SNe Ia, Implications, Interpretations, Lambda-CDM...

[coldcreation]

The person's name completely escapes me at the moment and this may not be accurate as I read it many years ago and my memory of it is incomplete at best, but:

 

The very very first person to discover "the de Sitter effect" was ____. He did so by analyzing how much of one stars light would be received by another star. He found that the light dropped of non-linearly in de Sitter's metric and this is eventually called the de Sitter effect - or maybe he named it that (I don't know).

 

It seems to me that what he must have worked out was a brightness to distance function for de Sitter's original model. He was not solving for redshift, I remember that much.

 

If apparent and intrinsic brightness are to be presented very much differently with "de Sitter time" then perhaps we could get a hold of that paper. If I am right, it would have exactly what is needed.

 

-modest

 

There are some well known papers concerning the search to find the de Sitter effect using astronomical data (for velocity and distance) of objects such as stars and globular clusters: by Wirtz (1924, 1925), Lundmark (1925), Silberstein (1924) and Stromberg (1925). See The Tolman Surface Brightness Test for the Reality of the Expansion. IV. A Measurement of the Tolman Signal and the Luminosity Evolution of Early-Type Galaxies, by Lubin and Sandage, 2001. See also this post in the redshift z thread.

 

Or perhaps you were thinking about W. W. Cambell (Director of Lick Observatory on Mount Hamilton). Cambell studied the line shifts (redshifts) of stellar spectra in 1911 and gave the mystifying name “K effect” to the phenomenon. The Doppler effect was excluded early on as it seemed obvious that stars in our own galaxy were not racing away. It wasn’t until the 1930’s when Robert Trumpler found the same occurrence in star clusters (or globular clusters) that an explanation was given. He attributed the effect to a gravitational redshift (the displacement of spectral lines towards the red by the gravitational potential predicted by Einstein's GR), but it was found that the gravity on the surface of the stars was too weak to cause the observed spectral shifts. Max Born and Erwin Finlay-Freundlich made an attempt to explain the spectral modifications with “tired light” (as light travels through space it loses energy), but that failed to attract much attention amongst the experts. Trumpler continued believing this to be a gravitational effect well into the 1950’s (see for example Arp 1998, Seeing Red, Redshifts, Cosmology and Academic Science).

 

I'm not sure how much of this work was dedicated to the de Sitter effect interpretation though.

 

I'll see if I can pinpoint the work you make reference to...

 

 

 

CC

[modest]

There are some well known papers concerning the search to find the de Sitter effect using astronomical data (for velocity and distance) of objects such as stars and globular clusters: by Wirtz (1924, 1925), Lundmark (1925), Silberstein (1924) and Stromberg (1925). See The Tolman Surface Brightness Test for the Reality of the Expansion. IV. A Measurement of the Tolman Signal and the Luminosity Evolution of Early-Type Galaxies, by Lubin and Sandage, 2001. See also this post in the redshift z thread.

 

Or perhaps you were thinking about W. W. Cambell (Director of Lick Observatory on Mount Hamilton). Cambell studied the line shifts (redshifts) of stellar spectra in 1911 and gave the mystifying name “K effect” to the phenomenon. The Doppler effect was excluded early on as it seemed obvious that stars in our own galaxy were not racing away. It wasn’t until the 1930’s when Robert Trumpler found the same occurrence in star clusters (or globular clusters) that an explanation was given. He attributed the effect to a gravitational redshift (the displacement of spectral lines towards the red by the gravitational potential predicted by Einstein's GR), but it was found that the gravity on the surface of the stars was too weak to cause the observed spectral shifts. Max Born and Erwin Finlay-Freundlich made an attempt to explain the spectral modifications with “tired light” (as light travels through space it loses energy), but that failed to attract much attention amongst the experts. Trumpler continued believing this to be a gravitational effect well into the 1950’s (see for example Arp 1998, Seeing Red, Redshifts, Cosmology and Academic Science).

 

I'm not sure how much of this work was dedicated to the de Sitter effect interpretation though.

 

I'll see if I can pinpoint the work you make reference to...

 

 

 

CC

 

I believe you miss my point entirely.

 

None of the papers you present have a distance to brightness function for de Sitter's original model. At least, not where it is defined as anything more than a FLRW empty model.

 

The first person (who I'll try harder to find) to analyze de Sitter's model and discover the metric called for less bright objects than would be expected did indeed (if I remember correctly) solve this model for brightness vs. distance.

 

If you truly want to know if de Sitter's funky time metric would match SNe 1a data that would be an excellent place to look for the needed function. I'll look harder for who that was and what paper it was.

 

I probably shouldn't have mentioned it until I found the gentlemen's paper.

 

-modest

[Little Bang]

CC, I think about 90% of the observed red shift is due to the expansion of the universe, is that a fair statement?

[coldcreation]

CC, I think about 90% of the observed red shift is due to the expansion of the universe, is that a fair statement?

 

 

Are you referring to the SNe Ia redshift z, or the z of all objects combined. Are you implying that 10% of redhsifts are due to intrinsic motion (toward or away from the observer)?

 

Do you believe that spacetime is flat, that all the humps and bumps of curved space cancel each other out, that the z (redshift) going out from the source is compensated for by the z (blueshift) coming in to our frame?

 

You are certainly entitled to interpret the data as expansion, even as acceleration of expansion. So in that sense your statement is fair. I would caution, however, in that at least one other phenomenon could be responsible for z.

 

One of the examples is provided above: a globally hyperbolic spacetime curvature could simulate the same observations (see also the Redshift z thread). Halton Arp, of course, provides another mechanism for z. So Arp thinks, contrary to your above statement, that none of the redshift is cause by expansion. That too is a fair statement.

 

The fact is, we don't see objects (galaxies, SNe Ia, etc.) moving away from our reference frame. All we have to go by is an interpretation of the data based on models (and for now I see only two viable solutions: one is expanding and one is stationary). Observations (large-scale structure, stellar age, metallicity, CMB, element abundance, etc.) will ultimately (if it hasn't already) determine which view is correct.

 

 

 

These are obvious signs (empirical evidence) that modern cosmology’s golden age is in danger of terminating not with a BANG (the way it began) but with a string of whimpers.

 

 

 

 

 

CC

[bigsam1965]

Obviously not with the FLRW metric. If you think you can solve the friedman equations with significant negative K and no cosmological constant to get a fit with the SNe 1a observations then present it. Otherwise we need to take the word of the people who did the study and their peers.

 

- modest

 

I will take on your challenge, but first, in this post, let me demonstrate that the [math]{\Lambda}CDM[/math] standard cosmological model is not a viable cosmological model through examination of the energy flux equation at an observer. This proof is simple and very effectively renders the standard model irrelevant.

 

Proof:

 

Suppose that space is expanding, and is either coasting or accelerating. Also, consider a single source in the expanding Universe that emits photons some of which will eventually reach photon counters of telescopes. Compare the energy-flux equation at the observer for both a static universe and an expanding universe.

 

Definitions:

[math]H_0[/math] is the Hubble constant.

[math]c[/math] is the speed of light.

[math]z[/math] is the redshift due to expansion of space.

[math]F[/math] is the energy flux that reaches an observer from a source in units of watt per meter squared.

[math]F_r[/math] is the reference energy flux of the source if the source was [math]10[/math] parsec or [math]{10}^{-5}[/math] Mpc (megaparsec) from the observer.

[math]L[/math] is the effective luminosity (radiant power) in units of watt that crosses the source-centered spherical boundary at the observer.

[math]D[/math] is the actual relative dilated distance between observer and source.

[math]L_0[/math] is the intrinsic luminosity of the source.

[math]D_L[/math] is the relative luminosity distance between observer and source.

[math]M[/math] is the absolute magnitude of the source.

[math]m[/math] is the apparent magnitude of the source.

[math]\mu[/math] is the distance modulus and is the apparent magnitude minus the absolute magnitude of the source.

[math]F=L/4{\pi}D^2[/math] is the energy-flux equation at the source-centered spherical boundary located at the observer.

 

Now, for a static universe, [math]L=L_0[/math] and [math]D=D_L[/math]; therefore, the energy-flux equation for a static universe is

 

 

[math]F=L_0/4{\pi}{D_L}^2[/math] . (1)

 

 

Equation (1) is the energy-flux equation used in the standard model (Riess et al. 2004, Perlmutter&Schmidt 2003). Equation (1) leads to the distance modulus equation:

 

 

[math]\mu=m-M=-2.5log_{10}(F/F_r)=5log_{10}(D_L)+25[/math] . (2)

 

 

In the standard model, the FLRW metric is used with a nonzero cosmological constant to solve for [math]D_L[/math] to obtain the theoretical Hubble diagram that is compared to the observed SNe Ia Hubble diagram. The nonzero cosmological constant is interpreted by the proponents of the standard model as dark energy that is causing the universal expansion to accelerate. Equation (1) also leads to the dilated lookback volume equation:

 

 

[math]log_{10}(V)=0.6\mu+log_{10}(4{\pi}/3)-15[/math] , (3)

 

 

which agrees with galaxy count observations of the Durham Group (Metcalfe, et al. 2000, 2005) only in the nearfield of space.

 

For an expanding universe, there are two possibilities for the value of effective luminosity that crosses the source-centered spherical boundary of radius [math]D[/math] at the observer. If photon energy is conserved but stretched because of spatial expansion then [math]L=(1+z)^{-1}L_0[/math]. If photon energy is not conserved then [math]L=(1+z)^{-2}L_0[/math]. Therefore, in either case, for an expanding universe, [math]L[/math] is not equal to [math]L_0[/math]. However, in the standard model [math]L=L_0[/math] is used in Equation (1). Therefore, from Equation (1), for conservation of photon energy [math]D_L=(1+z)^{1/2}D[/math], and for nonconservation of photon energy [math]D_L=(1+z)D[/math].

 

Therefore, QED.

 

In light of the above proof, the standard [math]{\Lambda}CDM[/math] cosmological model is not viable as a candidate for describing the cosmological development of the universal expansion. [math]D[/math] is the distance that should be solved for in the Friedmann-Lemaitre metric, not [math]D_L[/math]. The next post will show a solution to the Friedmann-Lemaitre metric with a zero cosmological constant that fits both the Type Ia supernovae Hubble diagram and the galaxy counts of the Durham group.

[modest]

bigsam1965,

 

Did you write "General Relativistic Cosmology Bringing Cosmology Into Clearer Focus"?

 

I will have to explore your proof, but, I should say it is going to take a lot to convince me that the physics behind the standard model or Friedmann's solution is inherently flawed.

 

-modest

[bigsam1965]

Modest,yes. The proof is there. If you have questions about it let me know. Have fun.

[coldcreation]

I will take on your challenge, but first, in this post, let me demonstrate that the [math]{Lambda}CDM[/math] standard cosmological model is not a viable csomological model through examination of the energy flux equation at an observer. This proof is simple and very effectively renders the standard model irrelavant.

 

Proof:

 

Suppose that space is expanding, and is either coasting or accelerating. Also, consider a single source in the expanding Universe that emits photons some of which will eventually reach photon counters of telescopes. Compare the energy-flux equation at the observer for both a static universe and an expanding universe.

 

Definitions:

[math]H_0[/math] is the Hubble constant.

[math]c[/math] is the speed of light.

[math]z[/math] is the redshift due to expansion of space.

[math]F[/math] is the energy flux that reaches an observer from a source in units of watt per meter squared.

[math]F_r[/math] is the reference energy flux of the source if the source was [math]10[/math] parsec or [math]{10}^{-5}[/math] Mpc (megaparsec) from the observer.

[math]L[/math] is the effective luminosity (radiant power) in units of watt that crosses the source-centered spherical boundary at the observer.

[math]D[/math] is the actual relative dilated distance between observer and source.

[math]L_0[/math] is the intrinsic luminosity of the source.

[math]D_L[/math] is the relative luminosity distance between observer and source.

[math]M[/math] is the absolute magnitude of the source.

[math]m[/math] is the apparent magnitude of the source.

[math]mu[/math] is the distance modulus and is the apparent magnitude minus the absolute magnitude of the source.

[math]F=L/4{pi}D^2[/math] is the energy-flux equation at the source-centered spherical boundary located at the observer.

 

Now, for a static universe, [math]L=L_0[/math] and [math]D=D_L[/math]; therefore, the energy-flux equation for a static universe is

 

 

[math]F=L_0/4{pi}{D_L}^2[/math] . (1)

 

 

Equation (1) is the energy-flux equation used in the standard model (Riess et al. 2004, Perlmutter&Schmidt 2003). Equation (1) leads to the distance modulus equation:

 

 

[math]mu=m-M=-2.5log_{10}(F/F_r)=5log_{10}(D_L)+25[/math] . (2)

 

 

In the standard model, the FLRW metric is used with a nonzero cosmological constant to solve for [math]D_L[/math] to obtain the theoretical Hubble diagram that is compared to the observed SNe Ia Hubble diagram. The nonzero cosmological constant is interpreted by the proponents of the standard model as dark energy that is causing the universal expansion to accelerate. Equation (1) also leads to the dilated lookback volume equation:

 

 

[math]log_{10}(V)=0.6mu+log_{10}(4{pi}/3)-15[/math] , (3)

 

 

which agrees with galaxy count observations of the Durham Group (Metcalfe, et al. 2000, 2005) only in the nearfield of space.

 

For an expanding universe, there are two possibilities for the value of effective luminosity that crosses the source-centered spherical boundary of radius [math]D[/math] at the observer. If photon energy is conserved but stretched because of spatial expansion then [math]L=(1+z)^{-1}L_0[/math]. If photon energy is not conserved then [math]L=(1+z)^{-2}L_0[/math]. Therefore, in either case, for an expanding universe, [math]L[/math] is not equal to [math]L_0[/math]. However, in the standard model [math]L=L_0[/math] is used in Equation (1). Therefore, from Equation (1), for conservation of photon energy [math]D_L=(1+z)^{1/2}D[/math], and for nonconservation of photon energy [math]D_L=(1+z)D[/math].

 

Therefore, QED.

 

In light of the above proof, the standard [math]{Lambda}CDM[/math] cosmological model is not viable as a candidate for describing the cosmological development of the universal expansion. [math]D[/math] is the distance that should be solved for in the Friedmann-Lemaitre metric, not [math]D_L[/math]. The next post will show a solution to the Friedmann-Lemaitre metric with a zero cosmological constant that fits both the Type Ia supernovae Hubble diagram and the galaxy counts of the Durham group.

 

I have a question, but first, welcome to Hypography Science Forum Bigsam1965.

 

What can you tell us about the solution above for a static universe, i.e., what does your equation imply? Do you still, in that case, have the dilated lookback volume and accord with the galaxy counts of the Durham group?

 

It is my understanding that you have the relative luminosity distance between observer and source equal to the actual relative dilated distance between observer and source, and that the intrinsic luminosity of the source is equal to the effective luminosity that crosses the source-centered spherical boundary at the observer. Question: how does that effect geometry, if at all? In other words is the static universe model spherical, flat (Euclidean) or hyperbolic? It seems something is missing (the actual metric for this solution).

 

CC

[bigsam1965]

I have a question, but first, welcome to Hypography Science Forum Bigsam1965.

 

What can you tell us about the solution above for a static universe, i.e., what does your equation imply? Do you still, in that case, have the dilated lookback volume and accord with the galaxy counts of the Durham group?

 

It is my understanding that you have the relative luminosity distance between observer and source equal to the actual relative dilated distance between observer and source, and that the intrinsic luminosity of the source is equal to the effective luminosity that crosses the source-centered spherical boundary at the observer. Question: how does that effect geometry, if at all? In other words is the static universe model spherical, flat (Euclidean) or hyperbolic? It seems something is missing (the actual metric for this solution).

 

CC

 

Coldcreation, thanks for welcoming me to the forum. The proposed new solution is also a solution of the Friedmann-Lemaitre metric. I have not presented the new solution to the metric yet. I am also preparing lectures for next week. Be a little patient.

 

It is the standard model that is using [math]L=L_0[/math] and [math]D=D_L[/math], not the solution I am proposing. Using the static-universe energy-flux equation in the standard model leads to a standard-model over prediction of observed galaxy counts by the factor [math](1+z)^{3/2}[/math]. If the Universe really was static there would be no redshift due to the expansion of space. Since redshift is observed (and IMHO is correctly interpreted as due to spatial expansion), the static-universe energy-flux equation is not the correct form of the equation to use.

[bigsam1965]

In light of the above proof, the standard [math]{Lambda}CDM[/math] cosmological model is not viable as a candidate for describing the cosmological development of the universal expansion. [math]D[/math] is the distance that should be solved for in the Friedmann-Lemaitre metric, not [math]D_L[/math]. The next post will show a solution to the Friedmann-Lemaitre metric with a zero cosmological constant that fits both the Type Ia supernovae Hubble diagram and the galaxy counts of the Durham group.

 

The proposed cosmological model to replace the standard model uses the definitions and part of the proof presented in the initial post. From the above proof, the two possibilities are conservation of photon energy as space expands where [math]D_L=(1+z)^{1/2}D[/math] and nonconservation of photon energy as space expands where [math]D_L=(1+z)D[/math]. For nonconservation of photon energy as space expands, the spatial expansion must be decelerating to match the Hubble diagram of the Type Ia Hubble diagram. For conservation of photon energy as space expands, the spatial expansion must be coasting to match the Type Ia Hubble diagram. By transforming dilated time and dilated distance in the Friedmann-Lemaitre metric, without the cosmological constant, to proper time and proper distance, a coasting-universe solution can be obtained. As it turns out, conservation of photon energy coupled with a coasting Universe with [math]D=c{H_0}^{-1}z[/math] and the Hubble flow velocity [math]v_H=cz[/math] results in the best fit of the SNe Ia Hubble diagram, the galaxy count surveys of the Durham Group, and the flatness of space from the CMB data of WMAP. The Hubble diagram equation and dilated lookback volume equation for a coasting universe are

 

[math]\mu=m-M=2.5log_{10}(1+z)+5log_{10}(c{H_{0}}^{-1}z)+25[/math] , (4)

 

and

 

[math]log_{10}(V_D)=-1.5log_{10}(1+z)+0.6\mu+log_{10}(4{\pi}/3)-15[/math] . (5)

 

Adjusting the Hubble constant in Equation (4) to fit the SNe Ia Hubble diagram data results in a mean global value of 56.96 km/s per Mpc, which translates to a mean age of the universal expansion of 17.16 billion years. This Supports the Hubble constant work of the Sandage Consortium (Sandage, et al. 2006). The space of a coasting universe is flat, unbounded and expanding, not accelerating.

[PhysBang]

One of the examples is provided above: a globally hyperbolic spacetime curvature could simulate the same observations (see also the Redshift z thread). Halton Arp, of course, provides another mechanism for z. So Arp thinks, contrary to your above statement, that none of the redshift is cause by expansion. That too is a fair statement.

Given Arp's absolutely abyssmal track record, why do people keep invoking him? Seriously, the guy doesn't actually have an alternative explanation and his key examples keep folding whenever a better telescope is aimed at them. Gravitational lensing shows that there are two possible cases: a) all quasars are at their redshift distances, or :eek_big: some quasars are at their redshift distances and there is another class of quasars that look exactly like the other quasars that have an anomalous redshift. The only reason one has for believing in option ;) is to carry a torch for some extremely hypothetical idea with no actual evidence.

[PhysBang]

I'm not sure what the point of that was. The standard model doesn't use equation (1).

[bigsam1965]

Of course it does. Look at Riess et al 2004 or Permutter&Schmidt 2003.

[modest]

I'm not sure what the point of that was. The standard model doesn't use equation (1).

 

It does:

 

From “Problem Book in Relativity and Gravitation” page 528:

 

 

Let [imath]t`[/imath] denote time measured at the emission of photons.

Since [imath] V=d(R(t_1)r_1\delta)/dt`[/imath], and since [imath] dt`/dt=R(t_1)/R_0[/imath] because of the cosmological redshift, and noting that [imath]R(t_1)[/imath] can be considered constant since its change includes no transverse motion, we get: [imath]d_M=R_0r_1[/imath]

 

If the object has an intrinsic luminosity [imath]L[/imath] and we receive a flux [imath] \varrho[/imath], then:

 

[math] d_L=\sqrt{\frac{L}{4\pi{\varrho}}} [/math]

 

In a time [imath]dt`[/imath] it emits an energy [imath]Ldt`[/imath]. This energy is redshifted to the present by a factor [imath]R(t_1)/R_0[/imath], and is now distributed over a sphere of proper area [imath]4\pi(r_1R_0)^2[/imath], thus:[imath] \varrho=(Ldt`R/R_0)(4{\pi}r_1R_0)^{-2}/dt[/imath] and [imath] d_L={R_0}^2r_1/R(t_1)[/imath] Using [imath]R_0/R(t_1)=1+z[/imath], we have now obtained:

 

[math] (1+z)^2d_A=(1+z)d_M=d_L[/math]

 

 

Obviously much comes before this and much after before reaching Sam's equation 2, but equation 1 (written slightly different above) is used in getting [imath]d_L=(1+z)^2d_A=(1+z)d_M[/imath] which is then used in the SN 1a interpretation.

 

Would anyone like to support this derivation? I'm feeling out of my depth for sure.

 

-modest

[coldcreation]

...The proposed new solution is also a solution of the Friedmann-Lemaitre metric. I have not presented the new solution to the metric yet. I am also preparing lectures for next week. Be a little patient.

 

I wish I had patients. :doh:

 

“Patience is the companion of wisdom." (Saint Augustine)

 

"Patience is bitter, but it bears sweet fruit." (Turkish proverb)

 

“The key to everything is patience. You get the chicken by hatching the egg, not by smashing it.” (Arnold H. Glasgow)

 

“Patience serves as a protection against wrongs as clothes do against cold. For if you put on more clothes as the cold increases, it will have no power to hurt you. So in like manner you must grow in patience when you meet with great wrongs, and they will be powerless to vex your mind.” (Leonardo da Vinci)

 

"I have little patience with scientists who take a board of wood, look for its thinnest part, and drill a great number of holes where drilling is easy.” (Albert Einstein)

 

 

...If the Universe really was static there would be no redshift due to the expansion of space.

 

Obviously, if the universe was non-expanding (static) there would be no redshift due to the expansion of space: it would be due to something else.

 

I wouldn't assume the stationary model is false simply because a proof or argument offered thus far is invalid; this reasoning would be fallacious because there may be another proof or argument (based on empirical evidence) that successfully supports an alternative interpretation for redshift z.

 

 

Since redshift is observed (and IMHO is correctly interpreted as due to spatial expansion),...

 

Yes, redshift is observed. But how is it determined unambiguously that z is "correctly interpreted as due to spatial expansion"? It seems the possibility should be left open, in light of the SNe Ia data, that the observed décalage toward the less refrangible end of the spectrum and time dilation could have an origin entirely unrelated to spatial expansion.

 

Indeed, the fractional amount by which features in the spectra of astronomical objects are shifted to longer wavelengths may be due to the general relativistic phenomenon of globally curved spacetime, ie., an interpretation founded on the concept that the large-scale geometrical structure of the four-dimensional spacetime continuum is non-Euclidean (as seen from our frame of reference). This is the model that needs to be tested against observation.

 

Clearly, the SNe Ia data indicates a large deviation from linearity for which a viable metric remains to be found.

 

The fact that objects appear globally more redshifted the further they are from our observational platform (interpreted as expansion) and the new unexpected discovery of the dimness of early SNe Ia giving the impression they are further away than their redshifts indicate (today interpreted as an acceleration) incites a new broad-spectrum approach in the investigation and interpretation of redshift z. My contention is that the spectral line shifts should be attributed and treated as a Doppler-like effect (due to a change in the scale factor to the metric) only after the other possibility is excluded on observational grounds.

 

 

... the static-universe energy-flux equation is not the correct form of the equation to use.

 

What would be the correct form of the equation to use?

 

 

 

 

 

CC

[bigsam1965]

All physics is contingent and a healthy amount of skepticism is always wise. Other explanations are possible, although all of the alternative explanations I have seen have problems (see Ned Wright's website). I have remained conservative in my critique of the standard model. Remaining within the context of the general class of Friedmann-Lemaitre solutions, I noticed a problem with the standard model use of the energy-flux equation. When I corrected the problem, the resulting Friedmann-Lemaitre solution is in agreement with three areas of physical observation. IMHO this has stengthened the case for the Big Bang .

 

 

What would be the correct form of the equation to use?

 

CC

 

For conservation of photon energy as space expands and a coasting universe the correct energy-flux equation should be

 

[math]F=L/4{\pi}D^2=L_0(1+z)^{-1}/[4{\pi}(c{H_0}^{-1}z)^2][/math]

 

Dividing the energy-flux equation by the reference energy flux, then taking the log of the energy-flux ratio, then multiplying by -2.5 leads to Equation (4) in the original post.

[Little Bang]

Ok I have a question. Let's assume for this question that the universe is expanding at C and that Z is the result of that expansion. Would there be a way that we could determine the rate of change of the wave length over time. EMR in the early universe would be 10^googleplex Hertz. Over X amount of time let's say it would be 10^100. Could we determine the rate of change?