Current value of the scale factor(R₀)?

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Discussion Overview

The discussion centers around the current value of the scale factor (R₀) in cosmology, exploring its definition, implications, and the conditions under which it can be determined. Participants engage in a technical examination of the scale factor's role in cosmological models.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asks for the current value of the scale factor (R₀) and provides the relationship a = R(t)/R₀.
  • Another participant clarifies that R₀ is defined as the value of R(t) at time t=0, suggesting that more information is needed to provide a specific number.
  • Some participants assert that at the current epoch, R(t) equals R₀, implying that the scale factor is normalized to 1 at the present time.
  • There is a suggestion that the scale factor is arbitrary and can be adjusted depending on the cosmological model being used.
  • A participant presents a formula for R₀ that depends on the curvature of the universe and various density parameters, indicating that if the universe is not spatially flat, R₀ can be calculated using specific cosmological parameters.
  • Conversely, if the universe is spatially flat, R₀ is described as arbitrary.

Areas of Agreement / Disagreement

Participants express differing views on the nature of R₀, with some asserting it is arbitrary while others provide specific conditions under which it can be calculated. The discussion remains unresolved regarding a definitive value for R₀.

Contextual Notes

The discussion highlights the dependence of R₀ on cosmological parameters and the assumptions regarding the geometry of the universe, which remain unresolved.

EhsanZ
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What is the current value of the scale factor(R₀)?

a= R(t)/R₀

Give me the number.
 
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R0 is the value of R(t) at t=0.
Apart from that, need more information.
 
Since a = R(t)/R0, and we normalise to the current epoch, right now, R(t) = R0
 
<headslap> cosmology forum!
 
Sorry, is that directed at me?
 
No - I don't slap anyone elses head unless there is some sort of contractual obligation.
See post #2 ... mumble mumble I suppose had I shut up people would think I was being clever?
 
e.bar.goum said:
Since a = R(t)/R0, and we normalise to the current epoch, right now, R(t) = R0

Number?
 
It's a scaling factor, there isn't one. Maybe if you be more specific with your problem, we can help you. You can arbitrarily change it depending on your cosmology.
 
If the universe is not (spatially) flat, then

[tex]R_0 = \frac{c}{H_0} \sqrt{\frac{k}{\Omega_{m,0} + \Omega_{r,0} + \Omega_{\Lambda,0} - 1}}.[/tex]
If the universe is (spatially) flat, then [itex]R_0[/itex] is arbitrary.
 

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