Age of the Universe Guide, Meaning , Facts, Information and Description
The age of the Universe was estimated to be about 13.7 billion (13.7 × 109) years, with an uncertainty of 200 million years, by NASA's Wilkinson Microwave Anisotropy Probe project (WMAP). However this is based on the assumption that the underlying model that was used is correct. Other methods of estimating the age of the universe give different ages.Some recent studies, found the carbon-nitrogen-oxygen cycle to be two times slower than previously believed, leading to the conclusion that the Universe must be at least 14.7 billion years old.
The often quoted age of 13.7+/-0.2 Gyr for the age of the universe comes from the first year WMAP results: This measurement is made by using the location of the first acoustic peak in the microwave background power spectrum to determine the size of the decoupling surface (size of universe at the time of recombination). The light travel time to this surface (depending on the geometry used) yields a pretty good age for the universe. Assuming all the various models used are valid in getting to this number, the accuracy of actual data allows a margin of error around 1%.
However, this age is only accurate if the assumptions built into the various models being used are also accurate. This is referred to as strong priors and essentially involves stripping the potential errors in other parts of the model to render the accuracy of actual observational data directly into the concluded result. Although this is not a totally invalid procedure in certain contexts, it should be noted that the caveat, "based on the fact we have assumed the underlying model we used is correct", then the age given is thus accurate to the specified error (since this error represents the error in the instrument used to gather the raw data input into the model).
The age of the universe based on the "best fit" to WMAP data "only" is 13.4+/-0.3 Gyr (the slightly higher number of 13.7 includes some other data mixed in). This number represents the first accurate "direct" measurement of the age of the universe (other methods typically involve Hubble's law and maximum age of stars, etc). There is a sense of triumphantism in the scientific community surrounding results like this, and therefore a more careful analysis of the methods and assumptions used, tend to be overlooked.
This, of course, is a classic example of how different methods for determining the same parameter (in this case – the age of the universe) can give different answers with no overlap in the "errors". It is quite common to see two sets of uncertainties, one related to the measurement and other the related to the systematic errors of the model. In some cases, this can not be done.
The redshift of an object in a dynamic universe is related to a scale factor of that universe by the relation . Where represents the “scale” of the universe as seen at the redshift z, where the current scale is . The “scale” is just a device to measure the size of the universe, it can be thought of as the radius, but most people use the "scale factor" , which would be dimensionless regardless of how you represented .
The temperature of the universe is inversely proportional to its scale; somewhat analogous to a gas that would cool down if expanded, or heat up if compressed, the temperature of the universe is thus related to redshift as T=To(1+z). We can do a quick test by using the current temperature of 2.7K and the redshift of CMB as 1089 to calculate the temperature of the decoupling surface (this is the temperature of the universe when the CMB was emitted - around the dull red glow of a hot poker.)
One of the most important cosmological models is based on the Friedmann equations. This allows us to describe how the universe has evolved over time using an equation like this: . As you can see, things are starting to get a bit more tricky, but this equation simply relates the age of the universe to the redshift. This particular example has an additional term w, which comes from something called the equation of state, relating the pressure and density of the universe (p=wdc^2, where p is pressure, d is density and c^2 is the speed of light squared).
In a universe like our own, most of the contents is in the form of stuff that does not exert much pressure on its surroundings (clouds of hydrogen gas, stars etc). In this model, w=0 and is known as a pressureless, or "dust" model. Here , and throwing in our redshift of 1089 and a current age of the universe Gyr gives us around 380,000 years for the age of the universe when the CMB was emitted. This may not seem so tricky after all, but unfortunately, it is not quite that simple.
Embedded in these models is an assumption about time and an interpretation of metric distance which is not entirely correct. That is not to say that they are entirely wrong either: The metric distance defined between two points in an expanding universe increases over time. However, the General Theory of Relativity does not explicitly state how that change in distance should be interpreted. It is entirely valid to consider this change as a fundamental change in the underlying “concept” of distance (and the same situation would also apply to the concept of time).
This type of model immediately solves an important problem relating to our CMB calculation above. If the photons in the CMB went from being hot enough to fry a burger, how come those same photons can't even defrost one today? Where did all that energy go? Of course, this comes back to our idea of the change in the distance scale: The universe expands by a change in the unit system, so the temperature likewise changes with the unit system. In this context, the dimentionless temperature/scale of the universe can be thought of as being constant over the history of the universe, with no loss of energy in the CMB, just a change in the unit system.
Things do start to get technical here, but there is a nice confirmation of this model which actually validates it against recent observations. Coming back to the math, the change in the distance is related to time with the redshift relation . However, there is an additional change in time related to redshift as , which (the product of both) brings us back to the original form for our "dust" w=0 universe. The idea of time-variable time probably sounds bizarre, but this is expected since there is no "absolute" concept of time in General Relativity.
So this was a very round about way of saying that we can relate the temperature of the universe to the age of the universe. Since we can measure the current temperature and have a model to extrapolate back, all we need to know now is the origin of the graph and read off the age. The earliest valid point in the evolution of the universe is the Planck time. At this time, the universe had the Planck temperature at a state of essentially zero entropy. The Planck temperature is the maximum attainable temperature in the universe and can be thought of as the Hawking temperature of black hole with a radius of the Planck length.
The Planck temperature Tp comes out to around K, and we can state , where K and is the maximum redshift at the Planck time . We know that , so putting in the Planck time gives us an age of the universe of 11.667 Gyr. This is not the end of the story however: If time was absolute and never changed, then this would be the correct value, but we need to take into consideration the change in time over the age of the universe. This is a fairly simple integration and results in a age one third as much at 15.556 Gyr. The CMB temperature is known to a 2mK accuracy, and with some error in things like the Planck units (mainly from G), the accuracy of this age determination is around 24 Myr.
There is a simplification where if expressed in Planck units, the age (to/tp) is equal to the inverse square of the temperature (To/Tp) of the universe. Dividing To/Tp gives the current temperature expressed in the amount of the Planck temperature . Taking the inverse square gives which is the age in Planck units. Multiplying by the Planck time gives the 11.667 Gyr again. There are many other simple relations like this one, including the critical density as the Planck temperature raised to the forth power. In Planck units, the critical density is , which when multiplied by the Planck density gives g/cm^3.
This is an Article on Age of the Universe. Page Contains Information, Facts Details or Explanation Guide About Age of the Universe Calculation of the age from the temperature of the universe
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