# Cosmic microwave background polarization and detecting primordial gravitational waves

I have a few questions about primordial gravitation waves

• What are primordial gravitational waves? Wikipedia says that they are observed in the cosmic microwave background (CMB), but gravitational waves (GW) are totally different from the electromagnetic spectrum, so how can GW be observed in CMB?
• Why does the cosmic inflation makes GW? Normaly, GWs are made if great masses are inspiraling or if a rotating neutron star isn't a perfect sphere and has 'mountains'. At the cosmic inflation, there wasn't such an event, space was just inflating.
• How can we detect the primordial GW? I think they are very weak and they have very long wave periods, so they can't be detected by interferometers. Do we have an other kind of detectors (build, under construction or just an idea)?

I will try to answer specifically to your last question because I am more knowledgable on the experimental aspects of gravitational physics.

As you may know, the CMB is the oldest radiation that we can see in the universe. It can be referred to as the surface of last scattering for photons and it coincides with the moment the universe stopped to be an ionized plasma and became transparent: at the beginning, the universe was super hot but at the time of the CMB (epoch of recombination) the temperature lowered enough for neutral hydrogen to form.

It happened approximately 380 thousand years after the Big Bang, which means that no matter how good or big "telescopes" are, we cannot probe anything closer than that to the Big Bang with electromagnetic radiation.

This is not the case with gravitational waves. Gravitational waves would allow us to peer into regions inaccessible to EM radiation and much closer to the Big Bang: this could potentially unravel the nature of the earliest moments of our universe.

Cosmologists predict that the gravitational waves generated by inflation are not deterministic signals like the inspiral waveforms already measured by the LIGO/Virgo collaboration, but rather they should appear like a stochastic background. As it is often done with noise, it makes more sense to analyze stochastic signals in the frequency domain. In the frequency domain, the stochastic gravitational will have a power spectrum. The features of this spectrum depend highly on the model considered, but in general, there is an agreement that it would be "whitish", i.e. it would extend across a wide interval of frequencies.

At the moment ground-based detectors, which are sensitive around the audio frequencies, have not claimed a measurement of the stochastic GW background. Such detectors are tuned to see the inspiral and merger of compact objects and GW from Supernovae, which in the past were the most likely sources of GW, and were not designed to look for the mysterious signal of the primordial gravitational waves. That is understandable: if you want to do something that no one has ever done before, you might as well give you the better chances to succeed by aiming at sources you are pretty confident exist.

LISA, a planned space-based detector, is sensitive in a lower frequency band ($$10^{-5}$$ to $$10^{-2}\,\mbox{Hz}$$ approximately). There is some optimism regarding the detectability of primordial GW with LISA, but it is not the principal science goal of the mission.

Furthermore, LISA will be signal dominated and the presence of a stochastic background will be buried under thousands of other deterministic signals which will have to be subtracted one by one. Another complication is that LISA will be sensitive to another background: the background of unresolvable galactic sources (like binary systems of white dwarfs). This further effect could be orders of magnitudes larger than the stochastic background of primordial GW.

As mentioned, primordial GW could have left an imprint in the CMB: the most promising signature of this effect is clearly a “curl-like” (B-mode) polarization pattern in CMB polarization (cited from Gravitational waves from inflation, M.C. Guzzetti et al., 2016).

Finally, also pulsar timing arrays are analyzing to give upper limits on the parameters of the stochastic GW power spectrum.

A good (and probably a little tough) reference for your question is the review Gravitational waves from inflation, by M.C. Guzzetti et al. (https://arxiv.org/abs/1605.01615).

A presentation about the topic by one of the authors is also available at https://www.sif.it/static/SIF/resources/public/files/congr16/mc/Guzzetti.pdf

## Edit to include some mechanism of primordial GW production

To my knowledge, one of the basic mechanisms to produce GW in the inflation epoch is the following. The origin of the CMB anisotropies, which are the seeds of the structure that we see today in the universe, according to the cosmologists, resided in quantum fluctuations of the fields that describe the dynamics of the universe during inflation.

Therefore the accelerated expansion of the inflationary scenario was not "perfect" but there was some sort of perturbations. Both scalar perturbations and tensor perturbations could have been generated: the former are related to fluctuations the energy density of the Universe, while the latter constitute the real degrees of freedom of the gravitational field, i.e. gravitational waves.

In the paper I linked, the authors present several mechanisms to produce gravitational waves during inflation and the preheating phase. All such mechanisms can be divided into two categories

1. Vacuum oscillations of the gravitational field.
2. The presence of a source term in the GW equation of motion that leads to a classical mechanism of GW production.

They also provide a handy summary table:

• +1 but you could do with improving the answer to the middle question. – Rob Jeffries Apr 14 at 19:12
• @RobJeffries added some information regarding the middle question – Davide Dal Bosco Apr 16 at 18:26

Here is the wiki paragraph on how primordial gravitational waves could be seen in the CMB:

Primordial gravitational waves are gravitational waves that could be observed in the polarization of the cosmic microwave background and having their origin in the early universe. Models of cosmic inflation predict that such gravitational waves should appear; thus, their detection supports the theory of inflation, and their strength can confirm and exclude different models of inflation. It is the result of three things: inflationary expansion of space itself, reheating after inflation, and turbulent fluid mixing of matter and radiation

Italics mine.

There is ongoing research for polarization in the CMB distributions.

You state:

At the cosmic inflation, there wasn't such an event, space was just inflating.

It is the energy-momentum tensor that is distorting the space according to general relativity. In the early universe, all its energy was concentrated in the small volume expanding, so the residue of tremendous effects should be seen.

An experimental program is underway to further test inflation with more precise CMB measurements. In particular, high precision measurements of the so-called "B-modes" of the polarization of the background radiation could provide evidence of the gravitational radiation produced by inflation, and could also show whether the energy scale of inflation predicted by the simplest models