Based on hubbles law explain the expansion of universe
Answers
Hubble's Law, when written in this form,
v=H0D,
means: if D is the current distance of a galaxy, and H0 the Hubble constant, then v is the current recession velocity of the galaxy. So it tells you what the recession velocity of a galaxy is right now, not what it was in the past.
Basically, the Hubble Law is a consequence of the cosmological principle, i.e. that the universe on large scales is isotropic and homogeneous. This means that the expansion of the universe can be described by a single function of time, the so-called scale factor a(t), so that the distance to a faraway galaxy increases over time as
D(t)=a(t)Dc,
where Dc is a constant, called the co-moving distance to the galaxy; D(t) is known as its proper distance. Also, the present-day value of a(t) is set to 1 by convention, i.e. a(t0)=1, so that D(t0)=Dc.
If we take the derivative, then
v(t)=D˙(t)=a˙(t)Dc=a˙(t)a(t)D(t)=H(t)D(t),
with v(t) called the recession velocity and H(t)=a˙/a the Hubble parameter. This is the general version of Hubble's Law at cosmological time t, which at the present day takes the familiar form
v=H0D,
where v=v(t0), H0=H(t0) and D=D(t0). But in this form, Hubble's Law isn't very useful: it's a purely theoretical relation, because the recession velocity of a galaxy cannot be directly observed, nor does it say anything about the expansion of the universe in the past. It only tells us how fast a galaxy is moving from us right now, if you know its current distance.
However, there's a related quantity that we can observe, namely the redshift z of a galaxy, which is the change in wavelength of its photons as they travel through the expanding space:
1+z=λobλem,
with λem, λob the emitted and observed wavelength respectively.
Unlike the recession velocity, the redshift does give us information about the past, because the redshift of a photon accumulates over time, during its journey from the source galaxy to us. By comparing the redshifts of two galaxies, we can deduce information about the expansion rate in the past: suppose we observe two galaxies with distances D1>D2 and redshifts z1>z2, which emitted their light at times t1, t2 respectively. Then the difference in redshift z1−z2 will tell you how much the universe expanded in the time interval [t1,t2].
In other words, if the expansion of the universe were decelerating, we'd see that the redshift of distant galaxies accumulated a lot in the distant past, when the expansion rate of the universe was high. However, observations showed that the expansion of the universe first decelerated and then started to accelerate again (the transition from deceleration to acceleration occurred when the universe was about 7.7 billion years old). This means that there was a time when the expansion rate was at a minimum, during which the redshift of photons increased less.
Source- physics stackexchange