Weyl's original Gauge "Scale" Invariance and the search for a Metric to define Expansi

The Universe is said to be expanding. Indeed the expansion is being accelerated by the pressure of the vacuum energy of the Einstein's infamous Cosmological constant. The constant represents a positive energy-density and is a constant in the sense that every observer agrees that it is constant. We are a very particular set of inertial observers (the onlty concious ones) that take a perspective on the universe. Our measured value of the Hubble's constant (that relates recessional velocity of galaxies to their duistance from us) is argued to be representative of all other observers in the universe. Through the inverse of Hubbles constant we get (our) "Proper" age of the universe as 13.8 billion years.

Recall that pressure is a scalar quantity, not a vector being the scalar constant of proportionality that relates an (axial) vector surface element to a normal force to that surface. A negative gradient of pressure is called a force-density. In an expanding universe this scalar should be increasing as the surface element expands.

Is it the case that expansion makes sense in hte argument given that a scale is defined by the time-scale of atomic vibrations or their size. That the vibrations give rise to waves that are themselves streteched by the expansion means that such waves cannot be used as a fundamental ruler surely? Ok we have CMBR, its temperature decay and resultant stretch of radiation from gamma to the Infra red that we see today at 2.7K. Again though where is the fundamental "Scale" - or "Gauge" as Weyl coined it when extending Einstein's theory to Einstein-Maxwell when adding non sclae invariance to Einstein's no parallel transport around a parallelopiped (of space).

In the dust model of the universe we view the universe as a pressure-free non-viscous (perfect, non conducting of heat) fluid. The dust is static and is perfect in the sense that no heat is allowed to pass between the (huge) cells that comprise the continuum that is the universe. In the more realistic perfect fluid model the cells (which are of a scale that the universe is deemd homogeneous) experience pressure but no viscosity.