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Is it possible?



 
 
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  #11  
Old May 24th 14, 01:44 PM posted to sci.astro.research
Steve Willner
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Posts: 1,172
Default Is it possible?

In article ,
Phillip Helbig---undress to reply writes:
Consider the de Sitter universe, which has a cosmological
constant and no matter. The expansion law is exponential, i.e. the
acceleration increases with time. Since the Hubble constant is
dr/dt*1/R, it is constant in time. The parameter q is constant at -1.
It is defined as \frac{-\ddot R R}{\dot R^{2}} or
\frac{-\ddot R}{RH^{2}}. Since H is constant in time, \ddot R must
increase with time in proportion to R. So, of course, as with any
exponential, all derivatives are exponential.


Does this mean the acceleration is constant for a given metric
distance?

(Thanks for the study references, by the way.)

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  #12  
Old May 25th 14, 08:29 AM posted to sci.astro.research
Phillip Helbig---undress to reply
external usenet poster
 
Posts: 629
Default Is it possible?

In article , Steve Willner
writes:

In article ,
Phillip Helbig---undress to reply writes:
Consider the de Sitter universe, which has a cosmological
constant and no matter. The expansion law is exponential, i.e. the
acceleration increases with time. Since the Hubble constant is
dr/dt*1/R, it is constant in time. The parameter q is constant at -1.
It is defined as \frac{-\ddot R R}{\dot R^{2}} or
\frac{-\ddot R}{RH^{2}}. Since H is constant in time, \ddot R must
increase with time in proportion to R. So, of course, as with any
exponential, all derivatives are exponential.


Does this mean the acceleration is constant for a given metric
distance?


I think so, if by metric distance you mean proper distance.

In the de Sitter model, the Hubble sphere (where the rate of increase of
proper distance equals the speed of light) is at a fixed proper
distance. Since all derivatives are proportional to distance for
exponential expansion, I think this means that the acceleration (and all
other derivatives) are constant for a given proper distance.

In general, the size of the Hubble sphere changes with time, because the
Hubble constant changes with time. In the de Sitter model, the Hubble
constant is constant in time.

Recall that the metric of the Steady State universe is the same as the
de Sitter universe; the only difference is that the density of matter is
constant in the Steady State model whereas it thins out with expansion
in the de Sitter model. Since by construction nothing changes with time
in the Steady State model, this implies that acceleration would be
constant in time for a given proper distance.
 




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