
#145
Mar1812, 09:59 AM

P: 991

Cosmology scale factor equation: [tex]\frac{R_u(t_0)}{R_u(t)} = \frac{a(t_0)}{a(t)} = \frac{T_t}{T_0} = 1 + z[/tex] Universe total observable radius: [tex]R_u(t_0) = 4.399 \cdot 10^{26} \; \text{m}[/tex] Cosmic neutrino background radiation temperature at present: [tex]T_0 = 1.95 \; \text{K}[/tex] Cosmic neutrino background radiation temperature at neutrino decoupling time t: [tex]T_t = 1 \cdot 10^{10} \; \text{K}[/tex] [tex]R_u(t) = R_u(t_0) \left( \frac{T_0}{T_t} \right) = 4.399 \cdot 10^{26} \; \text{m} \times \left( \frac{1.95 \; \text{K}}{1 \cdot 10^{10} \; \text{K}} \right) = 8.578 \cdot 10^{16} \; \text{m}[/tex] Universe total observable radius at neutrino decoupling time t: [tex]\boxed{R_u(t) = 8.578 \cdot 10^{16} \; \text{m}}[/tex] Reference: Total amount of energy in the Universe  Orion1 #13 Timeline of the Big Bang  Hadron epoch  Wikipedia Neutrino_decoupling  Wikipedia Cosmic neutrino background  Wikipedia Red shift  Highest redshifts 



#146
Mar1812, 01:33 PM

P: 255





#147
Mar1812, 01:58 PM

P: 6

The rate of expansion (hubble constant) of the universe is equivalant to the sun moving 3/4 of a mile farther away in 100 years. Do the math. The solar wind adds solar particles to the solar system and universe. This causes distant objects to appear ever more distant as space becomes more opague. Space is not empty as recent articles have stated.




#148
Mar1812, 03:49 PM

P: 255





#149
Mar1812, 10:03 PM

P: 526

First of all, recessional velocity on large scales requires a frame of reference. The distance from this FoR is then multiplied by a scale factor, Hubble's constant. This is shown by Hubble's law: [tex]V=H_{0}D[/tex] Also, expansion only effects very large objects, such as galaxies or super clusters, not the Sun. Second, Hubble's constant is estimated by WMAP to be 70.8 ± 1.6 (km/s)/Mpc. So, an object that is very far away will appear to have an extremely high recessional velocity, your calculation was completely made up, and had no basis whatsoever. Also, the cosmic microwave background provides conclusive evidence the universe is expanding and cooling. 



#150
Mar1912, 03:18 AM

P: 255





#151
Mar1912, 11:25 AM

P: 526

Obviously, someone forgot to tell him that Hubble's law is only used for objects affected by the expansion of space. 



#152
Mar1912, 03:28 PM

P: 255

On a more practical note, I did some work on the Pioneer Anomaly many years ago and although the sign was obviously wrong, I calculated the effect of the Hubble flow when they were proposing a followup mission. It turns out to be only about an order of magnitude less than the anomaly so it might be possible to measure it with a carefully designed mission. 



#153
Mar2012, 06:47 AM

P: 991

Cosmology scale factor equation: [tex]\frac{R_u(t_0)}{R_u(t)} = \frac{a(t_0)}{a(t)} = \frac{T_t}{T_0} = 1 + z[/tex] Universe total observable radius: [tex]R_u(t_0) = 4.399 \cdot 10^{26} \; \text{m}[/tex] Cosmic gravitational wave background redshift at present: [tex]z \geq 10^{25}[/tex] [tex]R_u(t) \leq \frac{R_u(t_0)}{1 + z} = \frac{4.399 \cdot 10^{26} \; \text{m}}{1 + 10^{25}} = 43.99 \; \text{m}[/tex] Universe total observable radius at gravitational wave decoupling time t: [tex]\boxed{R_u(t) \leq 43.99 \; \text{m}}[/tex] Reference: Cosmic microwave background radiation  Wikipedia Cosmic inflation  Wikipedia Timeline of the Big Bang  Inflationary epoch  Wikipedia Cosmic gravitational wave background  Wikipedia Red shift  Highest redshifts 



#154
Mar2512, 04:14 PM

P: 991

The the LCDM model scale factor is defined as: [tex]a(t) = \left[ \frac{\Omega_m}{\Omega_v} \sinh^2 \left( \frac{3}{2} \sqrt{\Omega_v} H_0 t \right) \right]^{\frac{1}{3}}[/tex] Differentiating the scale factor function with respect to t: [tex]\frac{d a(t)}{dt} = \frac{d}{dt} \left[ \frac{\Omega_m}{\Omega_v} \sinh^2 \left( \frac{3}{2} \sqrt{\Omega_v} H_0 t \right) \right]^{\frac{1}{3}} = \frac{ \Omega_m H_0 \cosh \left(\frac{3}{2} \sqrt{\Omega_v} H_0 t \right) \sinh \left(\frac{3}{2} \sqrt{\Omega_v} H_0 t \right)}{\sqrt{\Omega_v} \left(\frac{\Omega_m \sinh^2 \left(\frac{3}{2} \sqrt{\Omega_v} H_0 t \right)}{\Omega_v} \right)^{2/3}}[/tex] The scale factor derivative function: [tex]\boxed{\frac{d a(t)}{dt} = \frac{ \Omega_m H_0 \cosh \left(\frac{3}{2} \sqrt{\Omega_v} H_0 t \right) \sinh \left(\frac{3}{2} \sqrt{\Omega_v} H_0 t \right)}{\sqrt{\Omega_v} \left(\frac{\Omega_m \sinh^2 \left(\frac{3}{2} \sqrt{\Omega_v} H_0 t \right)}{\Omega_v} \right)^{2/3}}}[/tex] Is this equation correct? Attachments: plot a(t), plot a'(t) Reference: LambdaCDM geometry  mathematical details  Wikipedia 



#155
Mar2512, 04:47 PM

P: 255

I'm not good enough at the math to quickly check your solution but I believe there is no analytic solution when there is more than one phase involved. The graph is initially matter dominated but becomes energy dominated so I think you have to perform an integration to get the curve.
However, the section "mixtures" here suggests it can be solved: http://en.wikipedia.org/wiki/Friedma...eful_solutions The "Lecture notes on Astrophysics" looks comprehensive too, though beyond my level. 



#156
Mar2612, 02:04 PM

P: 29

i was thinking about light.
a particle and/or a wave ? but what about darkness.? does darkness move at the speed of light? does light move at the speed of darkness? does light really bend around corners or is it pulled around by darkness? in a dark universe, does the universe expand when light appears? does light "push" darkness away ? but what if the universe is in a "bubble"? would the darkness get squashed? is light a constant in the universe.? does the universe expand at different speeds at different times depending on how much is being added at that particular time? 



#157
Mar2612, 05:19 PM

PF Gold
P: 11,047

http://en.wikipedia.org/wiki/Universe http://en.wikipedia.org/wiki/Physical_cosmology 



#158
Mar2612, 05:40 PM

P: 29

darkness is nothing but the absence of light..... ooosh so what came first, the darkness or the light? but i thought we knew or at least thought ,that there is no such thing as nothing 



#159
Mar2612, 06:52 PM

PF Gold
P: 11,047





#160
Mar2712, 07:42 AM

P: 991

These are the scale factor equations that I reviewed from reference 1 and 2. Inflation Hubble parameter (end of inflationary epoch): 'ref. 1 p. 34 (167)' [tex]H_i = \frac{1}{t_{i}} = \frac{1}{10^{32} \; \text{s}} = 10^{32} \; \text{s}^{1}[/tex] [tex]\boxed{H_i = 10^{32} \; \text{s}^{1}}[/tex] Inflation scale factor: 'ref. 1 p.35 (165)' [tex]a(t) \propto e^{H_i t} \tag{1}[/tex] Radiation scale factor: 'ref. 1 p. 22 (119)' [tex]a(t) = (2 H_0)^{\frac{1}{2}} \cdot t^{\frac{1}{2}} \tag{2}[/tex] Matter scale factor: 'ref. 1 p. 21 (115)' [tex]a(t) = \left( \frac{4 H_0}{2} \right)^{\frac{2}{3}} \cdot t^{\frac{2}{3}} \tag{3}[/tex] LCDM matter scale factor: 'ref. 2' [tex]a(t) = \left[ \frac{\Omega_m}{\Omega_v} \sinh^2 \left( \frac{3}{2} \sqrt{\Omega_v} H_0 t \right) \right]^{\frac{1}{3}} \tag{4}[/tex] Equations 2 and 3 appear to be describing a universe that is much younger. Attachments: plot 1, plot 2,3,4 Reference: Friedmann equations  useful solutions  Wikipedia Northern Illinois University  Physics 652  Astrophysics LambdaCDM  geometry  mathematical details  Wikipedia 



#161
Mar2712, 09:46 AM

P: 29

if light was more abundant than darkness at the start where as the reverse is true now, am i to believe then that the universe is getting smaller? what if it was expanding and contracting i ask about light "pushing" darkness (light pressure) clearing a path . so if we had darkness first with energy, then light energy appears,room has to be made for this light. could light then clear this "room" creating a vacuum redundant of energy once this light has lost its energy and gone..this then takes time to rebuild itself with dark energy matter, un til it over crowds sparking another light source and repeats the process. this would mean light energy is finite but that does not mean the universe cannot expand.. i could be way off and have no idea what im on about.but ive read some say that the universe is expanding fast than light... how do we measure this.do we measure it with light? if light is "pushing" then light will always be behind therefore it could be seen that anything infront of it is moving fast when really its not 



#162
Mar2712, 12:07 PM

P: 255




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