Alan Guth explains that the universe's total energy was actually conserved to a net of zero or very low value, because the above (positive) energy was exactly balanced by the negative energy of gravity. I can understand that attractive gravity has negative energy, but shouldn't repulsive gravity have positive energy?
 A: In what you read, Guth was developing the concept of inflation, and dark energy.  These concepts were not fully understood nor developed when he first wrote, so he used some vague terms for them.  Negative gravity is now called dark energy.    In the development of physics since then, Dark Energy is accepted to have a positive energy density, therefore the answer to your question is a "yes".
Here is a link to a related question about energy conservation in GR, where the answers address your question very clearly: Energy conservation in General Relativity
Note both this link, and the other one provided by @user4552 in the comments, note that the "Zero Energy Hypothesis" for our universe, which Guth referred to, is untrue, as the energy of the overall universe in GR is undefinable, and energy is not universally conserved in GR.
Note, for both links, one Physics SE poster argued that energy IS conserved, but only referenced his own paper -- which is NOT the way one shows consensus of physics experts SUPPORTS a POV, but instead tends to show the consensus rejects the POV.
A: I do not think you will get a definite answer to this question. So, I will throw some speculation into it.
There is no repulsive gravity. That does not mean attractive gravity can not be turned around into repulsion.
Take an example of repulsion explained in terms of exchange of (virtual) particles. Two bodies can throw particles to one another and this would enable them to get away from one another - repulsion. This is simple to understand in terms of conservation of momentum.
Now try to explain attraction in form of particle exchange! The particles have to take a turned around path. Basically, it is repulsion turned around into attraction in this case.
I am not trying to say this is how electromagnetic attraction/repulsion work. I am just stating one of the mainstream explanations of it.
Same way, natural outcome of "set of various tensors" is attraction. Any repulsion has to be this attraction turned around. Basically, it would be inversion of curvature of space. 
Nature just by itself, without intelligent intervention, is not capable of doing this inversion. That is why we have had no natural scenarios/objects to observe and experiment with this inverted curvature. This is unlike other fields of physics like electromagnetism where nature does provide us objects and scenarios to experiment with and formulate those fields. 
All scientists including Einstein formulated one way curvature. Because that is only one available to us for experimenting and formulating.
So, nature by itself is not capable of this inversion. Big Bang (inflation), & supernova explosions may be possible exceptions to this. We may not fully understand what goes on in there.
Dark energy is possibly an inversion of space curvature that escaped (ran away) at the time of inflation and spread into the universe, and was later overridden at local levels by local curvatures.
So, IMHO, no repulsive gravity, only attractive gravity turned around.
