I came across Ned Wright's webpage(adsbygoogle = window.adsbygoogle || []).push({});

http://www.astro.ucla.edu/~wright/tiredlit.htm which states that

alternative explanations for the redshift of galaxies would not be

consistent with the z-dependence of supernova lightcurves. However,

this assertion is not further substantiated and as far as I can see

any wavelength independent redshift mechanism should indeed result in

the change of the supernova lightcurves:

Consider a sinusoidal lightwave modulated by a lightcurve L(t), i.e.

E(f,t)=E0*sin(f*t)*L(t) .

By expanding L(t) into a Fourier Integral i.e.

L(t)= Int[dF*cos(F*t)*a(F)]

and drawing the sine function under the integral one gets

E(f,t)=E0* Int[dF*sin(f*t)*cos(F*t)*a(F)].

Using the addition theorems for trigonometric functions, this is

equivalent to (apart from a constant factor)

E(f,t)=E0* Int[dF*(sin((f+F)*t) + sin((f-F)*t)*a(F)].

Applying now a redshift factor (1+z) changes the frequencies to

(f+F)/(1+z) and (f-F)/(1+z), i.e. the signal becomes

E(f,t,z)=E0* Int[dF*(sin((f+F)/(1+z)*t) + sin((f-F)/(1+z)*t) *a(F)],

and by reversing the addition theorem and taking the sine- function

out of the integral again

E(f,t,z)=E0* Int[dF*sin(f/(1+z)*t)*cos(F/(1+z)*t)*a(F)] =

= E0*sin(f/(1+z)*t)* Int[dF*cos(F/(1+z)*t)*a(F)] =

= E0*sin(f/(1+z)*t)*L(t/(1+z)).

This means that not only is the wave frequency redshifted but also the

light curve broadened.

For anyone intererested, I have myself suggested that the redshift of

galaxies is in fact caused by the small scale electric field due to

the intergalactic plasma (a kind of counter-part to the Faraday

-rotation in a magnetic field) (for more details see

http://www.plasmaphysics.org.uk/research/#A11).

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# Redshift Mechanisms and Supernova Lightcurves

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