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Parvulus
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This replaces my early post about "variable G" (no such thing).
My point was (and is): setting the Hubble constant H(t) = 1 /t by ansatz, thus matching current observations that H(to) to = 1, has the consequence that the scale factor varies linearly with t.
a(t) = a(to) (t / to)
The resulting formula for luminosity distance as function of redshift:
DL = RH(to) (1 + z) Ln(1 + z)
where RH(to) = c / H(to) is the current Hubble radius, is a very good match to observations of SN Ia.
Now, a linear a(t) implies that the Friedmann equation does not hold (wrong), or that G varies linearly with t (wrong), or that both total density and the cosmological constant are zero and so the Friedmann equation becomes:
[da(t)/dt]^2 = -k c^2
with k = -1 for an open universe. The empty open universe is usually called Milne universe.
And here is the key (idea not mine, but from the papers below): at large scales (which is where the FRW metric holds) the net density gravitationally-wise can be zero if:
- there are even quantities of matter and antimatter, and
- antimatter has negative active and passive gravitational mass with respect to matter, and viceversa.
That is, matter attracts matter, antimatter attracts antimatter, matter and antimatter repel. Matter and antimatter thus have formed an "emulsion" over large scales so that the net gravitational mass and density is zero.
Benoit-Lévy, A. and Chardin, G. "A symmetric Milne Universe : A second concordant Universe?" SF2A-2008: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics Eds.: C. Charbonnel, F. Combes and R. Samadi. Available online at http://proc.sf2a.asso.fr , p.347, or
http://ozone.obspm.fr/~sf2a/proc2008/contrib/2008sf2a.conf..0347B.pdf
Benoit-Lévy, A. and Chardin, G. "Observational constraints of a Milne Universe". arXiv:0811.2149
My point was (and is): setting the Hubble constant H(t) = 1 /t by ansatz, thus matching current observations that H(to) to = 1, has the consequence that the scale factor varies linearly with t.
a(t) = a(to) (t / to)
The resulting formula for luminosity distance as function of redshift:
DL = RH(to) (1 + z) Ln(1 + z)
where RH(to) = c / H(to) is the current Hubble radius, is a very good match to observations of SN Ia.
Now, a linear a(t) implies that the Friedmann equation does not hold (wrong), or that G varies linearly with t (wrong), or that both total density and the cosmological constant are zero and so the Friedmann equation becomes:
[da(t)/dt]^2 = -k c^2
with k = -1 for an open universe. The empty open universe is usually called Milne universe.
And here is the key (idea not mine, but from the papers below): at large scales (which is where the FRW metric holds) the net density gravitationally-wise can be zero if:
- there are even quantities of matter and antimatter, and
- antimatter has negative active and passive gravitational mass with respect to matter, and viceversa.
That is, matter attracts matter, antimatter attracts antimatter, matter and antimatter repel. Matter and antimatter thus have formed an "emulsion" over large scales so that the net gravitational mass and density is zero.
Benoit-Lévy, A. and Chardin, G. "A symmetric Milne Universe : A second concordant Universe?" SF2A-2008: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics Eds.: C. Charbonnel, F. Combes and R. Samadi. Available online at http://proc.sf2a.asso.fr , p.347, or
http://ozone.obspm.fr/~sf2a/proc2008/contrib/2008sf2a.conf..0347B.pdf
Benoit-Lévy, A. and Chardin, G. "Observational constraints of a Milne Universe". arXiv:0811.2149
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