Inflation Is a Bridge between Microcosm and Macrocosm

Inflation occurs under the influence of a scalar field called the inflaton. To visualize a phenomenon so far from ordinary experience requires a particular effort of imagination, but it is possible. The small inhomogeneities in the distribution of matter in the observable Universe are the effect imprinted on a cosmological scale by quantum fluctuations that occurred during inflation

Michele Diodati
Jan 13 · 8 min read

What determined that sudden, unimaginable expansion of the Universe to which Guth gave the name of inflation? Can such an extraordinary phenomenon be justified from a physical point of view, or is it just an ad hoc conjecture designed to solve the problems left open by the Big Bang theory? Let’s try to understand it.

The physical explanation of the process put forward by inflation theorists has to do with the existence of so-called scalar fields. In its essence, a scalar field is a region of space in which a mathematical function allows to associate a scalar value to each point, that is, a quantity defined only by a number. Scalar fields affect the properties of elementary particles and, if they have constant potential, are indistinguishable from vacuum. In this regard, let us follow the explanation provided by the physicist Andrei Linde [1]:

Although scalar fields are not the stuff of everyday life, a familiar analogue exists. That is the electrostatic potential — the voltage in a circuit is an example. Electrical fields appear only if this potential is uneven, as it is between the poles of a battery or if the potential changes in time. If the entire universe had the same electrostatic potential, say, 110 volts, then nobody would notice it; the potential would seem to be just another vacuum state. Similarly, a constant scalar field looks like a vacuum: we do not see it even if we are surrounded by it.

These scalar fields fill the universe and mark their presence by affecting properties of elementary particles. If a scalar field interacts with the W and Z particles [2], they become heavy. Particles that do not interact with the scalar field, such as photons, remain light.

It is precisely a scalar field (or more than one, according to some models) that determines the exponential expansion of space in the inflation theory. To clarify, the Universe continued to expand even after the inflationary period. Still, the rate of expansion of space in a cosmos now filled with matter and radiation, not only is much lower than in the era of inflation but decreases over time (not considering the contribution of the so-called dark energy). It scales, in fact, due to the density of the energy, and this density decreases as space expands.

But during inflation, completely different conditions occurred. According to the theory, during that phase of rapid expansion, the Universe was not yet filled with matter and radiation. All the energy was concentrated in the void, a “false void” to put it better, that was the scope of a scalar field called the inflaton. Again according to the theory, unlike what happens with matter and radiation, the energy density of this (hypothetical) scalar field does not decrease with expansion but remains almost constant at all points where energy field potential is far from the minimum. It is in those points that inflationary expansion takes place.

When such a condition occurs, and until the scalar field precipitates locally at its minimum value, the vacuum exerts negative pressure, and gravity surprisingly acts no longer as an attractive force but as a repulsive force, generating a sudden and very rapid expansion of the space.

Schematic representation of the mechanism that determines inflation. The scalar field in an inflationary universe can be represented by imagining a sphere descending along the wall of a bowl. The farther the ball is from the bottom of the bowl, the higher is the potential energy of the inflaton. When the ball reaches the bottom, it reaches the minimum of energy too. Then, the oscillations around the minimum determine the re-heating of the Universe and the production of matter/antimatter and radiation, that is, the birth of the Universe according to the classic Big Bang scenario [image: Andrei Linde, The Self-Reproducing Inflationary Universe, Scientific American, 1994]

It all seems very abstract. So, it can be useful to resort to a visual representation to make it easier to understand the mechanism by which the potential energy of inflaton determines inflation. This is what the astrophysicist and science writer Ethan Siegel did in his book Beyond the Galaxy, from which I report the following passage [3]:

How does one visualize inflation, and how this inflationary phase comes to an end? I like to imagine a very flat surface, suspended high off the ground, made up of a tremendous number of rectangular blocks. These blocks are not locked together, but are held in place by some unseen force pushing in around their edges. And at the same time, there is a massive ball — maybe a bowling ball — rolling over the blocks. So long as the blocks stay in place and the ball rolls over them, the Universe inflates. Every additional block that the ball rolls over gives the Universe enough time to more than double in size. By time the ball rolls over 64 blocks, enough inflation has occurred to take something the size of the smallest possible particle in our Universe today and stretch it to the size of the entire visible Universe. […] But at some point, the rolling ball either encountered a weak spot in the blocks, or simply rolled for long enough that its cumulative effects caused just one single block to give way. When that happens, there is a cascading chain reaction around the ball, and all the blocks in your vicinity fall away, plummeting towards the ground. When the ground is finally reached by both the ball and the blocks, that signifies the end of inflation and the beginning of a Universe — one that is the same everywhere you look — that is filled with matter, antimatter and radiation, whose energy is determined simply by what height the blocks fell from. […] What we are left with at the end of inflation is a Universe that can be described by a hot, dense, expanding but cooling phase: the very thing we identify with the Big Bang.

During inflation, the temperature drops by several orders of magnitude (from 10²⁷ K to 10²² K according to some theoretical models). But once the inflaton field has precipitated around its minimum value, inflation ends, and the temperature returns to previous values. It is the phase called cosmic re-heating. It is at this crucial stage that the decay of inflation leads to the creation of a huge number of particles, which literally arise from the void. From then on, the Universe continues to expand and cool in the way traditionally described by the Big Bang model.

But what evidence do we have that things really took place as inflation theory predicts? As we know, the exponential expansion of space described by the inflationary model elegantly solves the three problems of the horizon, flatness, and missing monopoles, which the Big Bang theory, on its own, was unable to explain. But is there anything more? It seems so, and it leads us to even more disconcerting scenarios of a cosmos that expands 10⁵⁰ times in a tiny fraction of a second.

Inflation begins when the Universe has submicroscopic dimensions, of the order of Planck’s length, and ends when space has expanded enormously, far beyond the boundaries of the observable Universe. It means that inflation has a unique property — that of building a bridge between the microcosm and the macrocosm. More specifically, it means that the quantum fluctuations of vacuum energy, which influence the local values ​​of inflaton (the scalar field that drives inflation), instead of being confined to the submicroscopic world produce visible effects on a cosmological scale.

The fluctuations in vacuum energy, which occurred during inflation due to the intrinsic indeterminacy of quantum phenomena (following the uncertainty principle defined by Heisenberg), eventually translated into subtle differences in the distribution of matter that filled the Universe once inflation was over. In fact, the energy released at the end of the inflationary phase was converted into an ocean of particles. It is as if those fluctuations had remained “frozen” in the texture of space-time, producing a visible echo in the density variations in the distribution of matter created at the end of the inflationary phase.

The traces of those original quantum fluctuations are visible today both in the anisotropies present in the CMB, the cosmic background radiation, and in the distribution of galaxies in the observable Universe. The inflation theory predicts that the traces impressed by such fluctuations have a property, that of scale invariance. In other words, by analyzing the imperfections of the CMB with increasing levels of detail, it should be possible to find patterns that repeat themselves equal, or very similar, as the scale changes. It is a bit like if the image of a virus taken from an electron microscope was reproduced at ever higher scale factors until it reached the size of a cluster of galaxies.

Values of the scalar spectral index, which measures the scale invariance of the CMB. The various measurements carried out so far align around a value slightly lower than 1 (the gray vertical line visible in the graph), following what the main models of the inflationary Universe predict [NASA LAMBDA Archive Team]

Surprising as it may seem, the CMB observations made over several years by the COBE, WMAP and Planck satellites, supplemented by other experiments that have studied the distribution of galaxies in the Universe, have confirmed that indeed there are patterns that repeat almost unchanged at different scales. The prediction of scale invariance, at least as regards some models of inflationary Universe, seems to be confirmed by the data. The parameter defining it, called the scalar spectral index, has recently been measured at 0.9667 ± 0.0040, a value slightly less than 1, consistent with those inflationary models that predict that the fluctuations imprinted on a larger scale are somewhat more significant than those that appear imprinted on smaller scales.

There is also another potentially observable effect of quantum fluctuations occurring during the inflationary epoch, namely the traces left by gravitational waves emitted as a result of fluctuations in the gravitational field. According to the theory, such waves should have left a well recognizable trace in the polarization of the photons that make up the CMB. Unfortunately, until now, although various experiments have tried to detect such traces, the signature of the gravitational waves emitted at the time of the inflation, if it exists, has not yet been found (although in 2014 the researchers of the BICEP2 experiment mistakenly believed they had found it).

In 2014 the BICEP2 collaboration released this image, which shows a particular polarization of the CMB photons, considered as the trace left in the cosmic background radiation by primordial gravitational waves produced during the inflationary expansion of the Universe. Unfortunately, subsequent analyses conducted on the data collected by the Planck satellite showed that the announcement of the discovery had been premature. Those polarization modes were attributable not to primordial gravitational waves, but, more likely, to dust diffused in the Milky Way [Harvard-Smithsonian Center for Astrophysics]

Notes

[1] Andrei Linde, The Self-Reproducing Inflationary Universe, Scientific American, November 1994.

[2] The elementary particles that mediate the weak interaction.

[3] Ethan Siegel, Beyond the Galaxy: How Humanity Looked Beyond Our Milky Way And Discovered The Entire Universe, World Scientific 2015.


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Michele Diodati

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Science writer with a lifelong passion for astronomy and comparisons between different scales of magnitude.

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