The Age of the Universe

The belief that the universe as a whole is ageless and unchanging has largely prevailed in human thought since ancient times, with few notable exceptions, and even survived the Copernican and the Newtonian systems. In the 1920’s, the pioneering work of Georges Lemaître and Edwin Hubble set the foundations of evolutionary cosmology within the frame of General Relativity. Since then, the concept of cosmic age has entered the domain of physical science, opening up a rich and highly debated motif of modern cosmology. Today the age of the universe is estimated from a variety of independent observational probes. The most accurate measurement comes from recent observations of the cosmic microwave background by the Planck satellite, indicating a cosmic age of 13.8 billion years with an accuracy of ±0.2%. This result is consistent with independent lower limits from the age of the oldest known astrophysical objects, such as globular clusters, white dwarfs and low-metallicity stars. 1 Time and Timeless: the Birth of Astronomy Our perception of the passage of time has been largely shaped by the astronomical environment of our planet. The daily and seasonal rhythms of sunlight and the repeatable motion of the stars in the sky, in contrast with the ephemeral movements of earthly objects, were essential for our ancestors to develop a notion of duration and time flow. While Sun-related periodicities were most apparent, it was probably the Moon, with its mysterious recurring phases, that most deeply fascinated early sky watchers.1 The emergence of agricultural societies and the development of navigation made astronomical time measurements even more crucial. The Babylonians and the Egyptians carefully recorded the movements of stars and planets for millennia, producing some of the first precise calendars complete with seasonal and lunar phases, even including prediction of eclipses. The stability of the sky was a reassuring mystery. The brightness and relative positions of the stars did not change for countless generations.  A number of archaeological records suggest that the lunar cycle was observed in the Upper Paleolithic by several independent human groups (e.g., Marshack 1991, Barrow 1995). OpenAccess. © 2022 Marco Bersanelli, published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. https://doi.org/10.1515/9783110753707-021 The silent and perfectly repeatable trajectory of celestial objects was clear evidence of their divine nature. So, while astronomical motions stimulated early measures of time, the sky as a whole was perceived as timeless. Remarkably, although the cosmic dance of stars and planets was lacking any hint of time direction, nearly all ancient civilizations developed some legendary accounts for an origin of the world. These were stories populated by innumerable gods and goddesses, whose births were intertwined with the creation of earthly creatures.2 It is unclear to what extent these myths were thought to refer to some historical past, but in some cases, it is possible to speculate on the age of the world according to the different traditions. For the Egyptians, based on the age of their first god Ptah, the world would be 50,000 to 150,000 years old, depending on interpretations.3 The Sumerian cosmos, as reconstructed from the ancient Sumerian King List, was as old as 400,000 years (See Van De Mieroop (2004).4 Greeks and Romans hardly mentioned any creation date.5 Censorinus, starting up his history of the world, modestly stated: “If the origin of the world had been known to man, I would have begun there”.6 Interestingly, however, even peoples advanced in astronomy such as the Babylonians developed their mythical cosmogonies with no reference whatsoever to observed astronomical phenomena. Once created, the physical universe was imagined to remain perfectly changeless. Two notable exceptions are worth mentioning. The first is the Hindu tradition, which held time itself to be cyclic. Hindus did not contemplate a single creation event, but an everlasting cosmic cycle with a succession of global deaths and rebirths. They extrapolated the regular patterns observable at human  Most Mesopotamian cultures in the period 3000– 1000 BC developed creation myths with significant similarities (Kragh 2007, 7– 13). The Egyptians, for example, held that Geb, the god of the earth, and Nut, goddess of the sky, were originally united, and that the world was formed when their bodies were separated by Shu, god of the air and of the atmosphere. This separation initiated the proliferation of living creatures and human beings, together with a complex hierarchy of deities of different ranks. The world was shaped from a primordial substance, a limitless expanse of a waters —likely a reminiscent of the life-bearing inundations of the Nile.  According to Diogenes Laërtius, the Egyptians believed that Ptah lived 48,863 years before Alexander the Great (Verbrugghe and Wickersham 2001), thus dating the creation 49,219 BC; Theophilus of Antioch, on the other hand, reported an age for the Egyptian cosmos of 153,075


1T ime and Timeless: the Birth of Astronomy
Our perception of the passageoftime has been largely shaped by the astronomical environment of our planet. The daily and seasonal rhythms of sunlight and the repeatable motion of the stars in the sky,i nc ontrast with the ephemeral movements of earthlyo bjects, weree ssential for our ancestors to develop an otion of duration and time flow.While Sun-related periodicities were most apparent,i tw as probablyt he Moon, with its mysterious recurringp hases, thatm ost deeplyf ascinated earlys ky watchers.¹ The emergence of agricultural societies and the development of navigation made astronomical time measurements even more crucial. The Babylonians and the Egyptians carefullyr ecorded the movements of starsand planets for millennia,producing some of the first precise calendarsc ompletew ith seasonal and lunar phases, even includingp rediction of eclipses. The stability of the sky was ar eassuring mystery.T he brightness and relative positions of the starsd id not changef or countless generations.
The silent and perfectlyr epeatable trajectory of celestialo bjects was clear evidence of theird ivinen ature. So, while astronomical motions stimulated early measures of time, the sky as aw hole was perceiveda st imeless.
Remarkably, although the cosmic dance of stars and planets waslacking any hint of time direction, nearlyall ancient civilizations developed some legendary accounts for an origin of the world. These werestories populated by innumerable gods and goddesses, whose births were intertwined with the creation of earthly creatures.² It is unclear to what extent these myths werethoughttorefer to some historical past,b ut in some cases, it is possiblet os peculate on the ageo ft he world accordingt ot he different traditions. Fort he Egyptians,b asedo nt he ageo ft heirf irst godP tah, the world would be 50,000 to 150,000 years old, depending on interpretations.³ The Sumerian cosmos,a sr econstructed from the ancient Sumerian KingL ist,was as old as 400,000 years (See Van De Mieroop (2004).⁴ Greeks and Romans hardlym entioned anyc reation date.⁵ Censorinus, starting up his history of the world, modestlys tated: "If the origin of the world had been known to man, Iwould have begun there".⁶ Interestingly,h owever,e venp eoples advanced in astronomys uch as the Babylonians developed their mythical cosmogonies with no reference whatsoever to observed astronomical phenomena. Once created, the physical universe was imagined to remain perfectlyc hangeless.
Twon otable exceptionsa re worth mentioning.The first is the Hindu tradition, which held time itself to be cyclic. Hindus did not contemplate asingle creation event,b ut an everlasting cosmic cycle with as uccession of global deaths and rebirths.T hey extrapolated the regular patterns observable at human  Most Mesopotamian cultures in the period 3000 -1000 BC developed creation myths with significant similarities (Kragh 2007,7-13). The Egyptians,for example, held that Geb,the godofthe earth, and Nut,g oddess of the sky,were originallyunited, and that the world was formed when their bodies were separated by Shu,g od of the air and of the atmosphere. This separation initiatedthe proliferation of livingcreaturesand human beings,together with acomplex hierarchy of deities of different ranks.The world was shaped fromaprimordial substance, al imitless expanse of aw aters -likelyareminiscent of the life-bearingi nundations of the Nile.  According to Diogenes Laërtius,t he Egyptians believed that Ptah lived4 8,863y ears before Alexander the Great (Verbrugghe and Wickersham 2001), thus datingt he creation 49,219 BC; Theophilus of Antioch, on the other hand, reported an agef or the Egyptian cosmos of 153,075 years (Grant 1958).  However,i th as been argued that these ages should be understood in units of lunar cycles rather than years, thus makingthe ageofthe Babylonian universe in line with the Egyptian tradition (Olson 1995).  Greek and Roman scholars traditionallyidentified the first eraofhistory as the "obscure" ádelon period, but did not attempt as ystematicd atingo fi ts beginning.  Censorinus, De Die Natali,Chapter1 . scale by huge factors and conceiveda na mazingly wide rangeo ft ime units, spanning from microseconds to billions of years.⁷ In their view,t he stability of the sky was not evidence of as tatic universe, but as ign of how insufficient our human condition is to appreciate the reality of the mutable cosmos.
Asecond exception werethe Jews. While their imageofthe physical universe was very much in line with other middle-eastern cultures of the time,⁸ theirn otion of creation was radicallydifferent.The intricate genealogyofgods and semidivinebeingstypicalofpolytheistic religions was sharplycontrasted by the free act of aunique and personal God. The beginning of the first verse of Genesis⁹ was not simplytemporal, but ontological. Creation was not shaping something out of some primordialsubstance, rather,itwas meant as calling into being every creature. All material thingsw erec onsidered ephemeral and contingent.N othing, even the whole universe, was understood as absolute and self-sufficient: The heavens will vanish like smoke, the Earth will wear out like ag arment (Isaiah 51,6 ). Cosmic time was seen as limited, both in the past and in the future. According to ancient Jewish chronologies, the creation of the world dated back 4339 BC or 3761 BC,d epending on tradition¹⁰.L ater on, the medieval Christian culturewould inherit the Jewish vision of time, and the world beginning was believed to be between 5300 and 5500 BC.

2G reek andM edieval Spheres
Mesopotamian and Egyptian astronomers, while unmatched in observational skill, did not reach-and perhaps never sought-ag eometrical synthesis of celestial motions. This step was to be taken by the ancient Greeks. The prevailing Aristotelian school held that the perfect repeatability of the motions of the stars demonstratedtheir superior nature. Anychangeorirregularity was consid- Asingle global period (one dayand night of Brahma) is about 8.64 billion years long,remarkably close to the order of magnitude the ageo ft he universe according to present-day scientific cosmology.But even such aBrahma day-night period is but asub-cycle of amuch longer eraof cosmic death and rebirth, comprising 100 "cosmic years",each composed by 360 "cosmic days". Thus,t he time elapsed since the start of the current Brahma creation is about 3:1 Â 10 14 years (22,000 times largert han the ageo ft he universe based on contemporary science). See Teresi (2003).  Adetailed reconstruction of the universe according to the Old Testament was done by Schiaparelli (1905).  "In the beginning God created the heavens and the earth" (Genesis 1,1).  The date3 761B Cm arks the start of the traditional Hebrew Calendar since the 4th century AD.
The Age of the Universe ered as ymptomo fi ncompleteness. The universe was ageless and its natural order was eternal. The divine natureo fc elestial bodies implied that they were perfectlyspherical and made of an everlastingpure substance. Their trajectories could onlyd erivef rom combinations of circular and uniform motions,i .e., motions without beginning nor end. Therefore, not onlyt he universe as aw hole, but alsoe very single movement in the sky was eternal. This was equivalent to requiringt hat time be marginalized from the celestial world. Beyond the outer boundary of the primum mobile,A ristotle believed that "therei sn either place nor void nor time" (Aristotle,De Caelo,I ,9 ). The outer edge of the universe was alsot he end of time.
The most refined version of Aristotle'sc osmos was the Ptolemaic model, completed around 150 AD.¹¹ It was an ingenious and sophisticated geometrical structure combiningavast number of nested spheres,c apable of accuratelya ccountingf or all celestial trajectories observable by naked eye. It remained the standard model of the universe for fifteen centuries.The medieval cosmos largely inheritedthe spatial structure from the Ptolemaic model. However,the notion of time was taken from the Jewisht radition. Time, as anyo therc reature, was regarded as finite and contingent.Inhis Confessions (ch. XI and XIII) St.Augustine pointed out that it is impossible to conceive at ime that is not part of God'sc reation.¹² Furthermore, Thomas Aquinas made an explicit distinctionbetween creation and beginning of time.¹³ In his notion of creation ex nihilo he affirmedc reation as the radical, ontological dependence from God of every creature, includingtime and the universe as awhole (see Carroll 2013). Coherently, he concluded that even an everlastingcosmos would be ac reated universe justa so ne with af inite age.
Conceiving time as finite and the universe as contingent,t he English Franciscan scholarR obert Grossetestew as inspired to think of something that would have horrified Aristotle. Relying on the principles of Scholastic physics, around 1220 he developedanaccount of the formation of the Ptolemaic universe  In the Almagest Ptolemyintroduced secondary motions (epicycles, eccentric, equant) which made the model quitei ntricate. The equant (punctum equans)w as an off-center point about which the epicycle moved with uniform angular velocity,t hus representings ome compromise with the foundingp rinciple of the model.  Also, in The literal meaning of Genesis (Book 4, Ch. 20,n .37),where he states: "Aperiod of time is concreated with creaturess ubject to time, and hencei ti sa lso undoubtedlyacreature. Fort herea re not and therec ould not have been and never can be anyp eriods of time that God did not create".  "Things are said to be created in the beginningoftime, not as if the beginningoftime werea measureofcreation, but because together with time heavenand earth werecreated" (St. Thomas Aquinas,1997, Q46,3 ,4 56). in time.¹⁴ He suggested that an initial seed of light instantaneously propagated into an expandings phere, thereby giving rise to spatial extension and starting ap hysical process in time. Interestingly,l ight was conceivedo fam oref undamental nature thans pace and time. Matter was draggedb yt he expanding light,thus decreasingindensity.Since accordingtoAristotelian physics vacuum is impossible, there has to be al ower limit of possibled ensities. Grosseteste thoughtt hatw hen the expanding sphere was maximallyr arefied, it stabilized to form the outer cosmic boundary. Then every part of the newlyf ormed sphere became asourceoflight propagating towardsthe center.Matter was again draggedb yt he light front,r eaching an ew limit of rarefaction and producing as econd sphere (that of Saturn). Similarly, by meanso fs uccessive light frontse manating inwards,a ll other spheres were formed, completinga ll the orbso ft he Aristotelian universe.
While Grosseteste'sc osmology maya ppear naïvet ou s, it represents ar are earlya ttempt to describet he development of af inite-age universe based on a conceptuallyc oherent physical system.

3N ewtona nd the DarknessP aradox
The most revolutionary aspects of the Copernican visionconcerned the periphery of the universe, rather than its center.A st he movements of the stars weree xplained in terms of Earth'sm otions, the lack of anym easurable parallax soon required stars to be placed at huge distances,f loating in boundless space. The Greek principle of circular uniform motion was still maintainedb yC opernicus, but was soon destroyed by Kepler'st hree laws of planets motion. The advent of Newtonian physics eventuallyc onsolidated the concept of absolute space and time. As he wrote: "Absolute, true, and mathematical time, of itself, and from its own nature flows equablywithout regardtoanything external" (Newton 1846,77) and similarlyf or space.
The extraordinary success of Newton'su niversal laws seemed to establish the definitive cosmic framework, convincing in its simplicity and prediction power.M oret han ever,t ime playedt he role of an inflexible and eternal axis. The Newtonian universe was spatiallyinfinite in all directions, everywherefilled with stars and subject to the same physical laws,w ithout temporal beginning nor end. However,a na nnoying detail was disturbing the picture:i ns uch uni- The cosmological vision of Grosseteste is found in his works De Luce, De motu corporali et luce and Hexameron. Fors ome mored iscussion, see Bersanelli (2012).
The Age of the Universe verse the night sky can'tb ed ark. This remarkable circumstance, first noted by Kepler and occasionallyd iscussed by astronomers along the centuries,¹⁵ is quite simple to see. Since the luminosity of as tar scales as the inverse square of the distance, G 1=r 2 ,and the number of stars in athin sphericalshell at distance r grows as n G r 2 ,the luminosity contributed by each shell is L G n L 0 , independent of distance.
As aconsequence, in an infinite and eternal universe the overall luminosity of the sky would divergea nd reach everywhere the brightness of the sun. Interestingly,the first appropriate suggestion of aw ay out of this dilemma came not from ascientist, but from an artistand writer.In1848 Edgar Allan Poe suggested that the paradoxw ould be solvedb y" supposing the distance of the invisible background so immense thatn or ay from it has yetb een able to reach us at all" (Poe 1848, 62). The darkness of the sky would be explainedi ft he universe itself had af inite age.

4T owards aB eginning of Time
The vision of an ageless universe wasa bout to crumble at the beginning of 20 th century.Between 1912 and 1924 VestoSlipher,from Lowell Observatory,Arizona, measured the spectraof4 1spiralnebulae, enigmatic faint diffuse objectswhose nature was much debatedatthe time,and found thatnearlyall of them showed aw ell-measurable shift towards longer wavelengths,o rredshift. Interpreted in terms of Doppler effect,this observation implied thatthose objectswerereceding with velocities of several hundred km/s, much largerthan typical stellar or planetary velocities. Something weirdw as going on. In the early1 920'sE dwin Hubble, at Mount Wilson Observatory,using an ingenious method basedonaparticular class of variable stars called Cepheids,¹⁶ was able to estimate the distance of af ew spiral nebulae. He found that they werea sf ar as am illionl ight years or more,¹⁷ demonstrating thatthey are indeedexternal galaxies similar to our Milky Way.
 The darkness of the night sky became known as "Olbers' paradox".Afull account is givenin Harrison 1987.  The use of Cepheids as distancei ndicators,d iscoveredi n1 912 by Henrietta Leavitt,i ss till cruciallyimportanttoday.Cepheids variablesare aspecific class of pulsatingstars that vary regularlyinbrightness with aperiod that correlates with their intrinsicluminosity.Once calibrated, measurements of the period allow astronomers to derive their brightness and, combined with the fluxr eceivedo nE arth, to derive their distance.  Todayt he distancet oM 31 is measured to be about 2:5t imes more.
By 1929 Hubbleh ad measured the distance of several galaxies of Slipher's sample, whose redshiftw as known, and by correlating their distance d with recession velocity v r he famouslyfound evidence of alinearrelationship, v r H 0 d, where H 0 is known as the Hubble constant (Fig. 1). Although Hubble himself was cautious about attaching astrongcosmologicalmeaning to this result,¹⁸ his finding was about to changeour cosmic vision. Not long before, in 1916,Albert Einstein had published his theory of General Relativity,w hose cosmological solutions could naturallye xplain the observedr ecession velocities. General Relativity predicts ad ynamic space, either expanding or contracting,w ith an evolution controlled by the gravitationalc ontent of the universe. However,E instein was not prepared to recognize an evolving cosmos.In1917heintroducedan additional term in his equations, without violating their mathematical coherence, and attributedtothis "cosmological constant" preciselythe value required to restoreastatic space.
However,Einstein'ssolution turned out to be unstable. Before Hubble'sempirical discovery,t he Russian physicist Alexandre Friedmann and the Belgian cosmologist GeorgesLemaître, independentlyderivedafamilyofrelativistic solutions for an expanding universe (Fig. 1). Lemaîtrei np articular, who was well aware of Slipher'sr edshift measurements,went beyond and using the available data found evidence of cosmic expansion two years before Hubble'sresult.¹⁹ Although based on less accurate data, he correctlyinterprets the redshift of galaxies as due to cosmic expansion, as opposed to aclassical Doppler effect within a static Newtonian space.²⁰ Lemaîtrer ealized thati fw el ivei na ne xpandingu niverse, then its average matter-energy densitymust decrease and the universe as awhole maybesubject to ad ramatic evolution history.B ye xtrapolatingb ack enough in the past,t he density of the universe would reach extremelylarge values. By 1931 he was convinced that the expansion we observet odays hould indeed be regarded as the aftermath of such an early, ultra-compact phase, that he called the "primeval atom".F or those who werer eadyt ot ake seriously this possibility, the question would naturallya rise: when did cosmic expansion begin?A nd can we observationally constrain such primordial era? In Lemaître'svision, for the first time, the concept of an ageo ft he universe became an element within as olid physical  See, e. g., Luminet 2014 and references therein.  Lemaître(1927)assumed the visual brightness of galaxies as distanceindicator,which introduced al arge spread in his data points.  In recognition of Lemaître'sfundamental contribution in 2018 the IAUdecided to rename the expansion law, traditionallyk nown as Hubble law, as "Hubble-Lemaîtrel aw". theory-General Relativity-and, at least in principle, subjectt oe xperimental verification.
Assumingthat the expansion rate did not changemuch in the past,acrude estimate of the ageofthe universe t 0 can be inferred as the inverse of the Hubble constant, t 0 v r =d 1=H 0 .The sample of galaxies measured by Hubble yielded a value H 0 % 500 km s À1 Mpc À1 ,which corresponds to t 0 % 1:8 Â 10 9 yr 1:8G yr.²¹ Lemaître'sestimate resulted in an even youngeruniverse, t 0 % 1:4G yr. These cosmic ages, however,weretoo shorttobetrue. The conflict was not with other astronomical observations, but with geological data.
In 1927 Arthur Holmes,apioneer in the measurement of rock ages from uranium-lead radiometric dating,s howed the ageo ft he Earth to be at least 3.0 Gyr.²² And of course, no object in the universe can be older than the universe itself!L emaître was aware of this problem and considered in his relativistics olution an on-zeroc osmological constant,²³ with ag eneric small value, as he realized it would have the effect of increasingt he present ageo ft he universe. Lemaître'sd efense of the cosmological constant,h owever,w as mostlyi gnored and set aside until recent times.  Hubble( 1929) showing the first solid evidenceo fl inear correlation between recession velocity and distanceo fg alaxies. Right: Af amily of solutions fort he expansionh istoryo ft he universe, as calculated by Lemaître( here, the horizontala xis is cosmic time, the vertical axis is an expansion scale factor). a) LemaîtreA rchive, manuscripts (1927), Louvain University. a) LemaîtreA rchive, manuscripts (1927), Louvain University.
 This means that for every mega-parsec (Mpc) in distance the recession velocity increases by 500 km/s.Aparsec (pc) is 3.26 light years. The unit Gyr( giga-year)i sab illion years.  See Dalrymple 2004,5 2.  This is the same parameter that Einstein initiallyi ntroduced with an ad-hoc value in his attempt to keep the universe static. Latero n, Einstein claimed that introducingt he cosmological constant was "the worse blunder of his life",and sincethen most cosmologists assumedthat it is simplyz ero.
The cosmic agedilemmacontributed to some skepticism against the concept of afinite-age universe by most eminent scientists in the field.Sir Arthur Eddington stated that "Philosophically, the notion of abeginning of the present order of nature is repugnant to me… Ishould like to find agenuine loophole" (Eddington 1931, 447-453). The fact that Lemaîtrewas acatholic priestraised suspicion that his idea of a primevala tom mayb ef orced in by his religious belief. However, while it'sl ikelyt hatL emaître'sp hilosophicalb ackground made him prepared to such apossibility,h ew as never drivenb yt heological prejudice but by scientific evidence (Lambert 2015). Einstein, in particular, was quite reluctant to consider cosmic expansion, let alone abeginning of the universe. When he met Lemaître for the first time at the 1927 SolvayC onference, after some appreciation for the mathematical results of the Belgianp riest, he bluntlyc oncluded that, however, "from the physical point of view,[ those results] appeared completely abominable";a nd in al ettert oD utch cosmologist Willem de Sitterh ew rote "This circumstance[ of an expandingu niverse] is irritating… To admits uch a possibilitys eems senseless" (Lemaître1 958, 129 -132).²⁴ Recently, an unpublished work by Einstein was uncovered which further confirms his aversion to an evolving universe (O'Raifeartaighe ta l. 2014; Castel-vecchi2 014). In 1931, as the observational evidence of expansion gained strength, Einstein conceivedac osmological solution in which the expansion was counter-effected by the creation of new matter from empty space, in such aw ay that the globala verage densityw ould remain unchanged in time. This work was never published.Almost two decades later, aconceptuallysimilar scenario was independentlyp roposed by Fred Hoyle, Herman Bondi and Thomas Gold, named "steadys tate" model (Hoyle 1948;G old 1948), which rivalled the 'Big Bang' scenario up to the early1 970's. The theory was openlym otivated by philosophical and aesthetic preferencef or ah omogeneous and isotropic universe with no beginning and no change-the so-called "Perfect Cosmological Principle"-and wasc apable of sound specific falsifiable predictions (Kragh 2007,1 84 -200). In these stationary cosmologies the flow of time would drive all sorts of processes on local scales, but the universe as aw hole, though expanding,w ould not have anyb eginning,t hus radicallys olving anya ge issue.
Indeed, besides philosophical inclinations, the "young" universe problem required as cientific explanation. In the 1940'st he dilemmag ot worse, as thermonuclear reactions were recognized to be the energy sourceofstars and placed stellar ages up to severalGyr.Finally, in the 1950'sthe fog started to dissipate. It was realized that the Cepheids and other standard candles that Hubbleu sedt o  See also Luminet (2014) and references therein.
The Age of the Universe measure galaxy distances werea ffected by systematic calibration errors.²⁵ That bias led to an overestimateo fH 0 by af actor~3,a nd to ac orresponding underestimate of the ageo ft he universe. Allan Sandage ( Tammann and Reindl 2012) greatlyi mproved the techniquest om easure distances and in the early6 0 ' sh e obtainedvalues for H 0 between 75 and 100 km s À1 Mpc À1 .The ageofthe universe was now in the range10to13Gyr,compatible within uncertainties with geological and astronomical limits.
The fascinating and fruitful debate between finite-age and age-less universe reached adefinitive turning point in 1965, when Arno Penzias and BobWilson at Bell Labs,N ew Jersey,s erendipitouslyd iscovered ab ackground of microwave photons comingf rom every direction of the sky with at emperature²⁶ of~3K. Robert Dicke'scosmology group at nearby Princeton Universityreadilyinterpreted the radiation as ar emnant of the primordial hot universe.²⁷ Within ad ecade or so, further observations confirmed that the radiation had the main features expectedfor afield of fossil cosmological photons.Asweshallsee, this ancient light,called cosmicmicrowave background (CMB), not onlyprovided adefinitive evidence thatw el ivei nahistoricalu niverse, but since then it has offered a uniqueo pportunity to measure cosmic aget ou nprecedented precision. To see how that is possible, we have to consider in some more detail how gravity affects cosmic expansion.

5G ravity vs.E xpansion
Estimating the ageofthe universe as the inverse of the Hubble constant assumes that the expansion rate has remained constant in the past.But is this arealistic assumption?A nd how can we tell?H erei sw hereG eneral Relativity demonstrates its amazingpower.AsLemaîtrefirst understood, expansion is aproperty of space itself,not amotion of galaxies within astatic space. Cosmic expansion  It was realized that therea re two classes of Cepheids,with different period-luminosity correlations.T he local Cepheidsu sed by Hubble to calibrate the correlation weres ystematically fainter than those in external galaxies,which resulted in an overestimateoftheir distance. Furthermore, for some of the most distant galaxies,s tar clusters werec onfused with individual stars,f urther contributingt oa no verestimateo fH 0 .  In radio and microwave astronomyitisconvenient to express electromagnetic brightness in terms of the temperatureo fa ne quivalent blackbodys ource. is quantified by an adimensional scale factor, at,which is normalized so that its present value is unity, at 0 1. Auniverse thatexpands at afixed rate is simplyd escribed by atH 0 t ,a nd its agei st 0 1 = H 0 .G ravity,h owever,m akes thingsm uchm ore interesting.A ccordingt oEinstein'sf ield equation, expansion is influenced by gravitationaleffects produced by the different matter and energy components that are present in the universe. The total matter-energy density, Ω 0 , can be expressed as the sum of in three terms: The first term, Ω R ,isthe energy densityofradiation, which includes photons and relativisticp articles such as neutrinos. The second term, Ω M ,i ncludes ordinary baryonic matter( the stuff that makes stars, planets and ourselves) as well as dark matter.²⁸ The third term, Ω Λ ,dubbed "dark energy",incorporates the energy density associated with an on-zeroc osmological constant.General Relativity shows that the value of Ω 0 determines the global curvatureo fs pace, so it's convenient to normalize these parameters so that Ω 0 1c orresponds to a zero-curvature( Euclidean) space. The three contributions Ω R ; Ω M ; Ω Λ changei n different ways with the scale factor at and thereforebecome dominant at different epochs of cosmic history.Radiation has the fastest decrease, proportional to a À4 ,t hus it dominated in the youngu niverse but it rapidlyb ecame negligible. Then matter density (which scales as a À3 )t ook over,a nd the universe entered the phase when local gravitationalc ollapse was able to form galaxies,s tars, planets, opening the waytothe complexity we seeand experience today. Finally, the term Ω Λ is independent of the expansion rate. Therefore, ap ositive value of Ω Λ ,evenifsmall, at some point will make dark energy the dominantform of energy with the effect of acceleratingt he expansion.
General Relativity shows preciselyh ow the density parameters,c ombined with av alue of the Hubblec onstant,d etermine the function at.F ig.2shows af ew solutions for at,a ssuming af ixed value of H 0 .The ageo ft he universe is the intersect of each model curvew ith the horizontal time axis. The redl ine corresponds to an ideal 'empty universe',i nw hich all density parameters are set to zero. In this caseofcourse gravity has no effect,the expansion rate is constant and t 0 1=H 0 .F or anyn on-zeroc hoice of the density parameters the expansion is influenced by the gravitationale ffect of the respectivem ass-energy  Therei ss trong observational evidencet hat about 80 %o ft he matter contributingt ot he gravitational fields of galaxies and clusters of galaxies is in some form of non-baryonic particles, called "dark matter",whose nature is yetu nknown.
The Age of the Universe contributions,resulting in different cosmic ages. Forexample, if Ω R Ω Λ 0and Ω M 1( the so-called "Einstein-De Sitter Model"), calculation shows that t 0 2=3H 0 .H igher values of matter density lead to shorter cosmic ages. In the case shown (Ω M 6, with Ω R Ω Λ 0) gravity is stronge nough to win over expansion and the universe will eventuallycontract and collapse in afinite time in the future. Note thatthe effect of Ω Λ > 0istointroduce an acceleration at late times (dotted curve), which impliesa nincrease of the present cosmic age.
In general, it is convenientt oe xpress the ageo ft he universe as the inverse of the Hubble constant times afactor, f ,which incorporatesthe gravitationaleffects of the density parameters: General Relativity specifies the function f ,a ss hown here for completeness: The values of the four free parameters-Hubble constant and the three density parameters²⁹-is not fixed by the theory.Ifweare able to accuratelymeasure their values, then the ageo ft he universe can be derivedw ith ac omparable accuracy.
In the mid 1990'sanumber of studies of galaxies distribution suggested a value Ω M % 0:3, corresponding to an open universe with t 0 % 12 Gyr. Although the uncertainties werel arge,s uch cosmic agew as hardlyc ompatible with the ageo fs ome old stellar clusters (Spergele ta l. 1997),³⁰ measured to be 13 -14 Gyr.C osmologys eemed to enter another embarrassing agec risis. Quite timely, however,another unexpecteddiscovery came on stage. Twoindependent groups using as pecific class of distant Supernovaea ss tandard candles,³¹ realized that the present expansion rate is higher thanitwas afew billion yearsago (Perlmutter et al. 1999;R iess et al. 1998).³² In other words, cosmic expansion is accelerating,which implies apositive value of Ω Λ (Fig. 2).Their fit to relativisticmodels suggested Ω M % 0:3( compatible with previous estimates) and Ω Λ % 0:7. The discovery that Ω Λ > 0, ap ossibility nearlyf orgotten since the times of Lemaître, was am ajor surprise for the physics community at large.The effect on the age of the universe was an increase by~2 Gyr,t hus resolving the aget ension with globular clusters.
Ac oherent picture seemed to emerge,b ut the measurement uncertainties werev ery large,o ver3 0%,a nd the issue of cosmic agew as stillw avering. Since then,o bservations of the relic CMBp hotons have playedac entral role in pinning down the value of the cosmological parameters,includingthose controllingt he ageo ft he universe.

6C osmic Agea nd Cosmic Edge
The discovery of the CMBtransformed the bold hypothesis of an initial hot state of the universe into aunique observational opportunity. The primordial hot and compressed plasma progressively cooledand rarefied underthe effect of expansion. After about 380,000 years, when the temperature dropped below~3000 K, neutral atoms could form from the primordialmixture of electrons and light nu- The total density Ω 0 is just their sum.  We will come back to ageo fg lobular cluster later in this work.  These wereaspecific class of explodingstars,called Supernovae type-Ia, which result from very repeatable process and therefore present an earlys tandardp eak luminosity which can be used to infer the distanceo ft he host galaxy.  The discovery led to the 2011 Nobel Prize to Saul Perlmutter,Brian Schmidtand Adam Riess.
The Age of the Universe clei (essentiallyh ydrogena nd helium). As matter became electricallyn eutral, suddenlyt he universe became transparent to light and the CMBp hotons could freelyp ropagate. At that time, known as 'recombination epoch',the wavelength of the photons was $ 0:5 À 1m icron, i. e., in the visible to near-infrared. Since then, the expansion has stretched their wavelength by af actor z$ 1100, shifting them into the microwave range(~few mm).The low energy of the relic photons, combined by the finite ageo ft he universe, fullye xplain the darkness paradox.
We see the CMBemerge from asort of cosmic photosphere, called "last scatterings urface",s urroundingu sn ear the edge of the observable universe. Such space-time surface represents ap hysical barrier to direct observation with light,asbeyond that limit the universe is opaque to electromagnetic radiation.³³ Despite the enormous number of galaxies,the voids between them are huge and the CMBtraveled nearlyunperturbed for almost the whole cosmic time, bringing to us ar emarkably faithful imageo ft he last scattering surface.
Since its first discovery,the CMBhas been agenerous sourceofcosmological information. Itst hermal origin is brilliantlyc onfirmed by its purelyb lackbody spectrum,m easured to exquisite precision (Mather et al. 1994) at at emperature T 0 2:725 AE 0:001 K. The correspondingr adiation energy density³⁴ turns out to be, Ω R % 10 À4 ,w hich is very small compared to the other density parameters. As aconsequence, the gravitationaleffect of radiation can be ignored in the calculation of the factor f,awelcome simplification in our attempt to measure the ageo ft he universe.
The CMBintensity is highlyisotropic, but not completely. This wasexpected because, in order to explain the formation of galaxies and of other cosmic structures under the action of gravity,primordial densityp erturbations needed to be present at the last scattering.Since the CMBphotons are influenced by the gravitational potential, their intensity traces the earlydensity perturbations and must appear to us as temperature differences from one direction to another in the sky. In 1992, NASA'sCOBEsatellitefirst detected such CMB anisotropies³⁵ at alevel of 0:001 7 at all angular scales largert han $ 7°. In 2000,N ASAl aunched the  In some future,wemight be able to detect the background of low-energy cosmic neutrinos, which cross unimpededt he hot primordial plasma and reach us directlyf romauniverse only $ 1s old. And if primordial gravitational wavescould be measured, these would getusadirectly to at inyf raction of as econd of the beginning.  The radiation density parameter includes also the contribution of neutrinos,a bout 68 %o f the photon energy density. WMAP satellite³⁶ which obtained full-sky maps of the CMBfluctuations with subdegree angular resolution and much improved sensitivity.The Planck satellite, launched in 2009 by the European SpaceA gency,r epresents the current state of the art of full-sky CMBo bservations.
The amplitude of CMBa nisotropies at different angular scales depends on the physical conditions in the hot primevalmedium, as well as on the geometry of the expandingspace in which the photons have travelled to reach us. Forthis reason, CMBa nisotropies encode aw ealth of cosmologicals ecrets that can be unveiled by accurate, high resolution measurements.The fundamental statistical information contained in aC MB map is captured by the so-called "angular power spectrum",aspherical harmonic expansion of the measured temperature fluctuations in the sky.The power spectrum quantifies the amplitude of the anisotropy as af unction of angular scale ,o rm ultipole`$ 1=.O ns cales below $ 1°,p rimordialf luctuations werep rocessed by acoustic oscillations drivenb y gravity and photon pressurei nt he baryon-photon fluid. The oscillations that happened to be in maxima of compression or rarefaction at the time of decoupling,p roduce peaks in the anisotropy power at specific angular scales. Therefore, the theory predicts ac haracteristic harmonic pattern (Fig. 3) whose details are very sensitivet ot he physical characteristics of the primordialp lasma,i ncludingt he value of the densityp arameters and of the Hubble constant.I n turn, accurate measurement of the CMBc an be used to extract the value of those parameters.

7T he Very First Light
The precise measurement of the main cosmological parameters was one of the key scientific objectiveso ft he ESAP lanck satellite,³⁷ launched by an Ariane 5 rocket from the launch pad in Kourou, French Guiana, on 14 May2009.The satellite took data uninterruptedlyfor four years, scanning the sky from an especially suitable orbit at 1.5m illion km away from Earth. The telescope, instruments and observing strategy wered esigned to reach an unprecedented combination of angular resolution (up to 0.1°), skyc overage( 100 %), wavelength range (from 0.3t o1 0m m),s ensitivity (ΔT/T~10 -6 ), calibration accuracy (< 0.1%). Local astrophysical emissions contributet ot he observed microwave signal and must be accuratelyremoved. The extreme sensitivity of Planck called for pre- Fort he excellent WMAP results see Bennett et al. (2013) and references therein.  https://www.cosmos.esa.int/web/planck. The Age of the Universe cision measurement not onlya tw avelengths dominated by the CMB (~3 -4m m), but also in spectral bands wheret he foregrounds are strong.T o cover such wide wavelength range, two complementary instruments were developed, using radiometric and bolometric detectors in theirbest windows of operation, cooled to cryogenic temperatures.³⁸ The two instrumentss hared the focal plane of a1.5-m off-axis telescope (Fig. 4). The ambitious performance of Planck was verified in ad emanding ground calibration campaign before launch, and has been wonderfullyc onfirmed by in-flight data.
To calibrate the CMBmaps, Planck (as well as WMAP and COBE/DMR) used the effect of the proper motion of our local rest frame with respect to the CMB itself. In fact,a sf or anyo therc osmic observer,o ur local motion produces by Doppler effect as light increase of the CMBt emperature in the direction of our velocity vector,and asymmetric decrease in the oppositedirection.³⁹ Interestingly,therefore, the CMBrepresents anaturalglobal rest frame to evaluatethe local velocity of anyc osmic observer relative to the expansion flow.This philosophicallyi ntriguing circumstanceh as alsot he very practical advantage of providing an earlyp erfect calibrator for CMBo bservations.  The final analysis of the Planck data has been recentlyc ompleted (Planck Collaboration, 2020a-b). The Planck data also include polarization and gravitational lensing,w hich provide further leveraget oe xtract cosmological parameters.F ig.5shows the full-sky map of temperature anisotropies after removal of the foreground emissions. Thec orresponding angular power spectrum is shown in Fig. 6. The blue solid line is the best fit to the simplest cosmological model, which includes six degrees of freedom encodingthe values of cosmological parameters.The redpoints are the Planck data. Hereone can appreciate the amazing agreement between the experimental data and the theoretical model. The Planck results on polarization and lensingb eautifullyc onfirm the best fit parameters and help break internal degeneracy.
The six-parameter fit yields aH ubblec onstant of 67.4 ±0 .5 km s -1 Mpc -1 , somewhat lower than previous estimates basedontraditional methods. The matter energy density⁴⁰ gives Ω M 0:315 AE 0:007, consistent with previous estimates but greatlyi mproved accuracy.A llowing the total densitya safree parameter⁴¹ provides very stringent limit on curvature, which is further tightened by combining Planck data with recent measurements of large-scale structure, yielding Ω 0 0:9993 AE 0:0019. We seem to live in av ery Euclidean universe: even with  Planck also measured the independent contributions frombaryonic and dark matter components,which account for 4.9% and 26.5 %, respectively,o ft he total energy density.  The standard6 -parameters fit assumes aflat geometry (Ω 0 =1), so fittingfor Ω 0 is an extension of the basic model.   <1%p recision we can'tdetect anyglobal curvature. The remainingenergy density is contributed by dark energy,w ith Ω Λ 0:685 AE 0:007, in agreement with the independent estimate of the acceleratedexpansion from type-Ia Supernovae, but again with much improved precision. The combination of these resultsyield an ageofthe universe of t 0 13:797 AE 0:023 Gyr. This level of accuracy (~0.2 %) is quite remarkable: it'slike guessing the ageofa50-years-old person with the precision of 1m onth.

8T he OldestO bjectsi nH ouse
These high precision resultsc all for independent crosschecks. Results from previous CMBe xperiments and other cosmological probes,while less accurate,a re generallyingood agreement with thoseofPlanck.⁴² Recently, however,improved measurements of the Hubblec onstant from traditional Cepheid-calibrated red- The Age of the Universe shift-distance methods⁴³ yielded values~8 %h igher thanC MB-based results (both Planck and WMAP),a nd of course ac orrespondingly younger universe, t 0~1 2.7G yr.Whether this tension, significant at~3.5 standard deviations, is a symptom of new physics,oritisdue to undetected systematic effects, is the subject of ar enewed debate on the value of the Hubble constant.
Ar adicallyi ndependent verification mayc ome from the limits imposed to the ageo ft he universe by the oldest stars (Fig. 8). Even as ingle object older than t 0 would represent as erious challenge. On the other hand, we have evidence that the first stars were bornjust~0.6 Gyrafter recombination (Planck Collaboration 2018a), so we expect the oldest stars to be~13.2 Gyr or~12.1 Gyrold, depending on the scenarios.Exploiting at best our understanding of stellar physics we have an opportunity to test cosmology-based estimates.
How can we identify very old stellar objects?Afirst wayistolook at globular clusters,families of 10 5 to 10 6 stars known to have formedvery earlyon. Astronomers can measure the ageofastar cluster by studying theirstellar population. Since more massive stars live shorter livesi nt heire quilibrium state (called "main sequence"), by looking at the most massive starsw hich are still in the main sequence one can infer the cluster age. Ar ecent studyo f2 2c lusters shows ages in the range1 0.8 -13.6 Gyr with typical uncertainty ±1.6G yr.Adetailed work on the cluster HP-1 yields an ageo f1 2.8±0.9G yr (O'Malley et al. 2017;K erber et al. 2019). Independent measures of globular clusters age come from whited warfs, compact stellar relics slowlyc oolingd own as they radiate their internal heat.Aclassic study ( Hansen et al. 2002)o fw hite dwarfs yield 12.7 ±0 .7 Gyr,f ullyc ompatible with main sequence agee stimates.
Another agetest comes from single, very old stars. We can recognize them by studying their composition. Just after recombination, 380,000 years after the Big Bang,t he onlye lements in the universe wereh ydrogena nd helium, as Carbon and heavier elements (called "metals" by astronomers) would onlyforminthermonuclear reactions in stellar cores. New starswerecontinuouslybornfrom the ashes of previous generations, with increasinga bundance of heavy elements. Therefore, stars with very little "metallicity" must be very old, and astronomers can quantify their agef orm detailed analysis of their spectra. As tudyo ft hree sub-giant ultra-low metallicity stars (Vanden Berg et al. 2014)g avea geso f 12.08, 12.56, and 14.27G yr with an uncertainty of ±0.8 Gyr.
The latter star (HD140283, known as Methuselah Star)a tf ace value has an agee veno lder than the value of t 0 measured by Planck, but well compatible within the uncertainty,while it is somewhat in tension (~2.7 standard deviations)  These programs used Cepheid-calibratedS upernovae type-Ia (Riess et al. 2018). with the youngeru niverse implied by the recent Cepheid-based estimateso fH 0 . Overall, stellar ages seem to prefer the CMB-drivenestimates, but the uncertainties are still too large.F uture progress in stellar astrophysics,aswell as on other independent approaches⁴⁴ to measure H 0 ,w ill surelyc ontributet ot he cosmic aged ebate.⁴⁵ 9AWonderful Space-Time VistaP oint Formillennia the notionofanageless and unchanginguniverse has been deeply rooted in human minds. The Aristotelian-Ptolemaic model encoded the vision of an eternal cosmos into ac omplex geometrical structure thats uccessfullyr eproduced all visibletrajectories in the sky.The Copernican revolution and the establishmento ft he Newtonian system represented two enormousp aradigm shifts, however,n either of them even touched the vision of ag loballyi mmutableu niverse. It is not surprising,t herefore, that when theoretical and observational hints of an evolving universe emerged, the transition to the new view was troubled and highlyd ebated, resisted even by some of the very same actors of the new emergent paradigm. The most shocking element was the notion that the universe itself mayh aveabeginning.I ns pite of Einstein'sr eluctanceh is General Relativity,asproposed by Lemaître and Friedmann and combined with observations by Hubbleand others, broughtt he concept of cosmic ageinto mainstream  Ap romisinga venue is to use gravitational wave "standards irens" (Feeney et al. 2019).  Forf urther discussion, see Jimenez et al. (2019). The Age of the Universe science. Since then, evaluating the ageofthe universe has become an ambitious objective of experimental work. Today, just ac enturyl ater,o bservations of the primordial CMBp hotons have led to an estimate of cosmic ageo ft 0 =1 3.8G yr with sub-percent accuracy,i ng ood agreement with most independent probes.
The time t 0 is the present ageofthe universe not onlyfor us,but for any cosmic observer.Furthermore, the CMBtemperature provides anatural cosmic clock, in asimilar wayasitoffers anatural reference frame to measure local velocities. As the universe expands, the CMBt emperature slowlyc ools down as T CMB tT 0 =at,aknown monotonic function of time. This is indeed av ery slow clock hand:with our current technology,toappreciatethe smallest conceivable temperature drop, say1μK, it would take4 ,700y ears. Of course, we can't wait that long,h owever,i ti sp ossible to measure now the temperature of the CMB as it was in the past,b yi ndirectlym easuring its temperature in regions that are sufficientlyf ar away.⁴⁶ These observations have been carried out and confirm the expectedc hange T CMB t,f urther provingt he reality of our evolving cosmic scenario.
Our measurements of cosmological parameters not onlyd etermine t 0 ,b ut also the epoch of an umber of global events that took place in cosmic history. Going backwards, these include the starto ft he accelerated expansion (t ≈ 9.8G yr), the formation of the first stars (t ≈ 0.6G yr), photon decoupling (t ≈ 0.38 Myr), primordial nucleosynthesis (t ≈ 100 s), electron-positron annihilation (t ≈ 30 s), decoupling of neutrinos (t ≈ 2s ), protons and neutrons formation (t ≈ 10 -4 s), and more.Insome sense, all these events are present to us now, as they are imprinted in space-time layers at different depths into the observable universe. We can'ts ee most of them directly( an otable exception is photon decoupling, beautifullyv isiblet ou st hrough the CMB), but in principle they are all out there. Interestingly though,asadirect consequenceofcosmic expansion, we would seet hem to last am uch longer time than they actuallyt ook for ah ypothetical local witness. Indeed, as observations confirm,⁴⁷ the duration Át of a past cosmic event is observed to last Át 0 Át=at.F or example, primordial nucleosynthesis, which lasted~5 minutes,i fo bserved now in the distant universe would appear to lastsome~120,000 years. Seen through our eyes, or through the  This has been done in two ways:byexploitingthe scatter of CMB photons off the hot gas in clusters of galaxies, known as thermal Sunyaev-Zel'dovich effect; and by measuringt he excitation by CMBphotons of C, CO or CN absorption lines in the spectra of distant quasars (Luzzi et al. 2015).  Cosmological time dilation was observed in SN Ia (Foley R.J. et al. 2005); and in Gamma Ray Bursts (Zhang et al. 2013). eyes of anyothercosmic observer,time indefinitelyslows down as we approach the beginning of time.
In retrospect,itisabsolutelyremarkable thattodayw eare discussing slight tensions at the few percent level about the ageofa13.8 Gyrold universe. On the other hand, we should not forgett hat our understanding of the universe is still incomplete, and becomesp articularlyu ncertain when approaching the very beginning of cosmic time. As history has shown, our notiono fw hat we mean by "universe" has deeplyc hanged in different epochs. It is entirelyp ossible that cosmologists of the next century willr egardo ur views as naive steps towarda new and deeper cosmic vision, hopefullyi ncorporating (not rejecting!) what we have learned so far.I fs ome of the current speculationsw illt urn out to be correct,w em ight be brought back to an ew incarnation of the traditional imageo fa ne verlasting and ultimatelyu nchangingc osmos;⁴⁸ or perhaps the next revolution in cosmology will be entirelys urprising and far from current ideas. But surelyf or the time being we can enjoy the awesome space-time panorama we have come to understand and contemplate.