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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.) -- Help keep our newsgroup healthy; please don't feed the trolls. Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA |
#12
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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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