Today, 13.73 billion years on: other objective indicators of the bang
Note: Gravitational waves which formerly featured on this page are now on a separate page: "Gravitational Waves".
The cosmic microwave background radiation (CMBR)*
The existence of the cosmic microwave background radiation released when photons were freed to begin their free movement throughout space had been predicted as long ago as the 1940s and 1950s. Its existence was accidentally discovered in 1964 by a German born American physicist Arno Penzias and an American physicist Robert Woodrow Wilson while they were working on an antenna intended for use with communication satellites[1].
Penzias and Wilson were trying to improve the quality of radio transmitted telescopes by eliminating all external radio noise. When they eliminated all the known sources of radio waves, they were still left with a residue that was surprisingly isotropic (evenly spread and of even temperature) even though they tried measuring the signal at different times of day and on different days. What they had discovered was in fact the afterglow of the big bang with a surprising uniformity of temperature no matter where it is measured throughout the universe. Detailed mathematical calculations have showed that the remnant photons from the creation event should have cooled to absolute zero, placing their frequencies in the microwave part of the spectrum, and for this reason, they are called the cosmic microwave background radiation[2] - "much the same as those in your microwave oven, but very much less powerful. They would heat your pizza only to minus 270.4 degrees Celsius, not much good for defrosting the pizza, let alone cooking it". [3]
"Although Penzias and Wilson had not been looking for cosmic background radiation, didn't know what it was when they had found it, and hadn't described or interpreted its character in any paper, they received the 1978 Nobel Prize in physics ... (Neither of them) altogether understood the significance of what they had found until they read about it in the New York Times". [4]
The CMBR used once to be available for all to see on old television sets when particular channels ceased transmission for the evening. The static or "snow" left on the screen emanated from the CMBR.
Penzias and Wilson’s accidental discovery in 1964 of the afterglow of the big bang in the form of the cosmic background microwave radiation, carried with it the observation that this radiation had a surprising uniformity of temperature no matter where it is measured throughout the universe. In other words, it was, and remains, isotropic. The question as to why is known as ‘the horizon problem’. The conventional big bang theory provides no answer to this, but its inflationary cosmology front end does.
When objects in far flung areas of space exhibit a near uniformity of temperature, it usually means that they have been in contact with each other, and the answer to the horizon problem lies in the prolonged and unimpaired contact and communication between all areas of space in the early stage of the universe’s life when in about a trillionth of a trillionth of a second ATB its size increased by a greater percentage than it has in the 13 billion years or so since. This is said to provide the reason for the evenness of temperature which is still evident, much like a bowl of hot soup left standing, if given time, will cool to the temperature of the surrounding atmosphere. So it is that, upon measurement by precision satellite instruments over the last decade, the temperature of the radiation in one part of the sky differs from that in another part by less than one thousandths of a degree[5]. No matter where you are in space, the temperature will always be the same: 2.75 Kelvin[6].
In 1998, as part of a project evocatively entitled “Project Boomerang” a telescope was carried over Antarctica by a balloon with the object of studying the cosmic microwave background. This revealed that the spatial geometry of the universe is flat and supported theories that it will expand forever and not collapse upon itself. The WMAP, launched in June 2001, was sent out to a distance of one million miles from earth on its far side of the from the Sun, where it imaged the whole of the microwave sky and not just a portion like Boomerang, confirmed to an accuracy of 1% that we live in a flat universe[7]. A similar result is achieved by measurements of the distance to observed supernovae.
An exponentially fast expansion of the universe in its early stages also solves the flatness problem.* Here, the word “flat” requires some elaboration. As Lawrence Krauss points out, a “flat” three-dimensional universe is not flat like a two-dimensional pancake or piece of paper is flat, but rather the three-dimensional space that all of us intuitively picture in which light rays travel in straight lines, meaning that the geometry of the universe is such that parallel lines will never cross, the angles in a triangle will always add up to 180 degrees, and the corners of cubes will always make right angles. This is to be contrasted with the much harder to picture three-dimensional space in which light rays, which trace the underlying curvature of space, do not travel in straight lines, implying an open or a saddle shaped universe, or a closed universe much like the surface of a sphere[8].
(By way of comparison, in four dimensional spacetime - with curvature that varies from place to place - the light travels in straight lines called geodesics which only appear curved, moving along the shortest possible paths open to them through spacetime. Here, ordinary Euclidean geometry is of no assistance and a differential geometry couched in the language of tensors is required to describe it)[9].
Bear in mind also that when we say the universe is flat, we mean flat on the grandest of scales. [10] Small scale bumps and wiggles are of no consequence in the overall big picture an d that includes phenomena such as black holes. "A black hole is a region of space–time where gravity is strong, and space–time is violently distorted… However, as one moves away from the black hole, the curvature of space–time gets less and less. Very far away from the black hole, space–time looks very much like flat space–time". [11]
When we blow up a balloon, a patch on its two dimensional surface will flatten as the balloon grows. So likewise following a cosmic expansion at an exponential rate in the aftermath of the big bang the observed universe became very flat, meaning that the total amount of matter and energy was and remains delicately poised between too much and too little. If there was too much matter and energy, the universe would collapse in on itself under its gravitational pull. If too little, it would continue to expand exponentially. A flat universe with a critical energy density also continues to expand, but it will be flat, and, as we have seen, a flat universe will obey the rules of Euclidean geometry governed by straight lines on a flat surface, encompassing the principle that the internal angles of a triangle will always add up to 180 degrees[12]. This is not the case on a curved surface such as a sphere like the Earth[13].
The trouble is, general relativity implies that a flat universe is far from guaranteed. In fact, it is a special, perhaps unlikely outcome. When matter or radiation is the dominant form of energy in the universe, as has been the case for most of its history, then even a slightly non flat universe will quickly deviate from the characteristics of the universe as it expands, leading to one which is “open” or “closed”. For the universe to still appear flat today, its early characteristics would have had to have been “absurdly” fine-tuned[14].
In fact, if the bubble multiverse theory (discussed on the page Branes and multiple universes) is correct, this should lead to a small amount of “saddle-shaped” negative spatial curvature in our universe, one where objects would travel through space not along straight lines as in a flat cosmos but along curves, even in the absence of gravity. Even though bubble universes are finite as seen from the perspective of the entire universe, observers inside a bubble would perceive their universe to be infinitely large, which would make space seem negatively curved. If we were inside one such bubble, space would likewise appear to be bent. Experiments studying how distant light bends as it travels through the cosmos are currently under way, and results should be known in the next two decades. If these experiments find any amount of negative curvature, they will support the multiverse concept. Conversely, the discovery of positive curvature would falsify the notion of a multiverse altogether [15].
The extragalactic background light [16]
Unrelated to the CMBR - a later manifestation of the big bang occurring all at once and about 400,000 years thereafter – there is another phenomenon which began during the period of star formation and has grown exponentially and continually ever since: the extragalactic background light (EBL). The EBL consists of all the photons of light radiated by all the stars and galaxies that have ever existed, at all wavelengths from the near visible ultraviolet through the visible to the far infrared, during all of cosmic history to the present, and includes all the light from bright galaxies plus galaxies too faint for telescopes to see[17]. It began to accumulate when the first stars and galaxies formed, roughly 200 million years after the big bang and new galaxies add their light all the time. It pervades the whole known universe, and because the universe is expanding, the photos emitted by galaxies over the history of the cosmos have spread throughout space and become dilute. Because of this expansion, light also undergoes a redshift: wavelength increases pushing the light towards the red side of the electromagnetic spectrum, outside the visible realm[18]. Of all the myriad of photons zipping around in a "gas" in extragalactic space, the EBL is second only in energy and intensity to the CMBR.
When we look at the night sky, to us it appears dark, but in reality it is filled with the accumulated light of all the galaxies that have ever shone in the universe’s history[19]. This light is difficult to detect because it has spread out throughout the expanding cosmos and because it is outshone by brighter nearby sources of light such as our solar system and the Milky Way. The EBL has a lot of competition at the same visible and infrared wavelengths. The Earth is located inside an extremely bright galaxy with billions of stars and immense clouds of glowing gas that outshine it. Sunlight scattered by all the dust near Earth’s orbit around the sun creates the zodiacal light, which is sometimes so luminous that from a dark spot at the right time of year it can be mistaken for an early dawn. This light shines in similar wavelengths to the EBL, and can create problems for measuring the latter[20].
Of recent times, astronomers have been able to measure the EBL by observing how photons from gamma rays from distant bright galaxies called blazars (galaxies with supermassive black holes emitting such rays) are dimmed when they collide with lower energy EBL photons such as visible starlight, and mutually annihilate to produce an electron and its antiparticle, the positron. The gamma rays in fact leave a cone of observable light when they travel through Earth’s atmosphere which cannot be seen from the ground, but which is measurable by observations made by the Fermi Gamma-ray Space Telescope, other NASA spacecraft and several ground-based telescopes of blazars located at different distances[21]. By measuring the unattenuated gamma ray brightness emitted from select blazars at the highest energies, and comparing the result with measurements of the attenuated gamma ray light received at Earth from the same blazars, scientists were then able the measure the EBL through its imprint on the gamma rays of various energies received from blazars located at different redshifts.
The detection of the EBL (in the sense of perceiving such a faint and diffuse signal) has given astronomers a means of analysing the evolution of galaxies, a picture of star and galaxy formation across the cosmic timeline, and a view of what happened during the peak of star formation, a so-called ‘cosmic high noon’ between 8 and 12 billion years ago. The EBL spectrum shows two bumps: one representing ultraviolet and visible light shining from stars and another larger bump in longer-wavelength far-infrared light, apparently from dust. The light has in fact preserved a record of cosmic history. During this period, dust absorbed much of the starlight and reradiated it in the infrared. The EBL affords a way of studying just how common dust-absorbed galaxies were during this era and thereby a means of understanding how rocky planets such as Earth formed, simply because these planets contain large quantities of cosmic dust[22]. Meanwhile, “all the time, supernovae are going off, gas clouds are glowing and new stars are being born to add their light to the pervading background that fills every inch of the cosmos”[23].
* The issues designate* - the CMBR, the horizon problem, the flatness problem - are considered in the Brian Cox documentary "Life of a universe: Part 1 - Creation" at https://www.youtube.com/watch?v=Or2Itbzxo6A
[1] Brian Greene, in The Hidden Reality - Parallel Universes and the Deep Laws of the Cosmos, Knopf, (2011) at 39 points out that the existence of this cosmic background microwave radiation was predicted in a paper by George Gamow and Ralph Alpher in the 1940s, but no one paid any attention. Gamow and Alpher received no recognition at all for their contribution, nor, as Bill Bryson points out, did a research team led by Robert Dicke who were working on the problem at the time of Penzias and Wilson's discovery.
[2] Greene, Ibid, 38-39.
[3] Stephen Hawking, Brief Answers to the very big questions, (Hawking's posthumous memoire) John Murray, London, 2018, 51.
[4] Bill Bryson, A Short History of Nearly Everything, Broadway Books, 2003, 12. The final sentence of the quote is attributed to Dennis Overbye in Lonely Hearts of the Cosmos.
[5] Greene (2005), 227; 287 ff; Gleiser, 78-9.
[6] Gleiser, 78.
[7] See Karen Masters (Dec 2006): http://curious.astro.cornell.edu/question.php?number=714 Also Lawrence M Krauss, A Universe from Nothing – Why there is something rather than nothing, Free Press, 2011, New York, 54-55.
[8] Ibid, 75. The consequence of a flat universe is that it will keep expanding forever. All other galaxies will be beyond our view, thereby obviating the need for future extragalactical astronomers: Lawrence Krauss, http://www.sydneyobservatory.com.au/2009/lawrence-krauss-explains-einstein%E2%80%99s-biggest-blunder-at-the-powerhouse-museum/
[9] See the section on General Relativity - "Converting the thought experiment into mathematical equations".
[10] https://www.space.com/34928-the-universe-is-flat-now-what.html
[11] Hawking, Stephen. Brief Answers to the Big Questions: the final book from Stephen Hawking (Kindle Locations 1225-1228). Hodder & Stoughton. Kindle Edition
[12] Gleiser, 76, 81, 75.
[13] However, see “Welcome to the Escher-verse”, New Scientist, 9 June 2012, 8-9, where recent theoretical work by Stephen Hawking suggests that the universe may not in fact be flat, but instead resemble a twisting, wiggly landscape of saddle-like hills. The article is discussed later in this paper in the context String theory and the cosmological constant – the flatness problem revisited.
[14] Lawrence M. Krauss, “A beacon from the Big Bang”, Scientific American, October 2014, 47 at 49. See also Bill Bryson, op cit, 16: a flat universe is one where gravity's critical density holds things together at just the right dimensions to allow it to go on indefinitely, in other words, in Goldilocks terms, it is "just right".
[15] Yasunori Nomura, "The quantum universe", Scientific American, June 2017, 22 at 29.
[16] See Alberto Dominguez, Joel R Primack and Trudy E Bell, “All the light there ever was: Why is the night sky so dark?”, Scientific American, June 2015, 26-31.
[17] Ibid 29.
[18] Ibid, 28.
[19] This is known as Olbers’ paradox after William Olbers, a German astronomer who asked the question why in the 1820s.
[20] Dominguez, Primack, Bell, op cit, 28-29.
[21] Ibid, 30-31.
[22] [23] Ibid, 31.
The cosmic microwave background radiation (CMBR)*
The existence of the cosmic microwave background radiation released when photons were freed to begin their free movement throughout space had been predicted as long ago as the 1940s and 1950s. Its existence was accidentally discovered in 1964 by a German born American physicist Arno Penzias and an American physicist Robert Woodrow Wilson while they were working on an antenna intended for use with communication satellites[1].
Penzias and Wilson were trying to improve the quality of radio transmitted telescopes by eliminating all external radio noise. When they eliminated all the known sources of radio waves, they were still left with a residue that was surprisingly isotropic (evenly spread and of even temperature) even though they tried measuring the signal at different times of day and on different days. What they had discovered was in fact the afterglow of the big bang with a surprising uniformity of temperature no matter where it is measured throughout the universe. Detailed mathematical calculations have showed that the remnant photons from the creation event should have cooled to absolute zero, placing their frequencies in the microwave part of the spectrum, and for this reason, they are called the cosmic microwave background radiation[2] - "much the same as those in your microwave oven, but very much less powerful. They would heat your pizza only to minus 270.4 degrees Celsius, not much good for defrosting the pizza, let alone cooking it". [3]
"Although Penzias and Wilson had not been looking for cosmic background radiation, didn't know what it was when they had found it, and hadn't described or interpreted its character in any paper, they received the 1978 Nobel Prize in physics ... (Neither of them) altogether understood the significance of what they had found until they read about it in the New York Times". [4]
The CMBR used once to be available for all to see on old television sets when particular channels ceased transmission for the evening. The static or "snow" left on the screen emanated from the CMBR.
- The horizon problem*
Penzias and Wilson’s accidental discovery in 1964 of the afterglow of the big bang in the form of the cosmic background microwave radiation, carried with it the observation that this radiation had a surprising uniformity of temperature no matter where it is measured throughout the universe. In other words, it was, and remains, isotropic. The question as to why is known as ‘the horizon problem’. The conventional big bang theory provides no answer to this, but its inflationary cosmology front end does.
When objects in far flung areas of space exhibit a near uniformity of temperature, it usually means that they have been in contact with each other, and the answer to the horizon problem lies in the prolonged and unimpaired contact and communication between all areas of space in the early stage of the universe’s life when in about a trillionth of a trillionth of a second ATB its size increased by a greater percentage than it has in the 13 billion years or so since. This is said to provide the reason for the evenness of temperature which is still evident, much like a bowl of hot soup left standing, if given time, will cool to the temperature of the surrounding atmosphere. So it is that, upon measurement by precision satellite instruments over the last decade, the temperature of the radiation in one part of the sky differs from that in another part by less than one thousandths of a degree[5]. No matter where you are in space, the temperature will always be the same: 2.75 Kelvin[6].
- Cosmic expansion and the flatness of space
In 1998, as part of a project evocatively entitled “Project Boomerang” a telescope was carried over Antarctica by a balloon with the object of studying the cosmic microwave background. This revealed that the spatial geometry of the universe is flat and supported theories that it will expand forever and not collapse upon itself. The WMAP, launched in June 2001, was sent out to a distance of one million miles from earth on its far side of the from the Sun, where it imaged the whole of the microwave sky and not just a portion like Boomerang, confirmed to an accuracy of 1% that we live in a flat universe[7]. A similar result is achieved by measurements of the distance to observed supernovae.
An exponentially fast expansion of the universe in its early stages also solves the flatness problem.* Here, the word “flat” requires some elaboration. As Lawrence Krauss points out, a “flat” three-dimensional universe is not flat like a two-dimensional pancake or piece of paper is flat, but rather the three-dimensional space that all of us intuitively picture in which light rays travel in straight lines, meaning that the geometry of the universe is such that parallel lines will never cross, the angles in a triangle will always add up to 180 degrees, and the corners of cubes will always make right angles. This is to be contrasted with the much harder to picture three-dimensional space in which light rays, which trace the underlying curvature of space, do not travel in straight lines, implying an open or a saddle shaped universe, or a closed universe much like the surface of a sphere[8].
(By way of comparison, in four dimensional spacetime - with curvature that varies from place to place - the light travels in straight lines called geodesics which only appear curved, moving along the shortest possible paths open to them through spacetime. Here, ordinary Euclidean geometry is of no assistance and a differential geometry couched in the language of tensors is required to describe it)[9].
Bear in mind also that when we say the universe is flat, we mean flat on the grandest of scales. [10] Small scale bumps and wiggles are of no consequence in the overall big picture an d that includes phenomena such as black holes. "A black hole is a region of space–time where gravity is strong, and space–time is violently distorted… However, as one moves away from the black hole, the curvature of space–time gets less and less. Very far away from the black hole, space–time looks very much like flat space–time". [11]
When we blow up a balloon, a patch on its two dimensional surface will flatten as the balloon grows. So likewise following a cosmic expansion at an exponential rate in the aftermath of the big bang the observed universe became very flat, meaning that the total amount of matter and energy was and remains delicately poised between too much and too little. If there was too much matter and energy, the universe would collapse in on itself under its gravitational pull. If too little, it would continue to expand exponentially. A flat universe with a critical energy density also continues to expand, but it will be flat, and, as we have seen, a flat universe will obey the rules of Euclidean geometry governed by straight lines on a flat surface, encompassing the principle that the internal angles of a triangle will always add up to 180 degrees[12]. This is not the case on a curved surface such as a sphere like the Earth[13].
The trouble is, general relativity implies that a flat universe is far from guaranteed. In fact, it is a special, perhaps unlikely outcome. When matter or radiation is the dominant form of energy in the universe, as has been the case for most of its history, then even a slightly non flat universe will quickly deviate from the characteristics of the universe as it expands, leading to one which is “open” or “closed”. For the universe to still appear flat today, its early characteristics would have had to have been “absurdly” fine-tuned[14].
In fact, if the bubble multiverse theory (discussed on the page Branes and multiple universes) is correct, this should lead to a small amount of “saddle-shaped” negative spatial curvature in our universe, one where objects would travel through space not along straight lines as in a flat cosmos but along curves, even in the absence of gravity. Even though bubble universes are finite as seen from the perspective of the entire universe, observers inside a bubble would perceive their universe to be infinitely large, which would make space seem negatively curved. If we were inside one such bubble, space would likewise appear to be bent. Experiments studying how distant light bends as it travels through the cosmos are currently under way, and results should be known in the next two decades. If these experiments find any amount of negative curvature, they will support the multiverse concept. Conversely, the discovery of positive curvature would falsify the notion of a multiverse altogether [15].
The extragalactic background light [16]
Unrelated to the CMBR - a later manifestation of the big bang occurring all at once and about 400,000 years thereafter – there is another phenomenon which began during the period of star formation and has grown exponentially and continually ever since: the extragalactic background light (EBL). The EBL consists of all the photons of light radiated by all the stars and galaxies that have ever existed, at all wavelengths from the near visible ultraviolet through the visible to the far infrared, during all of cosmic history to the present, and includes all the light from bright galaxies plus galaxies too faint for telescopes to see[17]. It began to accumulate when the first stars and galaxies formed, roughly 200 million years after the big bang and new galaxies add their light all the time. It pervades the whole known universe, and because the universe is expanding, the photos emitted by galaxies over the history of the cosmos have spread throughout space and become dilute. Because of this expansion, light also undergoes a redshift: wavelength increases pushing the light towards the red side of the electromagnetic spectrum, outside the visible realm[18]. Of all the myriad of photons zipping around in a "gas" in extragalactic space, the EBL is second only in energy and intensity to the CMBR.
When we look at the night sky, to us it appears dark, but in reality it is filled with the accumulated light of all the galaxies that have ever shone in the universe’s history[19]. This light is difficult to detect because it has spread out throughout the expanding cosmos and because it is outshone by brighter nearby sources of light such as our solar system and the Milky Way. The EBL has a lot of competition at the same visible and infrared wavelengths. The Earth is located inside an extremely bright galaxy with billions of stars and immense clouds of glowing gas that outshine it. Sunlight scattered by all the dust near Earth’s orbit around the sun creates the zodiacal light, which is sometimes so luminous that from a dark spot at the right time of year it can be mistaken for an early dawn. This light shines in similar wavelengths to the EBL, and can create problems for measuring the latter[20].
Of recent times, astronomers have been able to measure the EBL by observing how photons from gamma rays from distant bright galaxies called blazars (galaxies with supermassive black holes emitting such rays) are dimmed when they collide with lower energy EBL photons such as visible starlight, and mutually annihilate to produce an electron and its antiparticle, the positron. The gamma rays in fact leave a cone of observable light when they travel through Earth’s atmosphere which cannot be seen from the ground, but which is measurable by observations made by the Fermi Gamma-ray Space Telescope, other NASA spacecraft and several ground-based telescopes of blazars located at different distances[21]. By measuring the unattenuated gamma ray brightness emitted from select blazars at the highest energies, and comparing the result with measurements of the attenuated gamma ray light received at Earth from the same blazars, scientists were then able the measure the EBL through its imprint on the gamma rays of various energies received from blazars located at different redshifts.
The detection of the EBL (in the sense of perceiving such a faint and diffuse signal) has given astronomers a means of analysing the evolution of galaxies, a picture of star and galaxy formation across the cosmic timeline, and a view of what happened during the peak of star formation, a so-called ‘cosmic high noon’ between 8 and 12 billion years ago. The EBL spectrum shows two bumps: one representing ultraviolet and visible light shining from stars and another larger bump in longer-wavelength far-infrared light, apparently from dust. The light has in fact preserved a record of cosmic history. During this period, dust absorbed much of the starlight and reradiated it in the infrared. The EBL affords a way of studying just how common dust-absorbed galaxies were during this era and thereby a means of understanding how rocky planets such as Earth formed, simply because these planets contain large quantities of cosmic dust[22]. Meanwhile, “all the time, supernovae are going off, gas clouds are glowing and new stars are being born to add their light to the pervading background that fills every inch of the cosmos”[23].
* The issues designate* - the CMBR, the horizon problem, the flatness problem - are considered in the Brian Cox documentary "Life of a universe: Part 1 - Creation" at https://www.youtube.com/watch?v=Or2Itbzxo6A
[1] Brian Greene, in The Hidden Reality - Parallel Universes and the Deep Laws of the Cosmos, Knopf, (2011) at 39 points out that the existence of this cosmic background microwave radiation was predicted in a paper by George Gamow and Ralph Alpher in the 1940s, but no one paid any attention. Gamow and Alpher received no recognition at all for their contribution, nor, as Bill Bryson points out, did a research team led by Robert Dicke who were working on the problem at the time of Penzias and Wilson's discovery.
[2] Greene, Ibid, 38-39.
[3] Stephen Hawking, Brief Answers to the very big questions, (Hawking's posthumous memoire) John Murray, London, 2018, 51.
[4] Bill Bryson, A Short History of Nearly Everything, Broadway Books, 2003, 12. The final sentence of the quote is attributed to Dennis Overbye in Lonely Hearts of the Cosmos.
[5] Greene (2005), 227; 287 ff; Gleiser, 78-9.
[6] Gleiser, 78.
[7] See Karen Masters (Dec 2006): http://curious.astro.cornell.edu/question.php?number=714 Also Lawrence M Krauss, A Universe from Nothing – Why there is something rather than nothing, Free Press, 2011, New York, 54-55.
[8] Ibid, 75. The consequence of a flat universe is that it will keep expanding forever. All other galaxies will be beyond our view, thereby obviating the need for future extragalactical astronomers: Lawrence Krauss, http://www.sydneyobservatory.com.au/2009/lawrence-krauss-explains-einstein%E2%80%99s-biggest-blunder-at-the-powerhouse-museum/
[9] See the section on General Relativity - "Converting the thought experiment into mathematical equations".
[10] https://www.space.com/34928-the-universe-is-flat-now-what.html
[11] Hawking, Stephen. Brief Answers to the Big Questions: the final book from Stephen Hawking (Kindle Locations 1225-1228). Hodder & Stoughton. Kindle Edition
[12] Gleiser, 76, 81, 75.
[13] However, see “Welcome to the Escher-verse”, New Scientist, 9 June 2012, 8-9, where recent theoretical work by Stephen Hawking suggests that the universe may not in fact be flat, but instead resemble a twisting, wiggly landscape of saddle-like hills. The article is discussed later in this paper in the context String theory and the cosmological constant – the flatness problem revisited.
[14] Lawrence M. Krauss, “A beacon from the Big Bang”, Scientific American, October 2014, 47 at 49. See also Bill Bryson, op cit, 16: a flat universe is one where gravity's critical density holds things together at just the right dimensions to allow it to go on indefinitely, in other words, in Goldilocks terms, it is "just right".
[15] Yasunori Nomura, "The quantum universe", Scientific American, June 2017, 22 at 29.
[16] See Alberto Dominguez, Joel R Primack and Trudy E Bell, “All the light there ever was: Why is the night sky so dark?”, Scientific American, June 2015, 26-31.
[17] Ibid 29.
[18] Ibid, 28.
[19] This is known as Olbers’ paradox after William Olbers, a German astronomer who asked the question why in the 1820s.
[20] Dominguez, Primack, Bell, op cit, 28-29.
[21] Ibid, 30-31.
[22] [23] Ibid, 31.