After the big bang

Question

So much time has passed after big bang. We say that when we look at the night sky we see past.so when will the light from big bang showing how was it back then come to us and, show us how it existed.

Answer 1

Here is a pictorial of the history of the universe:

The x axis is the time taken to our present location and it is at 13.8billion years ago. The y axis is the expansion in space during the time axis.

One should realize that the universe is four dimensional and general relativity and also special relativity lead to the fact that each present three dimensional point was the beginning of the universe, because the expansion happened and keeps happening on all points of the universe. The decoupling of light at 380.000 years after the BB gives us the cosmic microwave background radiation at our present location

The image reveals 13.77 billion year old temperature fluctuations (shown as color differences) that correspond to the seeds that grew to become the galaxies. The signal from our galaxy was subtracted using the multi-frequency data. This image shows a temperature range of ± 200 microKelvin. Credit: NASA / WMAP Science Team WMAP # 121238 Image Caption 9 year WMAP image of background cosmic radiation (2012)

This is a map of microwave photon fluctuations from the black nody radiation curve, as observed in "empty" spaces of the sky. These thermal photons at the microwave frequency are a snapshot of what happened 380.000 years after the BB, when the photons of the soup of atoms and nuclei had a large enough mean free path to stop interacting by scatters. It is the best black body radiation curve we have.Due to the expansion of the universe the frequencies have degraded to microwave levels. To learn what happened before 380.000 years we use cosmological models to fit this plot. There is a hope that once gravitational wave detectors are developed we will be able to have a similar plot from times much closer to the Big Bang.

Answer 2

Light from big bang

I get an impression (which could be mistaken) that you're thinking of Big Bang as an explosion that results in a flash of light, amongst other things? However, the thing is, Big Bang wasn't an explosion and neither was there any light "immediately" after it. For the starters, Big Bang happened everywhere.

The Universe was a very hot and dense soup of sub-atomic particles after the Big Bang. It expanded rapidly, by several orders of magnitude ($10^{60}$), in a very short period of time (within $10^{-30}$ seconds) owing to Inflation. You'd notice that the Inflation epoch is marked in the diagram in the answer above soon after the Big Bang. An important thing to note here is that the temperature of the universe was still too hot for any photons to roam around freely. After this, the Universe still continued to expand, though at a much slower rate than what happened during Inflation. Over the next 380,000 years, the universe gradually cooled down enough for the sub-atomic particles to condense and form the first Hydrogen atoms, which meant that the light could then be "seen" for the very first time. We now call this first visible light — from 380,000 years after the Big Bang — as Cosmic Microwave Background (CMB).

So when will the light from big bang showing how was it back then come to us and, show us how it existed.

When the universe had cooled enough for the light to escape, the light was emitted everywhere, at once, while the Universe was and is still expanding (but prominently due to the effects of Dark Energy now). The temperature has since kept dropping; and all the regions where the light was emitted from kept moving further away from us with the increasing expansion of the space. Therefore, the detectable CMB has now become highly redshifted for us and too faint to be seen by the naked eye ($Z\approx\ 1100$). However, by observing and studying this highly redshifted CMB using WMAP and Planck satellites, we've managed to build models of how the Universe would have looked like 380,000 years after the Big Bang.

To see further back into the past, i.e. to observe how the things were before the CMB was released, we can't use Electromagnetic Spectrum anymore; instead the idea is to use Gravitational Waves as a tool. One such ongoing project is LIGO and its futuristic version might be LISA — see reference.

Note: This answer is more of a supplementary commentary to the technically more sound answer above by @annav. The only attempt is to possibly add some clarity on a few tidbits that are perhaps misunderstood in the initial stages of getting acquainted with the Big Bang.