I will try to answer in the view of General Relativity.

I quote directly from Einstein and Rosen paper :

The four-dimensional space is described mathematically by two congruent parts or "sheets", corresponding to $u > 0$ and $u < 0$, which are joined by a hyperplane $r = 2m$ or $u = 0$ in which $g$ vanishes. We call such a connection between the two sheets a "bridge". We see now in the given solution, free from singularities, the mathematical representation of an elementary particle (neutron or neutrino). Characteristic of the theory we are presenting is the description of space by means of two sheets. A bridge, spatially finite, which connects these sheets characterizes the presence of an electrically neutral elementary particle. With this conception one not only obtains the representation of an elementary particle by using only the field equations, that is, without introducing new field quantities to describe the density of matter; one is also able to understand the atomistic character of matter as well as the fact that there can be no particles of negative mass. The latter is made clear by the following considerations. If we had started from a Schwarzschild solution with negative $m$, we should not have been able to make the solution regular by introducing a new variable $u$ instead of $r$; that is to say, no "bridge" is possible that corresponds to a particle of negative mass.

A.Einstein, N.Rosen - "The Particle Problem in the General Theory of Relativity"

This was the paper that investigated ER bridges (wormholes). It would be useful to read the paper to understand further more why there can be no negative mass particles.

So, the total energy of the universe can not be zero, because there can be no particles of negative mass. So, in the light of mass/energy equivalence, the energy of the universe cannot be zero.

I will try to answer in the view of General Relativity.

I quote directly from Einstein and Rosen paper :

The four-dimensional space is described mathematically by two congruent parts or "sheets", corresponding to $u > 0$ and $u < 0$, which are joined by a hyperplane $r = 2m$ or $u = 0$ in which $g$ vanishes. We call such a connection between the two sheets a "bridge". We see now in the given solution, free from singularities, the mathematical representation of an elementary particle (neutron or neutrino). Characteristic of the theory we are presenting is the description of space by means of two sheets. A bridge, spatially finite, which connects these sheets characterizes the presence of an electrically neutral elementary particle. With this conception one not only obtains the representation of an elementary particle by using only the field equations, that is, without introducing new field quantities to describe the density of matter; one is also able to understand the atomistic character of matter as well as the fact that there can be no particles of negative mass. The latter is made clear by the following considerations. If we had started from a Schwarzschild solution with negative $m$, we should not have been able to make the solution regular by introducing a new variable $u$ instead of $r$; that is to say, no "bridge" is possible that corresponds to a particle of negative mass.

A.Einstein, N.Rosen - "The Particle Problem in the General Theory of Relativity"

This was the paper that investigated ER bridges (wormholes). It would be useful to read the paper to understand further more why there can be no negative mass particles.

So, the total energy of the universe can not be zero, because there can be no particles of negative mass. So, in the light of mass/energy equivalence, the energy of the universe cannot be zero.

I will try to answer in the view of General Relativity.

I quote directly from Einstein and Rosen paper :

The four-dimensional space is described mathematically by two congruent parts or "sheets", corresponding to u > 0 and u < 0, which are joined by a hyperplane r = 2m or u = 0 in which g vanishes. note 2 We call such a connection between the two sheets a "bridge". We see now in the given solution, free from singularities, the mathematical representation of a an elementary particle (neutron or neutrino). Characteristic of the theory we are presenting is the description of space by means of two sheets. A bridge, spatially finite, which connects these sheets characterizes the presence of an electrically neutral elementary particle. With this conception one not only obtains the representation of an elementary particle by using only the field equations, that is, without introducing new field quantities to describe the density of matter; one is also able to understand the atomistic character of matter as well as the fact that there can be no particles of negative mass. The latter is made clear by the following considerations. If we had started from a Schwarzschild solution with negative m, we should not have been able to make the solution regular by introducing a new variable u instead of r; that is to say, no "bridge" is possible that corresponds to a particle of negative mass.

A.Einstein, N.Rosen - "The Particle Problem in the General Theory of Relativity"

This was the paper that investigated ER bridges (wormholes). It would be useful to read the paper to understand further more why there can be no negative mass particles.

So, the total energy of the universe can not be zero, because there can be no particles of negative mass. So, in the light of mass/energy equivalence, the energy of the universe can not be zero.

I will try to answer in the view of General Relativity.

I quote directly from Einstein and Rosen paper :

The four-dimensional space is described mathematically by two congruent parts or "sheets", corresponding to $u > 0$ and $u < 0$, which are joined by a hyperplane $r = 2m$ or $u = 0$ in which $g$ vanishes. We call such a connection between the two sheets a "bridge". We see now in the given solution, free from singularities, the mathematical representation of an elementary particle (neutron or neutrino). Characteristic of the theory we are presenting is the description of space by means of two sheets. A bridge, spatially finite, which connects these sheets characterizes the presence of an electrically neutral elementary particle. With this conception one not only obtains the representation of an elementary particle by using only the field equations, that is, without introducing new field quantities to describe the density of matter; one is also able to understand the atomistic character of matter as well as the fact that there can be no particles of negative mass. The latter is made clear by the following considerations. If we had started from a Schwarzschild solution with negative $m$, we should not have been able to make the solution regular by introducing a new variable $u$ instead of $r$; that is to say, no "bridge" is possible that corresponds to a particle of negative mass.

A.Einstein, N.Rosen - "The Particle Problem in the General Theory of Relativity"

This was the paper that investigated ER bridges (wormholes). It would be useful to read the paper to understand further more why there can be no negative mass particles.

So, the total energy of the universe can not be zero, because there can be no particles of negative mass. So, in the light of mass/energy equivalence, the energy of the universe cannot be zero.