Infinite regress is possible if beginning is singular. You just need to know a little about math to imagine this. Just think of a curve which tends to infinity at origin/beginning. Each segment along this curve could be a cause. So you have infinite set of causes in area close to origin which take short segment of time.
The Borde-Guth-Vilenkin theory has demonstrated that past spacetimes cannot be infinite for a spacetime like ours that is, on average, expanding. To quote their abstract, “inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.”
I would also point to a little-discussed point that infinitely-expanding DeSitter spaces (e.g., empty spacetime with only zero-point energy) are not stable over infinite futures, at least according to current models.
I also think your argument runs into the quantum nature of reality. Eventually, you reach the Plank scale, and physics breaks down. Again, its the jumpy nature of a quantum vacuum, which is a product of the Uncertainty Principle, that prevents both truly zero energy from existing in the physical universe that prevents.
More generally, infinity is not a physical phenomenon that has ever been measured. An infinite future spacetime is entirely speculative.
This is the most important distinction. A theoretical infinity is imaginable, however a natural infinity is nonsensical.
I would also point out that the very notion of a physical curve is an assumption. Why would an initial state of the universe include a curve of any sort? A “curve” can also be described by a nonzero (or non-constant) first derivative. Why would dy/dx of any curve be nonconstant at time zero? Violates the law of conservation of information in physics.
Agreed. Go Blue.
The curve simply show the intensity in number of causes.