aa r X i v : . [ phy s i c s . g e n - ph ] J u l On the quantum description of the early universe
Gabriel R. Bengochea ∗ Instituto de Astronom´ıa y F´ısica del Espacio (IAFE),CONICET - Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Why is it interesting to try to understand the origin of the universe? Everything we observe today,including our existence, arose from that event. Although we still do not have a theory that allows usto describe the origin itself, the study of the very early era of the universe involves the ideal terrainto analyze the interface between two of today’s most successful physical theories, General Relativityand Quantum physics. But it is also an area in which we have a large number of observationaldata to test our theoretical ideas. Two of the fathers of Quantum physics, Niels Bohr and WernerHeisenberg, shared some thoughts that could be described with these words:
Quantum physics tellsus that there is a line between the observed and the observer, and therefore science should be limitedto what is observed. We must give up a complete, objective and realistic theory of the world . Thisarticle will orbit around these ideas and summarizes how it is that today, from recent works, we arein a position to try to challenge them (at least in part) through cosmology, seeking the quantumdescription of the early universe.
Keywords: Cosmology, Inflation, Quantum Cosmology, Quantum Foundations
I. INTRODUCTION
The Big Bang model describes the temporal evolutionof the universe as a whole. This model has mutated overthe decades, to incorporate the results of increasinglyprecise astronomical observations. In this way, today themodel contemplates, in addition to matter constitutedby atoms, the existence of cold dark matter (CDM); andfor only about 20 years, we think that 70% of the en-ergy density of the universe is found in something wegenerically call dark energy, presumably in the form ofa cosmological constant Λ. Also, our current standardΛCDM cosmological model includes a phase of rapid ex-pansion at the beginning of the history of the universecalled inflation . The theoretical pillars of inflation are,fundamentally, General Relativity and the Quantum the-ory.The inflationary paradigm is held among the major-ity of cosmologists as a successful model for addressingthe primordial inhomogeneities that represent the seedsof cosmic structure. In fact, the standard predictionfrom the simplest inflationary model is extremely consis-tent with recent observations from the Cosmic MicrowaveBackground (CMB) radiation [1]. Then, why think of al-ternative ideas? Why is the physical mechanism respon-sible for the generation of the primordial perturbationsstill a matter of debate?On the one hand, although we have an excellent expla-nation, we must remember that throughout the history ofscience we have had very good scientific explanations forsome natural phenomena, which were later inadequate inlight of new experiments or theories that allowed the pre-diction of new phenomena. In some contemporary scien-tific works we can read phrases such as ”The concordancemodel is now well established” or ”there seems little room ∗ [email protected] left for any dramatic revision of this paradigm”. But withthese statements we could be exaggerating our successes.Therefore, maintaining our critical vision and exploringnew ideas are scientifically healthy.On the other hand, as we mentioned above, inflation isbased on a combination of Quantum theory and GeneralRelativity, two theories that are difficult to merge at boththe conceptual and technical level. If we want to considerthe inflationary account as providing the physical mech-anism for the generation of the seeds of structure, suchaccount must contain an explanation for some recentlystaged problems, e.g. [2–4], as well as give a satisfactoryanswer to the following question: why does the quan-tum state that describes our actual universe not possessthe same symmetries as the early quantum state of theuniverse, which happened to be perfectly symmetric?Since there is nothing in the dynamical evolution (asgiven by the standard inflationary approach) of the quan-tum state that can break symmetries, the traditional in-flationary paradigm is incomplete in that sense. As wewill see below, this is closely related to what is known as the measurement problem in Quantum physics [5–8], andwhich is notoriously exposed in the case of the quantumdescription of the very early era of the universe.There are promising alternatives to standard formal-ism today that allow, on the one hand, to accommodateempirical evidence, and on the other, to construct an ob-jective and complete image of the world. In order to eval-uate and classify the possible alternatives to achieve this,Tim Maudlin stated the measurement problem in a for-mal and general way, showing that there are three state-ments that are mutually inconsistent [7]. In short: A)the physical description provided by the quantum stateis complete, B) quantum states always evolve accordingto the Schr¨odinger equation, and C) measurements al-ways have definite results. And in such a work, the au-thor concludes that any real solution will demand newphysics and that, in particular, the so-called collapse the-ories and hidden variables theories have a good chance ofsucceeding.In this article, with a pedagogical approach aimed atscience students, teachers and also non-expert colleagues,we will make a description of the quantum problems thatmust be faced when it comes to giving a description ofthe emergence of seeds of structures in the early universe.Throughout the manuscript, we will mention various ap-proaches to these problems and, following Maudlin’s con-clusions in [7], we will emphasize the proposals known as objective collapse theories .In Sect. II we will highlight some differences betweenclassical and quantum physics; in Sect. III we will de-scribe the measurement problem in Quantum physics; inSect. IV we will address the cosmological case; in Sect.V we will mention an approach that seeks to solve theaforementioned problem; and finally, in Sect. VI, we willpresent some conclusions. II. CLASSICAL VS. QUANTUM PHYSICS
Here we are going to refer to classical physics as thatdescribed by Newton’s laws (or by Einstein’s theories ofRelativity). We use these laws to calculate and predict,for example, what are the values of the position and ve-locity of an object at a given time. Given the values inan instant, Newton’s laws allow us to perfectly predictits trajectory in space. From this point of view, classicalphysics is objective, complete and realistic. Briefly, with objective we mean that it does not depend on someonemaking the measurements (it does not need an observer);it is complete because in the theory there is all the in-formation necessary to describe the properties of objects(that is, every element of reality has a counterpart intheory); and realistic because the elements of the the-ory really describe real objects that have properties withwell-defined values. Those objects exist in the world re-gardless of someone observing them and, with the theory,one can predict those values.On the other hand, in standard Quantum physics,physical properties such as the position or velocity ofan object in general do not have defined values until ameasurement is carried out . All the accessible informa-tion of a quantum system is contained in what we callits wave function . This function is not something thatone can observe, but it is what allows us to calculateprobabilities, with a rule for that purpose given by MaxBorn in 1926, which constitutes one of the postulates ofQuantum Mechanics. Probabilities for what? For thepossible values of the physical quantities that could be By ’standard’ Quantum physics we are referring to the so-called
Copenhagen interpretation , which is adopted by the vast major-ity of authors in textbooks. However, the various interpretationsof Quantum physics studied at present face the problems men-tioned in this article. See for example [9]. obtained (such as the position, for example), if we madea measurement with some appropriate device to measurethe physical property that we are interested in knowing(the position of the object in our example). With thistheory we have been able to describe in an extremelyprecise and successful manner numerous phenomena andexperiments: from atoms and elementary particles, tohow the Sun and the other stars shine, nuclear energy,lasers and all the electronics we use in our daily lives, tomention just a few examples. In fact, our idea is thatthe whole universe in its essence is quantum and thenour daily macroscopic theories would be just very goodclassical approaches to something deeper and more fun-damental. But how is it that the macroscopic objects ofour daily lives, being composed of atoms, do not seem tobe described by the physics that so successfully describesatoms?In 1927, Werner Heisenberg proposed what is knownas the Uncertainty Principle . This principle tells us thatthe better determined is the value of a certain physicalquantity in a certain quantum state (the position, forexample), the less determined will be the value of an-other conjugate quantity (its momentum, or velocity).Recall that, according to Newton’s classical physics, ob-jects have, at any time, all the values of all propertiesperfectly defined. On the other hand, quantum uncer-tainties, together with the Born probability rule, give usthe range in which the property values are most likelyto be if we made measurements. Until we make mea-surements, with devices designed to know the values ofobservable physical quantities, these (and even the prop-erties themselves) are not determined and they are notindependent. In this way, although we measure someproperties, others will remain undefined or will be al-tered. Then, the most general quantum state will be astate of superposition. By superposition we mean that,as the values of some properties are not determined, thequantum state is a ”combination” of the possible statesand the Born’s rule allows us to calculate, from the su-perposition, the probabilities of the possible values.Here is where the best-known pet in physics comesinto play: Schr¨odinger’s cat. Erwin Schr¨odinger was theone who managed to formulate in 1925, following theideas of Louis de Broglie, an equation (today known as
Schr¨odinger equation ), which determines how the wavefunction of a quantum system and its probabilities evolveover time. It is the pillar equation of Quantum physics.And with it we will raise what is known as the paradoxof Schr¨odinger’s cat. We will use the terms ’physical quantities’ and ’physical proper-ties’ of objects as synonyms.
III. THE MEASUREMENT PROBLEM INQUANTUM PHYSICS
The theoretical experiment that Schr¨odinger thoughtin 1935 consists of the following: inside a closed box with-out windows there is a cat. In the box next to it is a bottlethat contains a deadly poison and there is also a random atomic device with two possible states, with a 50% prob-ability each. One of the states of the device has a 50%probability of acting on a hammer breaking the bottle,releasing the poison and thus killing the cat, at some timethat we cannot know with precision. The other state hasa 50% chance of not acting, and therefore the cat willremain alive. But, and here comes the important point,Quantum physics tells us that the most general state ofthe atomic device is a combination of the two possiblestates. But both, the device and the bottle with the poi-son, the hammer, the cat and the box are made of atoms.Therefore, everything should be described by Quantumphysics, if this, as it is supposed, is applicable to every-thing in the universe. If the atomic device is initially ina quantum state of superposition, considering both theapparatus and the cat as quantum systems that interactwith each other, the state of the cat will get entangled with that of the device, and then, it will also be in astate of superposition until some measurement is made.If we wanted to know, for example, something about the” liveliness ” property, according to Quantum physics (inits standard interpretation), until we make a measure-ment of that property the most general quantum state isa superposition of the two possible states: alive-cat and dead-cat , with 50% probability for each possibility. Thatis, the cat is not alive or dead. There is no definite valueof the liveliness property . And it is a perfectly valid andpossible state for Quantum physics.The Schr¨odinger equation, which allows us to know theevolution in time of the state of any quantum system, de-termines that the cat (or our knowledge about the liveli-ness of the cat in the standard interpretation) will remainin the ” alive-dead ” superposition state until someone orsome device for this purpose makes a measurement (openthe box, for example). Schr¨odinger’s equation does notdestroy neither superpositions nor probabilities and doesnot break symmetries; it is deterministic and reversible.With determinist we mean that you can know perfectlyat every moment what the wave function of the systemis, and reversible because at all times we can calculatebackward or forward in time what the value of the wavefunction is. We will call this ” Process A ”.But after a measurement, something happens. Thewave function ” collapses ” and a well-determined value is But be careful: it is not that it could already have a value butwe do not know it because of our ignorance. It has no definedvalue yet, until a measurement is made. And when we measure,there are still many other properties that cannot have their valuesdefined simultaneously. obtained (for example, the life of the cat results in alive-cat ). This other process is random (it could have been dead-cat ), it is irreversible (once we measure, we cannotknow if before that the cat was alive, dead, or alive-dead)and, therefore, some information is lost. We will call thissecond process ”
Process B ”. Similarly, when a scientist prepares a system in a lab-oratory (particles in an accelerator, for example) in astate of superposition (for example, for the position) andthen that system interacts with some appropriate mea-suring device to measure the position, the states of theindicators and the needles of the apparatus will becomeentangled with those of the system and, then, the wholeset (system + apparatus) ends in a state of quantumsuperposition. While nothing or no one makes a mea-surement, the needles of the device would continue in astate of superposition. However, of course, this is neverobserved in the laboratory.Then, if Quantum theory is applicable to everything,why small objects such as atoms can remain in states ofsuperposition, but everyday objects, such as my chair orthe needles of a device, are not in a superposition of twoplaces at the same time?The general situation is, then, that until we make ameasurement, the most general state of a physical sys-tem is to be in a superposition of states, and quantumuncertainties, together with the Born’s rule, tell us theranges of possible and more likely values of the proper-ties. And then, when we carry out a measurement toknow some physical magnitude, the X position, say, thewave function collapses and a well defined value is ob-tained for X , compatible with the Uncertainty Principle.But how does a system go from a superposition ofstates for X to another state without superpositions,and with a well-defined value of X , if the Schr¨odingerequation does not destroy superpositions? If someone(or something for that purpose) made a measurement, itwould reveal to us in what state the system is. But some-thing external should cause the wave function to collapseto another well-defined state. On the other hand, it is im-portant to say here that, in addition, the concept ” mea-surement ” is not satisfactorily defined within Quantumphysics. How large must an object be so that its statecollapses and is not in a superposition? About the sizeof a cat? When does a measurement happen? Quan-tum theory does not tell us. There is no clear criterionof when we should use the evolution given by Process A and when to use
Process B that determines the collapseof the quantum wave function. This is known as ” themeasurement problem ” in Quantum physics, which canbe stated in a formal manner as, for instance, Maudlindid [7] and as we already mentioned in the Introduction . These processes are referred to as U process and R process re-spectively in [10] and as Process 2 and Process 1 respectively inEverett’s seminal paper [11]. For more details see, for instance, Refs. [8, 12]. Some people
In classical physics, things happen according to certainlaws, no matter if there are observers who decide whenand how to make measurements so that one or the otherlaw of evolution is applied. Why does the quantum realmseem to be so different?We have said that quantum evolution, dictated by theSchr¨odinger equation, cannot produce the collapse of thewave function. So what produces it? There are manyproposals that try to answer, from various perspectives,this question. We will mention some of them here.Some scientists, as Bohr did, argue that physics shouldtake care only of what is observed. That is, giving up anobjective theory, free of a description of the world bywhom it decides to observe. Others say it is the faultof the measuring device. The device interacts with theobject,
Process B is triggered changing the state and thecollapse occurs. But how large must an apparatus be toact as an apparatus? Is an electron orbiting an atomicnucleus measuring the protons of the nucleus? Is it per-haps the observer who causes the wave function to col-lapse? And what does an observer represent? A human?A chimpanzee? A cat? These proposals are the bestknown of those that deny Maudlin’s statement B).Other authors argue that although the evolution ofquantum states is given at all times by the Schr¨odingerequation, the result obtained by an experimenter whenmaking a measurement is not the only one. Such is thecase of the many worlds approach (based on the originalidea of H. Everett [11]) where, once the measurement iscarried out, something happens in such a way that all thepossible results are obtained in (real or not) a diversity ofuniverses . Therefore, a state of superposition is nothingother than the promise of the existence of other worlds.Another well-known approach proposes that since anobject completely isolated from the rest of the world doesnot exist, the environment interacts with the object, al-ters its state causing the macroscopic superposition ofall possible states to disappear, triggering a sort of ”ef-fective collapse”, and thus resolving the whole problem .But what is the rule to apply to decide in each case wherethe object ends and where the environment begins andends? What or who decides what is and what is not en-vironment? We are? So the quantum nature of the world choose to deny the existence of this problem, stating that Quan-tum physics is only about calculations to predict probabilitiesand that when we make measurements in the laboratory every-thing fits perfectly. But we will see in ”the cosmological case”that this position cannot be sustained in a completely satisfac-tory manner. To be fair, in his seminal paper Everett only referred to ’ relativestates ’ Although this approach (known as quantum decoherence ) insome cases manages to partially solve the problem, it does notend up being a satisfactory solution and also usually requires anexternal observer to subjectively decide issues or carry out mea-surements. A detailed analysis of these and other problems ofthis approach that we are not mentioning here can be seen in[13, 14]. depends on our existence? This proposal and the Ev-erettian interpretations are some of the approaches thatsomehow discard Maudlin’s statement C).The reality is that none of this is well defined in Quan-tum theory and none of this has been able to completelysolve the measurement problem. So, the question howdoes a quantum system move from a state of quantumsuperpositions to another state without superpositions? ,to this day it does not have a complete and satisfactoryanswer.Why then is Quantum physics so successful if it hasthis measurement problem? The answer is that Quan-tum physics is about making measurements, and whenwe want to use the theory, in practice, dividing the worldbetween the observed and the observer is easy in a labo-ratory even though the theory does not provide us witha clear rule. In general, the separation between what isthe object of study and what constitutes the apparatusis very well defined. At the most, it will be enough to in-corporate more components to the quantum system untilthe predictions are no longer altered, and thus the resultswill be consistent with the observed. On the other hand,the aforementioned separation in laboratory situations isalways simple, because the scale of the quantum systemsof study (atoms, for example) is very far from the hu-man scale, from the scale of the devices and also fromthe resolution and precision of our devices.But this cannot be entirely satisfactory. Hartle, forinstance, mentions that the usual formulations of Quan-tum mechanics are inadequate for cosmology, since theseformulations assumed a division of the universe into ”ob-server” and ”observed” and that fundamentally quantumtheory is about the results of measurements. But mea-surements and observers cannot be fundamental notionsin a theory which seeks to describe the early universewhere neither existed [15].And here is when we move to the realm of the universeon large scales. The problem of quantum measurementworsens terribly in the cosmological case . Let’s see why. IV. THE COSMOLOGICAL CASE
The measurement problem, in the cosmological con-text, is a subject that has received much less attentionfrom the physics community. However, we should pointout that some researchers in the field, such as Hartle and One might argue that if Quantum physics is a description ofnature, it is reasonable to think that it would depend on theexistence of its descriptors. The measurement problem is pre-cisely that something outside the standard Quantum theory isneeded to solve it. For instance, observers or descriptors. But inthe cosmological case, to explain the early times of the universe,we will see that it will be difficult to feel comfortable with thisapproach. One of the first references where this was noted is in the Intro-duction of one of J. Bell’s works [16].
Penrose, have pointed out the need to generalize quan-tum mechanics to deal with cosmology [10, 15, 17–19].The proposal for generalization of quantum physics us-ing a scheme based on the realms of decoherent coarse-grained histories proposed by Hartle is an example, butwe will not discuss it here since it exceeds the scope ofthis article.As we mentioned in the Introduction, the Big Bangmodel, with which we seek to describe how the origin ofthe universe and its temporal evolution were to this day,fundamentally involves the two pillars of modern physics:Gravitation (Einstein’s theory of General Relativity) andQuantum theory.And more precisely, when we want to understand howthe first moments of the universe were and how the first”seeds” (the primordial inhomogeneities ) of the cos-mic structure emerged (and which then ended up in, say,galaxies), Quantum physics takes an extremely leadingrole in this description. These first moments of the uni-verse are described by a model we call cosmic inflation .Fundamentally with the work of Alan Guth in 1981[20], and by works of Andrei Linde, Paul Steinhardt, An-dreas Albrecht, Viacheslav Mukhanov, Alexei Starobin-sky and Stephen Hawking among others [21–27], theproposal arose that if at the beginning from its history( ∼ − seconds) the universe had gone through a briefinflationary phase of accelerated expansion driven by anexotic field called inflaton , some problems then knownfrom the standard hot Big Bang model could be resolvedand all of them with the same mechanism. We will notgo into detail here about what those problems were, sinceit is not the aim of this article.From a scientific meeting held in Cambridge, UK, in1982 (the Nuffield Workshop organized by Gibbons andHawking), and with the ideas of a 1965 Andrei Sakharovwork in mind [28], the mentioned authors began to showthat the emergence of the seeds of the structures in theuniverse could have occurred due to ” quantum fluctua-tions ” of the inflaton field during that same inflation-ary process. The gravitational evolution of those seedsgenerated in inflation, with the passage of time, wouldhave ended in everything we observe today in the sky;and that evolution, in addition, seems to be very wellreproduced with numerical simulations that are carriedout with large computer arrangements.One of the observational lines that has had more de-velopment and has achieved more data in recent decades,is the one that deals with the analysis of what is known Technically, these seeds of structure or ”inhomogeneities” arecalled cosmological perturbations . Therefore, we will use theterms inhomogeneities or perturbations interchangeably. Many physical phenomena of nature are described using fields.Such as the electric field, the magnetic field, the gravitationalfield, etc. The
Inflaton is an exotic scalar field, whose potentialenergy would have been dominant only at the beginning of theuniverse causing its expansion to be accelerated. Below it will be clear what we mean by this concept. as the
Cosmic Microwave Background (CMB) radiation.This cosmic background is electromagnetic radiation thatreaches us with a practically identical spectrum from alldirections of the sky (today with greater intensity inthe microwave range), and characterized with an aver-age temperature of only about 2.7 K. The existence ofthis radiation was predicted in the late 1940s by GeorgeGamow and others, but was discovered in 1965 by ArnoPenzias and Robert Wilson. We think that it comes fromthe time when the first neutral atoms in the universewere generated, about 380 thousand years after the BigBang. The statistical analysis of the small differencesin the temperature of this radiation that are observed inthe different directions of the sky constitutes the study ofwhat is called the anisotropies of the CMB. These verysmall temperature differences are one part in one hun-dred thousand. Theoretically, as the authors mentionedabove began to show, we expect these tiny temperaturedifferences to be present in the sky, since they would bethe result of the evolution of the seeds ( primordial pertur-bations ) generated at the beginning of the universe, andwhose origin we attribute it to the inflation mechanism.The surprising fact is that the anisotropies observed inthe sky are exactly like those predicted by the inflation-ary model, and without this model, today it would bequite difficult to explain the origin of what we observe .Then, here we have this situation: we observe largestructures (galaxies and clusters of galaxies) and alsosmall anisotropies in the temperature of the cosmic mi-crowave background. We assume that its origin datesback to the beginning of the universe, where the originalcosmic seeds must have existed. We do our calculationsand everything fits perfectly between theory and observa-tion. But where did those initial seeds come from? Howwere they generated during cosmic inflation?This is where our main protagonist of the article reap-pears: Quantum physics.How do we apply the Schr¨odinger equation of Quantumphysics to the case of the inflaton at the beginning ofthe universe? What do we think was the initial quantumstate of the primordial perturbations with which we makeour calculations to make theoretical predictions?At the moment when the inflationary phase begins tooccur, we have, on the one hand, the spacetime (whoseevolution is described by Einstein’s equations of Gen-eral Relativity) and, on the other hand, the inflaton fielddominating the energy budget of the early universe, pro-ducing the accelerated expansion, and whose quantuminhomogeneities we want to know how they emerged . Some recognized authors such as P. Steinhardt, R. Penrose, R.Brandenberger and others have been stressing that inflation hassome serious problems, see for instance [2–4]. And it is fair tomention that there are some variants and alternatives to theinflationary paradigm, including in that list, for example, modelsof cyclic universes. But to date they have not been able to besufficiently competitive. Although the most standard version proceeds by quantizing both
Then, Einstein’s equations tell us how spacetime (its cur-vature) reacts and is affected by the presence of the in-homogeneities of the inflaton field.We assume that far back in time, at the beginning ofinflation, the spacetime was the most symmetrical andsimple of all. It was isotropic (there was no privileged di-rection) and homogeneous (there was no privileged pointor place in space) . We also assume that the inhomo-geneities of the inflaton field were, at that same time, ina quantum vacuum state perfectly isotropic and homo-geneous. That is, a state with definite energy and whichalso had the same symmetries as the initial spacetime .We could start from a different initial situation, a littlemore complex, without some symmetries, or that alreadycontains the cosmic seeds of future galaxies beforehand.But then we would find the extra task of developing an-other theory to explain why the universe was born witha more complex situation and not the simplest.As with any quantum system, we can now calculate theexpected values and quantum uncertainties of perturba-tions in the quantum vacuum state. And, in the sameway as when we said that in a laboratory experiment,until a measurement does not occur for the position of aparticle in general it is not defined, that it is in a state ofsuperposition, and that the quantum uncertainty tells usin what range of possible values we can find most likelywhen we make a measurement, the same should now ap-ply to our case of the quantum universe. In the case ofthe laboratory, when we measure some physical propertythe wave function collapses, and then our devices give usdefined values.It is, then, when the central question of this articlearises: how do we arrive at an anisotropic and inhomoge-neous quantum state (with the seeds of structures), froma vacuum state, with superpositions, perfectly isotropicand homogeneous (without cosmic seeds)? We have saidthat the quantum state of a system contains all the in-formation of that system, and that the evolution of any spacetime and the inflaton field, here we will adopt the approachthat spacetime (at least since inflation) is always classic and thatquantization is done only to the inflaton field. This does notchange at all the central point of this article, the problems thathere are addressed and the conclusions. Before inflation occurs, spacetime may have been highly inhomo-geneous (as a product of physics that we do not yet know fullyand satisfactorily). The standard argument is that, once theaccelerated expansion that leads the universe to a Inflationaryphase starts, this produces that any inhomogeneity is suppressedexponentially. Therefore, at the beginning of inflation, spacetimeis typically assumed to be isotropic and homogeneous and thenthe anisotropies observed today in the CMB are thought of asthe exclusive result of the inflationary process. A vacuum state is one that, at least for some instant of time, hasa well-defined energy and is generally minimal. While at thispoint there is a technical problem that we will not address here,which has to do with the fact that there is no single mannerto choose a quantum vacuum state in an expanding universe,the consensus is that the initial vacuum state for cosmologicalperturbations was what is known as the
Bunch-Davies vacuum ,which is perfectly isotropic and homogeneous. quantum state is dictated by the Schr¨odinger equation,which does not break any symmetry or destroy quantumsuperpositions. Until the symmetries are broken and thequantum state changes, the space will remain isotropicand homogeneous, the curvature of the space will be thesame at each point and, therefore, there will be no chanceof a galaxy or anything else appearing in the future.Who or what made a measurement producing the col-lapse, the loss of the initial symmetries and the emer-gence of the seeds of structure at the beginning of theuniverse, giving non-null and well-defined values for theperturbations of the inflaton and spacetime? Was it anydevice? Any observer? The environment? Of course, wewant to think that none of this existed at the beginningof the universe .Typically, the most orthodox version of this analysisdraws on the Uncertainty Principle to say that the ini-tial ”quantum vacuum fluctuations” are the mechanismfor generating the seeds of the structures. From this ap-proach, quantum fluctuations have real existence in theuniverse. That is, quantum fields acquire real, random,but well-defined values at every time, and make the cur-vature of spacetime change (and oscillate like a spring,for example), in the same way as in Newton’s theory theposition of a tennis ball is taking defined values followinga trajectory in space. This contradicts what we under-stand of standard Quantum physics, and is not what wehave in mind when experimenters do their job in a terres-trial laboratory (they make measurements!). Quantumfluctuations are nothing other than quantum uncertain-ties . And a quantum uncertainty other than zero for For a discussion regarding that ”an environment” cannot solvethe problem, see for example Sect. 3.2.1 of Ref. [13]. Worksbased on decoherence [29–32] led to a partial understanding ofthe issue. Nevertheless, this argument by itself cannot addressthe fact that a single (classical) outcome emerges from the quan-tum theory. In other words, decoherence cannot solve the quan-tum measurement problem [14, 33], a complication that, withinthe cosmological context, is amplified due to the impossibilityof recurring to the ”for all practical purposes” argument in thefamiliar laboratory situation. Other cosmologists seem to adoptthe Everett ”many-worlds” interpretation of quantum mechanicsplus the decoherence process when confronted with the quantum-to-classical transition in the inflationary universe, e.g. [34]. Re-garding this point, we would like to refer the reader to otherRefs. [35–37] where arguments against decoherence and the Ev-erett interpretation are also presented. Note that the correct thing would be to talk about the quantumfluctuations of the inflaton field in the vacuum state. In fact,this lightness in the discourse is often accompanied by phrasessuch as ” the quantum fluctuations of the vacuum energy ”, whichis totally wrong since the quantum uncertainty of the energy inthe vacuum state is exactly zero. Some arguments involvingquantum vacuum fluctuations as a mechanism for solving theso-called cosmological constant problem also proved inadequate[38]. The word ” fluctuations ” in physics is often used (and confused)in several different contexts. It can mean the variations or therange of values for some characteristic of objects within a set(variations in the height of a set of chairs, for example); or it can the perturbations in the vacuum state, the only thingthat gives us, together with the Born’s rule, is the rangeof its most probable values, but that there are no definedvalues for the perturbations until a measurement is car-ried out. As in a laboratory, we must always talk aboutpossible measurement results so that Quantum physicspredictions make some sense. Therefore, under this anal-ysis approach, all points of space must remain equivalent,space remains isotropic and homogeneous, and there areno seeds of structure of any kind. Quantum vacuum fluc-tuations cannot be the seeds to form structures. The in-flaton field in its vacuum state has fluctuations (quantumuncertainties) but there are no inhomogeneities [35].The standard approach, then, cannot fully justify howthe initial perturbations appear in the early universe. Itrequires some process that acts ” as a measurement ”, asin the laboratory, and produces something like a collapseof the wave function changing the quantum state. Thisnew state must contain the perturbations or seeds of thecosmic structures. In the next section, we will analyzeone of the current proposals that aims to address thisissue.
V. FACING THE PROBLEM AND OTHERRELATED ISSUES
One of the approaches that seeks to address the afore-mentioned problem [removing the Maudlin’s statementB)] has, as its central idea, the proposal that in orderto solve the measurement problem in Quantum physics,non-standard quantum theories should be explored. The-ories where the collapse of the wave function is self-induced by some novel mechanism. Known as modelsor objective collapse theories , they are an approach dif-ferent from those mentioned above in Sect. III, and arecurrently of particular interest in the case of the quantumorigin of the primordial seeds of the structures. We willdescribe in this section some details about these ideas.From the mid-1970s and more intensely in the 1980sand 1990s, authors such as Pearle, Ghirardi, Rimini, We-ber, Penrose, Diosi and others [19, 39–43] began to seekand develop modifications to the Schr¨odinger equationto alter the evolution of the quantum state and that thecollapse of the wave function occurs, without externalobservers or devices present that have to make measure-ments; and in that way, solve the measurement prob-lem in Quantum physics. The main idea is that, withthe same theory, microscopic phenomena (excellently de-scribed by standard Quantum theory) as well as macro-scopic phenomena that do not show superpositions, canbe explained (in these theories, Schr¨odinger’s cat is aliveor already dead before we open the box). That is, they also refer to variations in different regions of something homoge-neous (such as waves in the sea); or, as in this article, it can alsorefer to quantum uncertainties. sought to achieve a theory that, with the same equationof evolution, can be described states of superpositions ofelectrons, for example, but also that it can explain whycats and everyday objects are not in superpositions.The modifications to the Schr¨odinger equation mustbe such that quantum superpositions for macroscopic ob-jects disappear and locate them in space, in the way wesee what happens in our daily lives. To do this, the equa-tion must incorporate some ” amplification mechanism ”that discriminates small objects from large, and that thedynamics itself causes the collapse and leads any initialquantum state to another, stochastically (to explain therandomness observed in the results of laboratory mea-surements), and reproducing the successful predictionsof the quantum probability rule proposed by Max Born.Detailed reviews can be found, for instance, in [44, 45].Guided primarily by the ideas of Diosi and Penrose, in2006 Sudarsky and collaborators proposed applying theideas of modifying the Quantum theory to the cosmo-logical case [46]. That is to say, to incorporate in theEinstein’s equations for the dynamics of the universe theeffects of the self-induced collapses of modified quantumtheories. Thus, during the period of cosmic inflation,there would have been spontaneous collapses in the ini-tial quantum vacuum states, similar to a measurement,so that the final result is a new quantum state with dif-ferent symmetries than the initial ones, without quantumsuperpositions, turning on the perturbations and givingthem non-zero defined values, altering the curvature ofspacetime, and thus creating the seeds of structure inthe universe. Without observers or measuring devices.With these modifications, theoretical predictions canbe made, which then allow these theories to be testedand thus be able to say something about their viabil-ity to explain the precise observations, for example, ofthe CMB. Some predictions have proved very interestingsince they have been able to explain certain observationalconstraints in a more natural and clear way than in thestandard case (see for instance, [47–57]) .These ideas continue to evolve. More recently, it hasbeen shown that this approach would allow addressingother questions of gravitational origin that have beenopen for many years. Such are the cases of the infor-mation paradox in black holes and the origin of darkenergy [65–68]. The proposal of some authors that otheruniverses besides ours could exist, is tied, in part, to theoccurrence of the inflationary phase at the beginning ofthe universe and to the theoretical problems mentioned Other authors have explored similar ideas and some of theseworks can be seen, for instance, in [58–60]. There is also anotherapproach, which denies Maudlin’s statement A) mentioned inthe Introduction, where it is argued that the quantum state doesnot contain all the information necessary for the description ofa quantum system. In this way, the addition of hidden variables and the equations that determine their evolution is required. Thebest known case is the de Broglie-Bohm model [61]. Applicationsto the cosmological case can be seen, for example, in [62–64] above. Therefore, this approach could also make the pos-sibility of the so-called multiverse a myth [69, 70].Modified quantum theories are not yet in their finalversions, they face their own questions and problems andare a challenging work in progress. To mention just afew of them, the origin and nature of the stochastic noisecontained in some versions of these theories are unknown(some people think that its origin could be gravitational[19, 42, 43, 71]); best known applications are still nonrel-ativistic (a relativistic model under exploration can befound in [72]), and collapse process appears to violatesome conservation laws. For example, particles gain en-ergy from the narrowing of wave functions by collapse.Recently, some authors explored the status of conserva-tion laws in classical and quantum physics. They foundthat in some contexts conservation laws to be useful, butoften not essential [73]. If this turns out this way, it canbe used to find, for example, a possible origin of darkenergy [68, 74]. A technical analysis of the various prob-lems that collapse theories face can be found for examplein [75, 76].
VI. CONCLUSIONS
The Big Bang, our model to describe the evolution ofthe universe, fundamentally combines two of the mostsuccessful theories developed in the twentieth century:General Relativity and Quantum physics. The modelsuccessfully describes and explains numerous cosmolog-ical observations. Even so, we know that it cannot bethe final version of the story. An extrapolation of thismodel to the very origin of the universe is not entirelyjustified, and could even result in too simplistic and dar-ing. To this day, we still do not have a fully satisfactory quantum theory of gravity that manages to unify boththeories. So we do not know, among other things, theorigin and nature of spacetime, nor the origin of quan-tum fields as the case of the inflaton.There are several proposals that try to respond, fromvarious perspectives, to the problems mentioned in thisarticle. Today all options have their advantages and theirown open problems. Within these proposals we have fo-cused particularly on those known as objective collapsetheories, which seek to achieve a Quantum theory thatsomehow is (in some sense) realistic, complete and ob-jective that challenge the thoughts of renowned scien-tists like Bohr or Heisenberg. These theories are one ofthe current candidates under study with which not onlycould the measurement problem in Quantum physics besolved, but the quantum origin of structures in the earlyuniverse could also be explained in a more complete andclear way.Some quantum secrets have not yet been revealed:could in the future the same mechanism be able to solvethe quantum measurement problem and, at the sametime, other gravitational problems that still have no sat-isfactory solutions? This approach, perhaps, could alsoserve as a guide in the search for a quantum theory ofgravity.
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