Confirmed cosmological time dilation z+1 from 8.7 bln years ago to 1.3 bln years ago

[Maksimiusz]

The Dark Energy Survey Supernova Program: Slow supernovae show cosmological time dilation out to z∼1
https://arxiv.org/html/2406.05050v1

Quote

We present a precise measurement of cosmological time dilation using the light curves of 1504 type Ia supernovae from the Dark Energy Survey spanning a redshift range 0.1≲z≲1.2. We find that the width of supernova light curves is proportional to (1+z), as expected for time dilation due to the expansion of the Universe.

Their redshift range corresponds to the universe age approximately from 8.7 bln years ago to 1.3 bln years ago. Cosmic time dilation is equal to z+1 or its reciprocal depending on whether we measure the past universe dilation with respect to us or the opposite. It’s not like the time dilation equal to Lorentz factor for both the observers moving with relative velocity.

This post is for all deniers of z+1 and 1/(z+1) cosmological time dilation formula.

Edited November 17 by Maksimiusz

[Maksimiusz]

Photon's wave period extends by the same factor as its length. Time dilation is the expansion of time. The problem with FLRW metric is that it doesn't take cosmic time dilation into account. For null geodesic, that is for a photon with no proper time the metric is [math]0 = -(cdt)^2+(a(t)dr)^2[/math]. The second term [math]a(t)dr[/math] is the equivalent of the expanding wavelength. [math]dt[/math] has to be multiplied by the same factor [math]a(t)[/math] to apply the cosmic time dilation. [math]a(t)dt[/math] is the equivalent of the extending wave period. As a consequence we have [math]0 = -(a(t)cdt)^2+(a(t)dr)^2[/math] which is the Minkowski metric for a photon after dividing the equation by [math]a(t)[/math], so [math]0 = -(cdt)^2+(dr)^2[/math] gives [math]cdt=dr[/math] that gives [math]ct=r[/math]. That's Hubble radius for the universe age. How do you like it as the observable universe radius as a result of the appliance of cosmic time dilation to FLRW metric?

Edited November 17 by Maksimiusz

[Mordred]

something tells me your a sockpuppet but just in case its already been shown there is relations between cosmological redshift and time dilation however they won't be accurate without corrections beyond Hubble Horizon you need to employ further corrections as the (1+z) relation is only accurate in the near field.

[Maksimiusz]

Quote

There is no formula for cosmological time dilation not any SR based formula pure and simple.

I am a sockpuppet and you are totally Full of Shit @Mordred.

[Mordred]

yep thanks for confirming thread reported you still fail to understand you cannot apply SR over the entire global metric beyond Hubble horizon.

Edited November 17 by Mordred