In a debate with Dr. William Lane Craig in March, 2014 theoretical physicist Sean Carroll has said the following in his opening speech:
If you have a universe that obeys the conventional rules of quantum mechanics, has a non-zero energy, and the individual laws of physics are themselves not changing with time, that universe is necessarily eternal. The time parameter in Schrödinger’s equation, telling you how the universe evolves, goes from minus infinity to infinity.1
But is it possible that the universe can have non-zero energy value? Let us suppose that the universe has non-zero energy value. In that case the universe will behave like a giant matter, because we now know that matter and energy are equivalent. This giant matter will create its own gravitational field that will try to extend beyond the universe, because here the entire universe itself is the matter that has created that field. But there is actually no space outside the universe where this field can extend. For this we can give two reasons. Scientists say that there was no space and time before the big bang. Space and time came into existence along with the big bang only. So there was no preexisting space-time within which this big bang occurred. Another reason is that this universe is also expanding at an accelerating rate. But when it is asked what it is expanding into, the answer we usually get from the scientists is that it is not expanding into anything, because the universe is not embedded into any higher space-time. So these two points suggest that there is no space-time outside the universe. Therefore universe as a whole cannot have any gravitational field that will extend beyond the universe. So, if it is the case that there is no space outside the universe, then in that case it cannot have any non-zero energy value.
Dr. Sten Odenwald has provided the following information on behalf of NASA Astronomy Cafe, part of the NASA Education and Public Outreach program:
‘General relativity tells us that what we call space is just another feature of the gravitational field of the universe, so space and space-time can and do not exist apart from the matter and energy that creates the gravitational field. This is not speculation, but sound observation.’2
So, if at any time of its evolution the universe has non-zero energy value, then it will create the gravitational field that will extend beyond the universe. As space is just another feature of the gravitational field, so in that case there will be space outside the universe. But cosmologists repeatedly say that there is no space outside the universe, because the universe is not expanding into anything. So universe having non-zero energy directly contradicts the statement that there is no space outside the universe.
Ref:
1. http://www.reasonablefaith.org/god-and-cosmology-the-existence-of-god-in...
2. https://einstein.stanford.edu/content/relativity/a11332.html