In 1927, Belgian priest and cosmologist G. Lemaître published an article that proposed that our universe was expanding.1 Lemaître’s idea was originally simply an explanation for the motion of what we now call distant galaxies; however, he broadened his ideas and presented these more ambitious thoughts to the British Royal Astronomical Society in 1931. At that meeting, he first publicly discussed his idea of a “primeval atom,” which was his term for the visible universe compressed to tiny size. He published this idea in 1931 in the journal Nature.2 We now call his idea the Big Bang, a term coined by astronomer Fred Hoyle on a BBC radio show in 1949.3 

While the Big Bang theory is now universally accepted by the scientific community, there is only one problem. The theory as envisioned by Lemaître is wrong. In order to agree with observations, Lemaître’s theory must be modified to include a period of superluminal expansion early in the history of the universe. This superluminal expansion is called inflation, and the term Big Bang is relegated to the period following inflation. In the following, I will first describe the problems that inflation can solve, then describe the theory of inflation itself. I will conclude by describing modern attempts to validate or falsify the theory.

In 1948 and 1949, physicists Ralph Alpher and Robert Herman published a series of articles4 in which they realized that the Big Bang would leave a relic in modern times. If the universe were once much hotter and filled with energy (both kinetic energy of particles that existed at the time and the energy of force-carrying particles, e.g., photons, gluons, etc.), the universe should still have a temperature, albeit one much cooled by the subsequent expansion of the cosmos. In the present time, the temperature of the universe would be near 0 K, resulting in a radio or microwave “hum” filling space. This hum has come to be called the cosmic microwave background (CMB).

Their work went unappreciated for many years. While there was some interest in the 1960s by Robert Dicke and others in searching for the CMB, it was discovered by accident by Arno Penzias and Robert Wilson (Fig. 1).5 Using a decommissioned radio antenna, they discovered that the universe was filled with a microwave signal, peaking at 160.2 GHz, and corresponding to a blackbody radiator with a mean temperature equal to 2.72548 ± 0.00057 K, and uniform to parts per hundred thousand, independent of direction.6 

Fig. 1.

Robert Wilson and Arno Penzias under the radio antenna they used to first observe the CMB. Credit: NASA.

Fig. 1.

Robert Wilson and Arno Penzias under the radio antenna they used to first observe the CMB. Credit: NASA.

Close modal

This uniformity is very hard to understand for the following reason. The CMB we see today is a fossil remnant of the temperature of the universe when it was about 370,000 years old. This light was emitted about 13.8 billion years ago and is just now arriving at Earth. Consider two sides of the sphere centered on Earth with sections labeled east and west, as shown in Fig. 2. If the light from the east side of the sphere is just arriving at Earth, it means that this light has not had time to travel to the west side. Thus, according to the standard Big Bang model, the distant universe we see in one direction has never interacted with the distant universe in the opposite direction; yet the CMB is identical, irrespective of direction. How can two locations that have never interacted be so similar? This is called the uniformity problem.

Fig. 2.

Light from the CMB is just arriving at Earth. This means that the CMB from one side of the visible universe has not arrived at the other side of the visible universe, implying that according to the classical Big Bang theory, the two sides have never interacted.

Fig. 2.

Light from the CMB is just arriving at Earth. This means that the CMB from one side of the visible universe has not arrived at the other side of the visible universe, implying that according to the classical Big Bang theory, the two sides have never interacted.

Close modal

The evidence illustrating the uniformity problem arises from the CMB, however, the CMB is the source of another tension within the traditional Big Bang theory. Here the problem arises not from the uniformity, but from small differences in the microwave remnant of the Big Bang.

In the early 1970s, several physicists realized7 that the CMB would not be perfectly uniform (Fig. 3). Shortly after the Big Bang, the universe would be full of a hot, dense plasma. This plasma would support sound waves of calculable length. Sound waves led to regions of higher and lower density, and these density variations would result in small temperature variations. These temperature variations would be imprinted on the CMB, with an expected variation of order ΔTT ∼ 10−5. These temperature variations were first observed in 1992 by the COBE (Cosmic Background Explorer) satellite,8 followed by improved measurements by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite9 and most recently by the Planck satellite.10 

Fig. 3.

While the CMB is very uniform, small temperature variations persist that are the relic of primordial sound waves. Red is warmer and blue colder, with a temperature variation of order ΔT/T ~ 10−5. Credit: European Space Agency and the Planck Collaboration.

Fig. 3.

While the CMB is very uniform, small temperature variations persist that are the relic of primordial sound waves. Red is warmer and blue colder, with a temperature variation of order ΔT/T ~ 10−5. Credit: European Space Agency and the Planck Collaboration.

Close modal

The distance between adjacent hot or cold spots is determined by the wavelength of sound waves when the light was emitted. The angular size as determined from Earth is determined by those wavelengths (although lengthened by the expansion of the universe) and the distance between Earth and the CMB. However, another factor comes into play—the curvature of space (Fig. 4). If space is flat, then normal Euclidean geometry applies, and the dominant angular separation between adjacent hot or cold spots is about 1°. If space is open (i.e., hyperbolic), the angular separation will appear smaller. If space is closed (i.e., spherical), the angular separation will appear larger. Measurements by many experiments have determined that space is flat,10 with a cosmological curvature parameter of 0.0007 ± 0.0019. (Note: mathematically flat implies a curvature of zero.)

Fig. 4.

The angular size of the fluctuations in the CMB as seen on Earth depends on the curvature of space. Observations are consistent with flat space. Credit: WMAP and Planck Collaborations.

Fig. 4.

The angular size of the fluctuations in the CMB as seen on Earth depends on the curvature of space. Observations are consistent with flat space. Credit: WMAP and Planck Collaborations.

Close modal

This is a surprising result. There is, a priori, no reason for space to have any particular curvature. If curvature can range from −∞ (negative curvature, hyperbolic shape) to +∞ (positive curvature, spherical shape), having a curvature of exactly zero requires an explanation. Why is space flat?

A final unexplained feature of space has to do with the non-observation of cosmic relics. In the 1970s, physicists explored a large number of grand unified theories (GUTs) based on a range of mathematical formalisms motivated by group theory.11 A common feature of many of these theories is the prediction of magnetic monopoles,12 which have thus far eluded discovery.13 While this discrepancy between prediction and observation could signal the death knell of this methodology for devising a GUT, if there were a mechanism that caused these magnetic monopoles to be dispersed over cosmic distances, this could save the group theory approach for devising GUTs. Indeed, the idea of cosmic inflation was first proposed to resolve this issue.

The origins of inflation theory arose from the work of many people working independently. One of the architects of the theory was Alan Guth, who was a postdoc at the Stanford Linear Accelerator Center (now SLAC National Accelerator Laboratory). He has written a book describing the origins of inflation theory, which contains a more detailed history.14 Guth’s contribution to inflation theory began with a seminar in 1979, in which he was trying to solve the problem of the non-observation of monopoles. Through conversations with his colleagues, he came to realize that his model, which he named inflation, also would solve the uniformity and flatness problems. He published his theory in 1981.15 

Guth’s theory assumed that the universe was filled with a scalar field very early in the history of the universe (of order 10−36 seconds after the beginning). As the universe expanded, it fell into a metastable energy state, during which inflation occurs. This “false vacuum,” as it is misleadingly called, essentially results in a form of repulsive gravity and a wildly expanding universe. While the details remain uncertain, the basic idea is that for about every 10−36 seconds that passed, the universe doubled in size. After approximately 100 doubling cycles, quantum tunneling allowed the universe to transition to a stable state (“true vacuum”), and the superluminal expansion stopped. [It is perhaps useful to explain the meaning of “false” and “true” vacuum. Essentially, the energy density of the vacuum depends on a combination of parameters—electron charge, speed of light, etc. It might be possible that certain combinations of these parameters result in a local minimum in the curve of energy as a function of those parameters. This local minimum is called the false vacuum. However, there is a combination of parameters that results in a lowest energy. This configuration is the true vacuum. A schematic of this for a single, unspecified, parameter is shown in Fig. 5(a).]

Fig. 5.

The energy profile of the inflation process. The universe resides temporarily in a false vacuum (metastable state), before transitioning to the true vacuum (stable state). (a) An older (Guth) inflation paradigm, where the transition occurs through quantum tunneling. (b) A more modern inflation paradigm, where the transition occurs without tunneling. (a) represents a metastable state that is more stable than (b), but each reflects a form of metastability.

Fig. 5.

The energy profile of the inflation process. The universe resides temporarily in a false vacuum (metastable state), before transitioning to the true vacuum (stable state). (a) An older (Guth) inflation paradigm, where the transition occurs through quantum tunneling. (b) A more modern inflation paradigm, where the transition occurs without tunneling. (a) represents a metastable state that is more stable than (b), but each reflects a form of metastability.

Close modal

These numbers are not meant to be taken as precise, but rather to give a qualitative sense of the process. One hundred doubling periods leads to an expansion factor of 1030. And the actual expansion time is unknown, although the order of magnitude mentioned here is approximately correct. What is known is that the inflationary period spanned from about 10−36 seconds to about 10−33–10−32 seconds, and the minimum necessary expansion factor is about 1028, although it could be greater. This expansion is extraordinary. A volume with the radius of 10−15 meters underwent an expansion to a minimum of 1013 meters in less than 10−32 seconds. To add some intuitive scale, this is equivalent to a volume the size of a proton growing to a volume with a radius approximately equal to the aphelion of the orbit of Pluto in a fraction of a second and far exceeding the speed of light. (This does not violate relativity, as relativity applies to the motion of objects through space, not the expansion of space itself.)

Once the phase transition occurs, the energy released in the phase transition becomes a more familiar form of energy, heating the early universe and eventually transitioning into matter. And the expansion that is commonly called the Big Bang is a vestigial remnant of inflation. Essentially, inflation is thought to be the impulse that began the expansion of our universe: inflation first and Big Bang second.

Inflation solves the uniformity problem because it starts with a portion of an infant universe that is in thermal equilibrium, and therefore all parts of the universe were in contact and thus were uniform. After the superluminal expansion, the visible universe retained the initial uniformity, despite portions no longer being in causal contact. Given that the entire universe is much larger than the visible universe, there is probably a distance at which the universe is nonuniform; however, this discontinuity is beyond the event horizon that defines the visible universe. In simple terms, any such discontinuity is so far away that the light from that location has not had time to arrive at Earth.

Inflation theory also provides an explanation for the flatness problem. If the early universe had some curvature, the expansion of the universe would reduce that curvature by a factor of at least 1028. The situation is similar to what one encounters with Flat Earth believers. Earth is essentially a sphere, and yet it appears flat enough on the ocean or the plains of Kansas to fool the unwary. Given the enormous expansion factor (proton → solar system), any initial curvature would no longer be evident.

Finally, inflation solves the cosmic relic problem. If, as some GUT theories suggest, magnetic monopoles formed in the early universe, perhaps the inflationary expansion simply carried them away from one another far enough that scientists have failed to find them. Essentially, there would be none in the vicinity of Earth to find. (If you’re wondering why ordinary particles like electrons or protons would also not be isolated, there are two reasons. One, magnetic monopoles must be heavy, or we could create them today. Accordingly, if they exist, they would have been created only in the early universe. In contrast, electrons and protons are relatively light and able to be created under current conditions. Thus, while primordial electrons might have experienced the same fate as the magnetic monopoles, additional electrons, protons, and other familiar particles were created after the inflationary period.)

Guth’s initial inflation proposal is not without its problems. Indeed, in Guth’s initial paper, he noted many issues. The closing words of his 1981 paper say, “the inflationary scenario seems like a natural and simple way to eliminate both the horizon and the flatness problems. I am publishing this paper in the hopes that it will … encourage others to find some way to avoid the undesirable features of the inflationary scenario.”

While Guth notes several issues with his initial model, perhaps the most crucial is that the transition from false to true vacuum is through quantum tunneling and therefore abrupt. This abrupt transition [Fig. 5(a)] leads to rapid energy dissipation and therefore not enough energy to form the particles we see in the universe today.

This problem was addressed in 1982 by Andrei Linde16 and independently by Andreas Albrecht and Paul Steinhardt,17 when they introduced what is called “slow roll” or “new” inflation. This version modified Guth’s original model so that the inflationary period did not end abruptly. In doing so, the transition from false to true vacuum was smoother, allowing for more efficient transformation of energy that reheated the universe and allowed for the creation of matter [Fig. 5(b)].

What is described here are the most salient features of inflationary theory. In reality, there are many different inflation theories, with different models forming the basis of the energy driving inflation, arising from different mechanisms and making somewhat different predictions. A thorough review can be found in Ref. 18, however, the key point of inflation is the transition from a metastable to stable state, releasing energy that drives an exponential growth of the scale of the universe for a short while, followed by a phase transition that releases that energy to heat the universe, leading to the energy and matter we see today.

Without observational confirmation, a theory is just a theory. What is the evidence supporting inflation theory?

As has been already discussed, there are properties of the universe that are consistent with inflation theory. The geometry of the universe is nearly flat, and the universe is uniform in regions that are causally disconnected. Furthermore, no magnetic monopoles have been observed.

However, all of these observations existed to some degree or another before inflation theory was devised. Indeed, inflation theory was invented in part to explain these observations. Observations of phenomena uniquely predicted by inflation theory are necessary.

One problem is that there are many different implementations of inflation theory, using different particle physics models. Thus, testing inflation theory is a complicated thing; however, there are some commonalities within the various models. Most of them arise from the following chain of logic.

In the preinflation universe, the laws of quantum mechanics rule. This means that there were tiny variations in the energy fields of the nascent universe. Then inflation began, with the consequence that these quantum fluctuations were blown up to cosmic scales. The nature of spacetime is such that it can be distorted by energy and matter concentrations, and these distortions can travel throughout the universe. The familiar term for such variations is “gravitational waves,” which were predicted by Einstein in 1916, and the gravitational waves created by merging black holes were discovered a century later.19 

The quantum fluctuations of the preinflation universe, grown to cosmic sizes by inflation, are predicted to have left an imprint on the universe in the form of primordial gravitational waves. These gravitational waves would persist to the modern day. If these waves exist, their existence should be observable in subtle ways.

The cosmic microwave background is a snapshot of the light in the early universe. If inflation-generated primordial gravitational waves exist, they will have consequences on the polarization of CMB light. There are two types of polarization of relevance, with a variety of names. There is a circular polarization pattern, which arise from tensor terms in the field equations, and a linear pattern, formed by scalar terms. These patterns are also called B-modes, unfortunately named after the circular shapes of magnetic fields around current-carrying wires, and E-modes, which are linear in form. B-modes (tensor-origined) are predicted as a consequence of primordial gravitational waves.

Note that primordial gravitational waves also can make E-mode polarization, but B-modes are a more definitive signature of inflation. Furthermore, many things can polarize the CMB, including density fluctuations that gave rise to galaxies, as well dust in the Milky Way itself. The B-mode fluctuations due to primordial gravitational waves are subtle, hidden within a larger background.

The simplest measure of inflation-induced B-modes is through a parameter called r, or the “tensor-to-scalar” ratio (i.e., B-mode to E-mode). A value of r = 0 implies no inflation.

In 2014, an experiment called BICEP2 (Fig. 6) announced20 the observation of B-modes, with r=0.20.05,+0.07 and excluded the possibility of r = 0 with a significance of 7σ. However, as mentioned before, searching for B-mode polarization is quite difficult. Within 6 months, the BICEP2 collaboration, working in conjunction with the Planck collaboration, walked back these early claims. Eventually, it was determined that what BICEP2 had observed was contamination created by dust in the Milky Way.

Fig. 6.

The BICEP2 telescope (left) is located near the South Pole. In 2014, researchers using this facility announced the discovery of inflation, only to have to retract the claim within a year. An upgraded BICEP telescope has now ruled out several inflation models, but some remain viable. Credit: Steffen Richter, Harvard University.

Fig. 6.

The BICEP2 telescope (left) is located near the South Pole. In 2014, researchers using this facility announced the discovery of inflation, only to have to retract the claim within a year. An upgraded BICEP telescope has now ruled out several inflation models, but some remain viable. Credit: Steffen Richter, Harvard University.

Close modal

However, the search for B-modes continued. In 2021, a collaboration of scientists using the upgraded BICEP3 detector and the Keck Array announced r < 0.036,21 a number that is consistent with r = 0. This measurement rules out many models of inflation; however, some remain viable. It is difficult to make a general statement, but most inflation models predict r > 10−4. The experimental bound is two orders of magnitude greater than this threshold; however, the researchers predict that by the end of the decade, a sensitivity of 0.001 should be achieved. An accessible explanation of their result and the implications can be found in Ref. 22.

While experimental confirmation of inflation remains elusive, the theory remains attractive. A future experiment, tentatively named CMB-S4, will help clarify the situation and perhaps make a definitive measurement. CMB-S4 was recently one of the projects that received strong endorsement for future development by the Particle Physics Projects Prioritization Panel.23 In the meantime, researchers continue to study the problem, including developing alternative theories.

1.
G.
Lemaître
, “
Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques
,”
Ann. Soc. Sci. Bruxelles
A47
,
49
59
(
1927
);
G.
Lemaître
, “
A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulae
,”
Mon. Not. R. Astron. Soc.
91
,
483
490
(
1931
, translated).
2.
G.
Lemaître
, “
The beginning of the world from the point of view of quantum theory
,”
Nature
127
,
706
(
1931
).
3.
F.
Hoyle
, “
Continuous creation
,”
Radio Times, No. 1328
, BBC, Mar. 27,
1949
.
4.
R.
Alpher
and
R.
Herman
, “
Evolution of the universe
,”
Nature
162
,
774
775
(
1948
);
R.
Alpher
and
R.
Herman
, “
Remarks on the evolution of the expanding universe
,”
Phys. Rev.
75
,
1089
(
1949
);
R.
Alpher
and
R.
Herman
, “
Reflections on early work on ‘Big Bang’ cosmology
,”
Phys. Today
41
,
24
34
(
1988
).
5.
A. A.
Penzias
and
R. W.
Wilson
, “
A measurement of excess antenna temperature at 4080 Mc/s
,”
Astrophys. J.
142
,
419
421
(
1965
);
R. H.
Dicke
et al, “
Cosmic black-body radiation
,”
Astrophys. J.
142
,
414
419
(
1965
).
6.
D. J.
Fixsen
, “
The temperature of the cosmic microwave background
,”
Astrophys. J.
707
,
916
920
(
2009
).
7.
E. R.
Harrison
, “
Fluctuations at the threshold of classical cosmology
,”
Phys. Rev. D
1
,
2726
2730
(
1970
);
P. J.
Peebles
and
J. T.
Yu
, “
Primeval adiabatic perturbation in an expanding universe
,”
Astrophys. J.
162
,
815
836
(
1970
).
8.
G. F.
Smoot
et al, “
Structure in the COBE differential microwave radiometer first-year maps
,”
Astrophys. J. Lett.
396
,
L1
L5
(
1992
).
9.
E.
Komatsu
et al, “
Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Cosmological interpretation
,”
Astrophys. J. Suppl. Ser.
192
,
18
(
2011
).
10.
Planck
Collaboration
, “
Planck 2018 results. VI. Cosmological parameters
,”
Astron. Astrophys.
641
,
A6
(
2020
);
Planck
Collaboration
, “
Planck 2018 results. VI. Cosmological parameters
,”
Astron. Astrophys.
652
,
C4
(
2021
).
11.
R. L.
Workman
et al (
Particle Data Group
),
Review of Particle Physics, Prog. Theor. Exp. Phys.
2022,
083C01
(section 93, “Grand unified theories”) (
2022
).
12.
J.
Preskill
, “
Magnetic monopoles
,”
Annu. Rev. Nucl. Part. Sci.
34
,
461
530
(
1984
).
13.
R. L.
Workman
et al (
Particle Data Group
),
Review of Particle Physics, Prog. Theor. Exp. Phys.
2022
,
083C01
(section 95, “Magnetic monopoles”) (
2022
).
14.
A.
Guth
,
The Inflationary Universe: The Quest for a New Theory of Cosmic Origins
(
Perseus Press
,
New York
,
1997
).
15.
A.
Guth
, “
Inflationary universe: A possible solution to the horizon and flatness problems
,”
Phys. Rev. D.
23
,
347
356
(
1981
).
16.
A.
Linde
, “
A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems
,”
Phys. Lett. B.
108
,
389
393
(192).
17.
A.
Albrecht
and
P.
Steinhardt
, “
Cosmology for grand unified theories with radiatively induced symmetry breaking
,”
Phys. Rev. Lett.
48
,
1220
1223
(
1982
).
18.
R. L.
Workman
et al (
Particle Data Group
),
Review of Particle Physics, Prog. Theor. Exp. Phys.
2022
,
083C01
(section 23, “Inflation”) (
2022
) and 2023 update; .
19.
B.
Clegg
, “Gravitational waves: How Einstein’s spacetime ripples reveal the secrets of the universe” (
Icon Press
,
New York
,
2018
).
20.
P. A. R.
Ade
et al (
BICEP2 Collaboration
), “
Detection of B-mode polarization at degree angular scales by BICEP2
,”
Phys. Rev. Lett.
112
,
241101
(
2014
).
21.
P. A. R.
Ade
et al (
BICEP/Keck Collaboration
), “
Improved constraints on primordial gravitational waves using Planck, WMAP, and BICEP/Keck observations through the 2018 observing season
,”
Phys. Rev. Lett.
127
,
151301
(
2021
).
22.
D.
Meerburg
, “
Squeezing down the theory space for cosmic inflation
,”
Physics
14
,
135
(
2021
).

Don Lincoln is a senior scientist at Fermi National Accelerator Laboratory. He uses data collected using high-energy particle accelerators to study the laws of nature and has co-authored over 1500 papers. He is also an avid popularizer of frontier physics and has written several books for the general public, most recently Einstein’s Unfinished Dream: Practical Progress Towards a Theory of Everything. He also writes for online venues like BigThink, CNN, Forbes, and others. He also makes videos on the Fermilab YouTube channel and with Wondrium. www.facebook.com/Dr.Don.Lincoln/