Scale invariance Definition and 15 Threads

Hello, In the plane, using Cartesian coordinates ##x## and ##y##, an equation (or a function) is a relationship between the ##x## and ##y## variables expressed as ##y=f(x)##. The variable ##y## is usually the dependent variable while ##x## is the independent variable. The polar coordinates...

https://arxiv.org/pdf/1710.11425.pdf The dark matter/dark energy issues has not made any sense to me since 1996 when it was evident that the ratio of dark matter increased as the volume of space measured increased. This was an obvious affect of empty space in the dark matter question that was...

https://www.sciencedaily.com/releases/2017/11/171122113013.htm A University of Geneva researcher has recently shown that the accelerating expansion of the universe and the movement of the stars in the galaxies can be explained without drawing on the concepts of dark matter and dark energy…...

Yesterday, I was thinking about a problem I had encountered many years before, the central force problem with a ##V(r) \propto r^{-2}## potential... If we have a Hamiltonian operator ##H = -\frac{\hbar^2}{2m}\nabla^2 - \frac{A}{r^2}## and do a coordinate transformation ##\mathbf{r}...

I understand the inflation predicts a nearly scale invariant power spectrum but some have claimed this was predicted before inflation (by Harrison and Zeldovitch?) My understanding is that perfectly scale invariance would predict ns=1 but inflation predicts ns =.96. So did the prior prediction...

I often wonder about how little I understand vacuum, and only recently I've been paying attention to this "vacuum energy" hypothetical. I see it being associated with things as small as spontaneous emissions to things as large as the expansion of the universe. This is a huge range of length...

In the book "Statistical physics for cosmic structures" at p. 171 a read a definition of scale invariance (leading to the so called scale invariant power spectrum) given as the requirement that ##\sigma^2_M(R=R_H(t)) = constant##, where ##R_H(t)## is the horizon, i.e. the maximal distance that...

Hey guys! I was reading the following paper http://arxiv.org/abs/hep-ph/0703260 for Georgi and I have a conceptual question about it. Howard Georgi was talking about this Unparticle Physics theory and at the base of his analysis is the principle of scale invariance. So Georgi is saying what if...

Why have the density perturbations of all lengths a relation to the constant radius c/H? I suppose this is the origin for scale invariance and gaussianity.

Hello everyone. I'm studying the fixed point of theory in the context of QFT. First of all, let me say what I think I understood about fixed points and then I'll state my question. Suppose we have a theory with a certain running coupling ##\lambda(\mu)##. If we have, for example, an UV fixed...

Hi, Are Einstein's field equations without the cosmological constant scale invariant? If so does the addition of the cosmological constant break the scale invariance? John

Consider a random walk (in any dimension) with N steps and a step size of 1. Take a real number \alpha > 0 and consider another random walk which takes \alpha^2 N steps but wil step size \frac{1}{\alpha}. I immediately noticed that the mean deviation after the full walk in both cases is the...

One of the foundations of General Relativity is diffeomorphism invariance - the fact that the laws of physics are invariant under smooth coordinate transformations, and thus the laws must involve tensors. My question is, why doesn't this imply scale invariance; after all, isn't a change of...

Max Tegmark has provided a four part taxonomy of multiverse theories (http://arxiv.org/abs/astro-ph/0302131). The first type can be labeled the "bubble universe" multiverse, in which universes like ours are scattered throughout an infinite space in every direction. Going the other direction...

Clauset and Young, in their new paper http://www.arxiv.org/PS_cache/physics/pdf/0502/0502014.pdf , apply standard modern statistics to a database of terrorist strikes ordered by the number of people killed or injured. They find that extreme cases, such as 9/11, are not outliers, but find their...