Age of our Universe (Hubble's law)

[nuwan]

Hey Im a Physics Student doing Ma Edexcel GCE Als. I came accross a problem under cosmology In the txt book they hav given a equation for the age of the universe using the hubble constant .

 

 

By rearranging hubbles law (V=Hod) they have come up

with the equation

 

1/Ho =time of the universe

 

 

 

what I want to know is whether this correct if it is correct then Ho is a constant Ho= 2.3 * 10^-18.

If we calculate the age of the universe using this equation today and after 1000 years if we do the same there want be a age difference how could this be is the hubble constant changing or is there some thing wrong with the equation

 

name of the Book is Physics for A2 By Tim Akrill And Graham George

Publisher Hodder Education

Endorsed by Edexcel

 

Im realy looking forward For An answer

 

:-)

[ajb]

One over the Hubble constant gives you a reasonable answer to the age of the Universe. It gives a scale to the expansion.

 

It is of course idealised.

 

You can improve a little on this by taking into account some of the details of the Universe. For a flat matter dominated Universe we have the age as [math]\frac{2}{3 H_{0}}[/math].

 

One can also make more general statements than this, but they are all like [math]\propto \frac{1}{H_{0}}[/math].

 

Now "Hubble's constant" is confusing if not poor nomenclature. It is not really a constant as such, [math]H_{0}[/math] refers of the Hubble parameter today, which is constant by definition. It will be different in the future as it was in the past, but not by a measurable amount on the time scale you suggest.

[Spyman]

The ‘ultimate fate’ and age of the universe

 

The value of the Hubble parameter changes over time either increasing or decreasing depending on the sign of the so-called deceleration parameter q which is defined by

 

[math]q=-(1+ \frac{\dot{H}}{H^2})[/math] .

 

In a universe with a deceleration parameter equal to zero, it follows that H = 1/t, where t is the time since the Big Bang. A non-zero, time-dependent value of q simply requires integration of the Friedmann equations backwards from the present time to the time when the comoving horizon size was zero.

It was long thought that q was positive, indicating that the expansion is slowing down due to gravitational attraction. This would imply an age of the universe less than 1/H (which is about 14 billion years). For instance, a value for q of 1/2 (once favoured by most theorists) would give the age of the universe as 2/(3H). The discovery in 1998 that q is apparently negative means that the universe could actually be older than 1/H. However, estimates of the age of the universe are very close to 1/H.

http://en.wikipedia.org/wiki/Hubble%27s_law

[cosmos0]

13.7 billion years (1/Ho) is the distance to the Hubble sphere.. the age of the Universe has to be recalculated..

 

Let me explain. If the recession speed due to space expansion exceeds the speed of light, the photon would never reach the observer, this is why there exists a horizon of the visible Universe (the Hubble sphere), beyond which light would never reach us. Historically the age of the Universe was computed from the loockback time between a redshift zero and infinity, which yields 1/Ho. Note that this measure gives the lookback time to the Hubble sphere because the redshift must converge towards infinity at the horizon of the visible Universe. Here is a reference showing the calculations with a De Sitter Universe (http://www.jrank.org...-back-time.html). Another reference where the age of the Universe is computed with the look-back time between a redshift of zero and infinity: http://www.mpifr-bon...DiplWebap1.html. See A.36 et A.37.

 

Using another approach we can show that an apparently steady Hubble coefficient in the light travel distance framework is equivalent to a time-varying Hubble coefficient in the Euclidean framework of order two (i.e. Universe expanding at a steady acceleration pace). This approach gives an age of the Universe of about 20-25 billion years. This figure is compatible with the age of the Universe obtained from the datation of old stars. According to Chaboyer (1995) who analysed metal-rich and metal-poor globular clusters, the absolute age of the oldest globular clusters are found to lie in the range 11-21 Gyr. Bolte et al. (1995) estimated the age of the M92 globular cluster to be 15.8 Gyr. Th/Eu dating yields stellar ages of up to 18.9 Gyr (Truran et al., 2001). A paper describing this appoach is available online: http://fr.calameo.co...33338c183febd92

Edited June 30, 2011 by cosmos0

[csmyth3025]

Posted 7 June 2010 - 12:36 PM

 

Hey, I'm a Physics Student doing Ma Edexcel GCE Als. I came across a problem under cosmology. In the text book they have given an equation for the age of the universe using the Hubble constant .

 

 

By rearranging Hubble's law (V=H_od) they have come up

with the equation

 

1/H_o= time of the universe

 

 

 

What I want to know is whether this correct. If it is correct, then H_o is a constant: H_o= 2.3 * 10^-18.

I have to admit that despite the explanations given in the replies to the OP cited above I'm still not sure what the SI value of H_o means.

 

As I understand it, the Hubble parameter today is given as approximately 71 km/s per Mpc, although the value ranges:

 

NASA's WMAP site summarizes existing data to indicate a constant of 70.8 ± 1.6 (km/s)/Mpc if space is assumed to be flat, or 70.8 ± 4.0 (km/s)/Mpc otherwise...

(ref. http://en.wikipedia..../Hubble%27s_law )

 

A parsec is given as:

 

For studies of the structure of the Milky Way, our local galaxy, the parsec (pc) is the usual choice. This is equivalent to about 30.857×10¹² km

(ref. http://www.iau.org/public/measuring/ )

 

Thus, a Mpc (a million parsecs) would be equal to 30.857 x 10¹² km x 10⁶ = 3.0857 x 10¹⁹ km.

 

Accordingly, the inverse of the Hubble parameter would be:

 

(3.0857 x 10¹⁹ km) / (71 km/s)= 0.04346 x 10¹⁹s = ~4.35 x 10¹⁷s or about 13.8 billion years - which is the approximate age of the universe.

 

This much I understand.

 

What has me scratching my head is the reciprocal of this number: 2.3 x 10^-18/s. What does this number tell you? Does it tell you by how much, on average, each unit of measure (meters, kilometers, or light years) increases each second from the beginning of the universe to the present day?

 

It's understood, of course, that this factor would only apply to distant objects that are not gravitationally bound.

 

Chris

 

Edited to add last sentence.

Edited July 11, 2011 by csmyth3025