Section 1.1: Understanding the Universe Types

Many are aware that our universe appears to be on the brink of accelerating expansion—or perhaps it isn’t. But the concept of infinity?

Within the framework of Big Bang cosmology and general relativity, the universe's geometry and ultimate fate can be categorized into three primary types:

1. Closed Universe: This model features positive curvature, resembling a sphere's surface. If you were to travel straight in such a universe, you would eventually return to your starting point. This scenario suggests a finite space that may eventually collapse into a Big Crunch.
2. Flat Universe: Characterized by zero curvature, similar to a flat sheet of paper, this situation represents a critical balance between open and closed universes. A flat universe will continue to expand indefinitely but at a slowing pace. It can theoretically extend infinitely.
3. Open Universe: This type has negative curvature, akin to a saddle's surface. An open universe possesses infinite space and will expand forever, but at an accelerating rate.

The first video, What Shape Is The Universe?, explores the various geometries that define our universe, shedding light on these complex concepts.

Section 1.2: Observational Evidence

Recent observations, particularly from the Planck satellite and WMAP, indicate that our universe is nearly flat. The density parameter (Omega) is very close to 1, signaling a flat universe. However, given the uncertainties in measurements, we cannot completely dismiss the possibility of a slightly open universe.

It is evident that the likelihood of a closed universe decreases as more data accumulates.

The Concept of "Infinity" in Physics

Infinity presents a challenging concept within physics. Often, infinities signify gaps in our understanding or suggest a theoretical breakdown. When discussing an infinite universe, critical philosophical and scientific questions arise. Is the idea of a physically infinite universe even meaningful? Could it imply that such solutions are not "real" in a practical sense?

When students first encounter the physics of colliding billiard balls, they learn about momentum and energy conservation. This principle allows the derivation of equations that predict collision outcomes. In an idealized model where the balls are perfectly elastic and free from energy loss, two mathematical outcomes can emerge.

The first outcome aligns with our intuitive understanding of billiards: after a collision, the balls bounce off, each moving in a direction defined by their angles and the conservation laws. The second outcome, while mathematically sound, suggests the balls pass through one another without interaction.

Not every mathematical solution corresponds to a physical reality, and it's vital to rely on empirical evidence and intuition to determine which solutions hold significance in the real world.

Reconsidering Non-Infinity

This consideration mirrors solutions found in differential equations, such as Einstein’s field equations, which often reveal numerous potential scenarios, including infinite ones. Such infinities are usually dismissed through initial and boundary conditions. Infinite fields are typically grounds for exclusion, so I propose that the universe may not be infinite.

Although the open and flat models align closely with observations, it is not actually the infinity that corresponds to the data; it is the finite densities and cosmic microwave background distribution. When adhering to traditional boundary conditions—which imply an infinite spatial boundary—I believe these favored scenarios may be non-starters. We should investigate the closed universe hypothesis more thoroughly.

Is There Room for a Closed Universe?

While observational data increasingly distances itself from the closed universe model, some studies analyzing cosmic microwave background (CMB) data suggest potential evidence supporting a closed universe. A 2019 study utilizing Planck satellite data even hinted at a slight preference for this model, though it faced skepticism within the scientific community.

From a theoretical perspective, the closed universe provides a finite space volume, offering a more manageable context for certain cosmological and quantum gravitational issues. Certain cosmic inflation models, which describe rapid expansion shortly after the Big Bang, could also result in a closed universe.

In the realm of science, particularly cosmology, there is always some flexibility. Measurement uncertainties and varying interpretations based on models mean the closed universe concept isn't entirely dismissed; it’s just that current evidence leans toward a flat geometry. As technology progresses and our observations refine, our understanding may evolve, either reinforcing the flat universe idea or reigniting the debate.

This is indeed an intriguing time in cosmology, and I find it astonishing that I overlooked the significance of the 'infinite' aspect in this open/closed discussion. Very few people openly address this topic.