The Quest for Cosmic Inflation

Gravitational Waves

What was the universe like at the beginning of time? How did the universe come to be the way it is today? These are perhaps the biggest and the most exciting questions about the nature of the universe. Scientists believe that the answer to these questions can be found through precision measurements of the CMB. But to understand why and how those measurements are being made, we need to study the interplay of CMB with gravitational waves whose existence were predicted by Albert Einstein in 1916. During cosmic inflation, quantum fluctuations should have created these waves, which would be imprinted in a component of the CMB.

But first, what are gravitational waves?

Einstein found that his field equations of general relativity (linearized weak-field equations) had wave solutions: transverse gravitational waves, which travel at the speed of light and carry away energy. But he realized that the amplitudes of these waves would have to be extraordinarily small and was unsure whether they could be detected at all and until 1957, there was considerable debate about the physical reality of gravitational waves.

In Section 3 we learned that objects bend space-time, and the curvature of space-time tells objects how to move. It is the influence of curved space-time that manifests itself as gravity. Massive celestial objects moving under the influence of gravity emit gravitational waves which are ripples that squeeze and stretch the fabric of space-time. Gravitational waves, like light waves, carry energy away from the objects that emit them. However, the rate of energy loss is extremely low, hence gravitational waves are very difficult to detect and the waves caused by most celestial movements have no measurable effect. The most likely detectable sources of gravitational waves are merging black holes and exploding stars.

Detection of Gravitational Waves

Figure 8-5
Figure 8. CMB as observed by Planck showing temperature fluctuations representing the seeds of stars and galaxies of today.

Nevertheless, experiments to detect gravitational waves began as early as the 1960s. Not surprisingly, none of the early experiments were able to detect them although there were tantalizing hints of their existence. The big breakthrough came in 1974 when Russell A. Hulse and Joseph H. Taylor made observations on the binary pulsar 13 PSR1913+16, a system consisting of two compact neutron stars orbiting each other with a maximum separation of one solar radius. The rapid motion suggests that orbital period of the system should decrease on a much shorter time scale because of the emission of a strong gravitational wave signal. The scientists found that the binary pulsar’s the orbital period changes with time, and this change is in exact agreement with the prediction from general relativity for the loss of energy and angular momentum due to gravitational wave emission (Figure 8). Hulse and Taylor won the 1993 Nobel Prize in Physics for this remarkable result.

Yet, the excellent agreement between the observed value and the theoretically calculated value of the orbital path was seen as an indirect proof of the existence of gravitational waves. Direct demonstration of their existence finally came in a PRL paper published in February 12, 2016, decades after Hulse and Taylor’s work and a century after Einstein’s original predictions, by the LIGO (Laser Interferometer Gravitational-Wave Observatory) group, a world-wide team of more than 1,000 scientists, together with scientists from the Virgo collaboration in Europe. A portion of the abstract is quoted below:

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0 × 10−21. It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1σ.

In this case the LIGO scientists detected a pair of such orbiting black holes that whirled closer and closer together by losing energy through the emission of gravitational waves. Eventually they collided at nearly one-half the speed of light to form a single massive black hole about 1.3 billion years ago. The scientists estimate that the two black holes were about 29 and 36 times the mass of the sun. Their merger produced a massive 62 solar-mass spinning black hole—3 solar masses less than the sum of the initial black holes. The missing mass was converted into energy according to Einstein’s formula  with a peak power output of about 50 times that of the whole visible universe. This energy was emitted as a final strong burst of gravitational radiation that distorted space-time and travelled through the universe at the speed of light, passing through matter unimpeded, until it reached the earth more than a billion years after the merger. But by the time the signal reached the earth, it became exceedingly feeble and needed the incredible sensitivity of the LIGO detectors and ingenuity of thousands of scientists to identify its signature.

The LIGO experiment consists of twin observatories—one in Livingston, LA, and the other in Hanford, WA—located 3,000 km apart. These observatories are designed to operate in unison. Their construction cost the National Science Foundation a colossal 1.1 billion dollars and took 40 years to build. The observatories had just come online after a major upgrade when they sensed the coincident signal GW150914 from the collision event that arrived at 09:50:45 UTC on 14 September, 2015 (Figure 9). The signal was converted into an audible sound, or chirp, based on the frequencies of the waves as they arrived at LIGO’s detectors. The chirp is the “echo of the marriage” of the two black holes in the cosmic cataclysm that happened billions of years ago.

Gravitational Waves PRL
Figure 9.The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (L1, right column panels) detectors. Times are shown relative to September 14, 2015 at 09:50:45 UTC.

Laser light is split into two beams by the L-shaped interferometers at the Livingston and Hanford observatories in such a way that light travels back and forth down the 2.5 mile (4 km) long arms (Figure 10) which are tubes of diameter 4 feet, kept under a near-perfect vacuum. The beams are used to monitor the distance between mirrors precisely positioned at the ends of the arms. No light would be registered at the photodetector if it traversed precisely the same distance in the arms, because the two light waves would combine to interfere destructively, thereby cancelling each other. But if gravitational waves slightly stretched one arm and compressed the other, the two beams would no longer completely subtract each other, producing an interference pattern at the detector. This pattern would contain information about how much the two arms have lengthened or shortened, which in turn would tell us about what produced the gravitational waves.

Figure 10.Simplified diagram of an Advanced LIGO detector (not to scale). A gravitational wave propagating orthogonally to the detector plane will have the effect of lengthening one 4-km arm and shortening the other during one half cycle of the wave.

This is indeed what happened on September 14. The gravitational-wave signal arrived at the LIGO observatory in Louisiana first, and then just 7 milliseconds later it reached Washington State. The time lapse allowed physicists (a) to map the collision between black-holes at a particular spot in the southern sky (b) to verify that gravitational waves travel at the speed of light. This meant that the gravitons, which are the carrier particles of the gravitational force, are massless. According to some theoretical models, the accelerating expansion of the universe could be explained if gravitons have mass—thus the concept of “dark energy” is unnecessary under this scenario. However, the LIGO disproves this viewpoint having found no evidence of massive gravitons.

black hole collision

The LIGO result is a landmark discovery, significant for several reasons. It is the (a) first ever direct detection of gravitational waves (b) the strongest confirmation yet for the existence of binary black holes and (c) confirmation of general relativity because the property of these black holes agrees exactly with what Einstein predicted almost exactly 100 years ago.

Astronomy, before LIGO, relied on light for astronomical observations: visible light for the first star gazers, ultraviolet and infrared light for the Hubble Space Telescope, microwaves and radio waves blasting from the cores of galaxies. LIGO has opened up a new observational window which will allow scientists to view the universe and some of its most violent phenomena in an entirely new way using gravitational waves instead of light. And for the first time we can use ears as well as eyes to observe the cosmos.

Gravitational waves would also allow researchers to study what happened during the Big Bang nearly 14 billion years ago, as these waves have travelled freely through the hot plasma of the early universe and whose signature may be around even today. Scientists are already trying to identify signals of the primordial gravitation waves, but to understand how, one needs to get to grips with the science behind evolution of the universe, which is the subject of our next topic.

History of Evolution of the Universe

In the early moments of Big Bang, the universe went through a period of exponential expansion. Such an inflationary phase provides an explanation of why the universe looks the same in every direction, because, in the early universe, there would be time for light to travel from one region to another.

Figure 11. Gravitational waves may arise from inflation, a faster-than-light expansion after the Big Bang. The bottom part of this illustration shows the scale of the universe versus time. Specific events are shown such as the formation of neutral Hydrogen at 380,000 years after the big bang. Prior to this time, the constant interaction between matter (electrons) and light (photons) made the universe opaque. After this time, the photons we now call the CMB started streaming freely. The fluctuations (differences from place to place) in the matter distribution left their imprint on the CMB photons. The density waves appear as temperature and “E-mode” polarization. The gravitational waves leave a characteristic signature in the CMB polarization: the “B-modes”. Both density and gravitational waves come from quantum fluctuations which have been magnified by inflation to be present at the time when the CMB photons were emitted. Credit: Wikimedia Commons, the free media repository.

The universe was a very dark place until around 400 thousand years after the Big Bang. There were no stars, no galaxies and the entire universe was made up of a plasma consisting mainly of fundamental particles such as protons and electrons, all of which were unbound and recoiling with photons (unbound charged particles are called ions and the ionized gas is called plasma). But in the plasma, the particles and photons were tightly coupled and indistinguishable. As spacetime rapidly expanded due to cosmic inflation, the universe cooled down. The electrons and protons began to combine to form neutral hydrogen atoms (hydrogen atoms with one electron and one proton).  This process of pairing up is called recombination and it occurred about 380,000 years after the Big Bang.  The universe which was opaque before the recombination, became increasingly transparent as more and more free electrons became bound to the protons. Light could now travel unimpeded since it was not so much scattered by the free electrons (also by free protons but to a significantly lesser extent), giving rise to the cosmic microwave background (CMB). CMB is actually the free-streaming photons through the universe freshly released from the great primordial fireball.

Thus, the universe went from being a plasma (ionized) to a neutral gas during the epoch of recombination, the earliest phase in the cosmic history that can be studied by means of the light emanating in form of CMB. But very little is known about the early universe before the release of CMB, because it was opaque to all electromagnetic radiations.

According to the theory of inflation, gravitational waves were most likely produced during cosmic inflation, just after the Big Bang. Consequently, these waves could be used to look back to, say, a trillionth of a second after the Big Bang, provided we know how to find the signatures of these primordial gravitational waves.

In March 2014, researchers of the BICEP2 telescope made a dramatic announcement that they had indeed discovered the fingerprint of gravitational waves etched into the CMB. Interestingly, this claim was made more than a year before the direct detection of gravitational waves and triggered massive interest in them. The story unfolded in a very public arena but the claim turned out to be premature. Thus the search for the answer to the question as to what was the universe like at the beginning of time still continues. Since then, BICEP2 has greatly increased the number of detectors in their setup and other groups have also joined in the hot pursuit. That story will be recounted in the next Section.

13 A pulsar is a neutron star, a dead star that has collapsed down to a very dense state and emits a periodic signal (it is observed to pulse). These signals are highly regular. In fact, pulsars are some of the best clocks in nature, and this allows extremely precise measurements of their motion. Binary pulsars are systems where a pulsar orbits a companion, such as a white dwarf or neutron star (even another pulsar).

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