The Assumptions
The above image shows the evolution of the size of the observable universe ('radial' axis) plotted against time (horizontal axis) from the big bang to the present. The current model of the flat universe relies on rapid expansion (inflation) followed by a period of slower expansion followed again by acceleration in more recent times. The assumptions outlined below have been the foundation of the Cosmological Principle and are the key pillars supporting the current flat universe model. They are considered to be, by most cosmologists, unshakable and are often stated as matter of fact.

Homogeneity
Homogeneity, the first pillar of the Cosmological Principle, assumes that the density of the universe is the same at every point. If somehow you were able to travel to a distant quasar near what appears as the edge of our observable universe, distances to stars and galaxies would be much the same there as they are around here. Small local variations, of course, are allowed but variations on a large scale (by definition, structures (clusters of galaxies, for example) over 1.2 billion light years in size) would undermine the Cosmological Principle.
Homogeneity, the first pillar of the Cosmological Principle, assumes that the density of the universe is the same at every point. If somehow you were able to travel to a distant quasar near what appears as the edge of our observable universe, distances to stars and galaxies would be much the same there as they are around here. Small local variations, of course, are allowed but variations on a large scale (by definition, structures (clusters of galaxies, for example) over 1.2 billion light years in size) would undermine the Cosmological Principle.

Isotropism
Isotropism, the second pillar of the Cosmological Principle, is the assumption that there is no up or down in the universe. No north or south pole. No grain, In other words, there is no preferred orientation so that observations made in one direction would be similar to observations made in any other direction and that this aspect would hold true for observations made from any point in the universe. Small local variations would not violate the isotropic nature of the cosmos. However, patterns or graininess on a large scale would undermine the Cosmological Principle.
Isotropism, the second pillar of the Cosmological Principle, is the assumption that there is no up or down in the universe. No north or south pole. No grain, In other words, there is no preferred orientation so that observations made in one direction would be similar to observations made in any other direction and that this aspect would hold true for observations made from any point in the universe. Small local variations would not violate the isotropic nature of the cosmos. However, patterns or graininess on a large scale would undermine the Cosmological Principle.

Inflation
The current theory holds that long before the first trillionth of a second had elapsed, following the big bang, the space that would come to be our observable portion of the universe, expanded from a mere point to the size of a grain of sand. Remarkably to some, inflation occurred all over, meaning there was no corresponding area of compression. Inflation is not something that we can observe directly. Inflation has been assumed. And, assuming the universe started with the big bang, inflation is the only explanation we have that provides a solution to how the universe was able to retain its homogeneous characteristics. But the premis of inflation does raise some serious questions, not the least of which are, what drove it and how is it allowed under the standard model of physics.
The current theory holds that long before the first trillionth of a second had elapsed, following the big bang, the space that would come to be our observable portion of the universe, expanded from a mere point to the size of a grain of sand. Remarkably to some, inflation occurred all over, meaning there was no corresponding area of compression. Inflation is not something that we can observe directly. Inflation has been assumed. And, assuming the universe started with the big bang, inflation is the only explanation we have that provides a solution to how the universe was able to retain its homogeneous characteristics. But the premis of inflation does raise some serious questions, not the least of which are, what drove it and how is it allowed under the standard model of physics.

Dark Energy
It is claimed that dark energy makes up over two thirds of the mass/energy the universe. Dark energy was invented to account for the accelerating expansion of the universe. However, it has never been detected in any experiment, nor does the standard model of physics accommodate it. For all intents and purposes, dark energy is a fictitious force and acts merely as a placeholder for a phenomena that is not understood.