Cosmic inflation doesn’t violate energy conservation.

"History of the Universe – gravitational waves are hypothesized to arise from cosmic inflation, a phase of accelerated expansion just after the Big Bang". (Wikipedia, Cosmic inflation)

“The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. In the case of a closed system, the principle says that the total amount of energy within the system can only be changed through energy entering or leaving the system. Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another”.(Wikipedia, Conservation of energy)

“For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite.” (Wikipedia, Conservation of energy)

The fact is that energy can change in the closed system if the system changes its form. So if a closed system expands there is less energy for filling the space that turns larger or smaller. The idea is similar to putting a balloon filled with water in a vacuum chamber. That system expands the balloon when the pressure decreases. So cosmic inflation means that there is less energy compared to space when space expands. The expansion is interaction. When pressure outside the system decreases the outside pressure presses it into its form. And otherwise, internal pressure pushes the system larger.

When the system’s size grows but the gas atom’s number in the system is the same, expansion decreases the power of the internal system. Energy acts in a similar way as gas. 

That doesn’t mean that the energy of the water decreases compared to outside because the difference between pressure levels stays the same. And quantum fields or energy act like water. So if we compare energy to gas or water expanding space means that pressure in the system decreases, but in the same way, differences in pressure levels in and out of the system are always relatively the same. 

If we push that ball we can increase pressure inside it. That means it's possible to affect energy density or energy strength by changing the system’s size. But the main question about the universe is this: Is the universe itself a closed system that recycles energy? Or does the universe leak, which means that the wave movement escapes from the universe faster than the universe expands? 

The universe itself is not any vacuum chamber. The space outside the universe is enormous. Or maybe it is infinite. That means there should be no resistance against the universe and its expansion from outside. But inside the universe, gravity pulls particles and wave movement back to the center of that thing. 

"In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the very early universe. Following the inflationary period, the universe continued to expand, but at a slower rate. The re-acceleration of this slowing expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago." (Wikipedia, Cosmic inflation)

Above: The model of cosmic inflation. 

When the universe started to freeze, material formed that bound energy into particles. That formed space between those particles. When energy bound into material there was less free energy and that turned energy between material objects chaotic. Material is like ice bites in water. Material is one energy form. But when energy turns into material that is away from free energy. 

When we think about closed systems we must realize that those systems involve multiple internal systems. In the universe, the system is not homogenous. There are many energy levels in the universe. Materia is one energy form or densely packed energy. We must send an energy impulse to the system so that we can release energy that is stored in the material. When energy is packed in the atom or subatomic particles or bonds between atoms that energy is away from somewhere. There is a lot of energy in the universe. 

But because the universe is not endless there are limited energy resources. The thing that destroys the system is free energy. Free energy is energy that is not bound to material. And that energy causes oscillation. When we use energy we simply bind free energy into material. Materia itself is a denser form of energy. When the universe expands quantum fields in the universe turn weaker. 

That causes a situation where energy flows faster away from material and sooner or later, the material turns into wave movement. That means that the free energy in the system increases. And that causes the entropy in the system to increase. Free space in the system means that energy flows to that empty space. Energy must flow all the time. And it always travels to a lower energy level. The universe’s expansion means that the free energy state in the universe rises and rips material into pieces. That realizes energy that is stored in the material. 

So energy doesn't vanish. It just changes its form and power. But energy and information themselves are infinite. They cannot vanish. They can just turn denser or they can turn less dense. And that means there is no death in the quantum world. Energy is information and information can change its form but it cannot vanish. It can turn so weak that it's hard to see. Or it can take the form that we cannot understand. It can be so chaotic that we cannot separate and interconnect those bites into their original form. 

https://bigthink.com/starts-with-a-bang/cosmic-inflation-violate-energy-conservation/

https://en.wikipedia.org/wiki/Conservation_of_energy

https://en.wikipedia.org/wiki/Cosmic_inflation