Cosmology - The Expanding Universe

The Hubble Redshift

In the early 1900’s, the state of the art telescope, Mt Wilson, a 100-inch telescope, was the biggest telescope then. Hubble was one of the prominent scientists, who worked with that telescope. He discovered there were galaxies outside the Milky Way. Extragalactic Astronomy is only 100 years old. Mt Wilson was the biggest telescope until Palmer Observatory was built which had a 200-inch telescope.

Hubble was not the only person observing galaxies outside the Milky Way, Humason helped him. They set out on measuring the spectra of nearby galaxies. They then observed a galactic spectrum was in the visible wavelength range with continuous emission. There were emission and absorption lines on top of the continuum. From these lines, we can make an estimate if the galaxy is moving away from us or towards us.

When we get a spectrum, we assume the strongest line is coming from H-α. From literature, the strongest line should occur at 6563 Å, but if the line occurs somewhere around 7000Å, we can easily say it is redshifted.

From the Special Theory of Relativity,

$$1 + z = \sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}$$

where, Z is the redshift, a dimensionless number and v is the recession velocity.

$$\frac{\lambda_{obs}}{\lambda_{rest}} = 1 + z$$

Hubble and Humason listed down 22 Galaxies in their paper. Nearly all these galaxies exhibited redshift. They plotted the velocity (km/s) vs distance (Mpc). They observed a linear trend and Hubble put forward his famous law as follows.

$$v_r = H_o d$$

This is the Hubble Redshift Distance Relationship. The subscript r indicates expansion is in the radial direction. While, $v_r$ is the receding velocity, $H_o$ is the Hubble parameter, d is the distance of the galaxy from us. They concluded far away galaxies recede faster from us, if the rate of expansion for the universe is uniform.

The Expansion

Everything is moving away from us. The galaxies are not stationary, there is some expansion harmonic always. The units of the Hubble parameter are km sec⁻¹Mpc⁻¹. If one goes out a distance of – 1 Mpc, galaxies would be moving at the rate of 200 kms/sec. The Hubble parameter gives us the rate of expansion. As per Hubble and Humason, the value of $H_o$ is 200 kms/sec/Mpc.

The data showed all galaxies are moving away from us. Thus, it is apparent that we are at the center of the universe. But Hubble didn’t make this mistake, as per him, in whichever galaxy we live, we would find all other galaxies moving away from us. Thus, the conclusion is that the space between galaxies expand and there is no center of the universe.

The expansion is happening everywhere. However, there are some forces that are opposing expansion. Chemical bonds, gravitational force and other attractive forces are holding objects together. Earlier all the objects were close together. Considering the Big Bang as an impulsive force, these objects are set to move away from each other.

Time Scale

At local scales, Kinematics is governed by Gravity. In the original Hubble’s law, there were some galaxies which showed blue-shift. This can be credited to combined gravitational potential of the galaxies. Gravity has decoupled things from the Hubble’s law. The Andromeda Galaxy is coming towards to us. Gravity is trying to slow things down. Initially the expansion was slowing down, now it is speeding up.

There was a Cosmic Jerk because of this. Several estimates to the Hubble parameter has been made. It has evolved over the 90 years from 500 kms/sec/Mpc to 69 kms/sec/Mpc. The disparity in the value was because of the underestimation of distance. The Cepheid Stars were used as distance calibrators, however there are different types of Cepheid stars and this fact was not considered for the estimation of the Hubble parameter.

Hubble Time

The Hubble constant gives us a realistic estimate of the age of the universe. The $H_o$ would give the age of the universe provided the galaxies have been moving with the same velocity. The inverse of $H_o$ gives us Hubble time.

$$t_H = \frac{1}{H_o}$$

Replacing the present value of $H_o, t_H$ = 14 billion years. Rate of expansion has been constant throughout the beginning of the Universe. Even if this is not true, $H_o$ gives a useful limit on the age of the universe. Assuming a constant rate of expansion, when we plot a graph between distance and time, the slope of the graph is given by velocity.

In this case, the Hubble time is equal to the actual time. However, if the universe had been expanding faster in the past and slower in the present, the Hubble time gives an upper limit of age of the universe. If the universe was expanding slowly before, and speeding up now, then the Hubble time will give a lower limit on age of the universe.

$t_H = t_{age}$ − if rate of expansion is constant.
$t_H > t_{age}$ − if universe has expanded faster in the past and slower in the present.
$t_H < t_{age}$ − if universe has expanded slower in the past and faster in the present.

Consider a group of 10 galaxies which are at 200 Mpc from another group of galaxies. The galaxies within a cluster never conclude that the universe is expanding because kinematics within a local group is governed by gravitation.

Points to Remember

Cosmology is the study of the past, present and future of our Universe.
Our universe is ∼14 billion years old.
The universe is continuously expanding.
Hubble parameter is a measure of the age of the universe.
Current value of H_o is 69 kms/sec/Mpc.

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