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Quantum Origin of the Primordial Fluctuation Spectrum and Its Statistics

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Quantum Origin of the Primordial Fluctuation Spectrum and Its Statistics PHYSICAL REVIEW D 88, 023526 (2013) Quantum origin of the primordial fluctuation spectrum and its statistics CORE Metadata, citation and similar papers at core.ac.uk Provided by CONICET Digital Susana Landau, 1, * Gabriel Leo´n, 2,3, † and Daniel Sudarsky 3,4, ‡ 1Instituto de Fı´sica de Buenos Aires, CONICET-UBA, Ciudad Universitaria—Pab. 1, 1428 Buenos Aires, Argentina 2Dipartimento di Fisica, Universita` di Trieste, Strada Costiera 11, 34151 Trieste, Italy 3Instituto de Ciencias Nucleares, Universidad Nacional Auto´noma de Me´xico, Me´xico D.F. 04510, Mexico 4Instituto de Astronomı´a y Fı´sica del Espacio, Casilla de Correos 67, Sucursal 28, 1428 Buenos Aires, Argentina (Received 3 July 2012; revised manuscript received 23 April 2013; published 26 July 2013) The usual account for the origin of cosmic structure during inflation is not fully satisfactory, as it lacks a physical mechanism capable of generating the inhomogeneity and anisotropy of our Universe, from an exactly homogeneous and isotropic initial stateassociated withthe early inflationary regime. The proposalin[A. Perez, H. Sahlmann, and D. Sudarsky, Classical Quantum Gravity 23 , 2317 (2006)] considers the spontaneous dynamical collapse of the wave function as a possible answer to that problem. In this work, we review briefly the difficulties facing the standard approach, as well as the answers provided by the above proposal and explore their relevance to the investigations concerning the characterization of the primordial spectrum and other statistical aspects of the cosmic microwave background and large-scale matter distribution. We will see that the new approach leads to novel ways of considering some of the relevant questions, and, in particular, to distinct characterizations of the non-Gaussianities that might have left imprints on the available data. DOI: 10.1103/PhysRevD.88.023526 PACS numbers: 98.80.Cq, 98.80. Àk I. INTRODUCTION of anisotropies and inhomogeneities that characterize our late Universe. This issue is sometimes characterized as the At what point in the cosmic evolution do the actual ‘‘transition from the quantum regime to the classical re- primordial inhomogeneities arise? In other words, when gime,’’ but we find this a bit misleading: most people would does our Universe depart from the exceedingly high homo- agree that there exist no distinct and separated classical and 1 geneity and isotropy that is thought to result from the first quantum regimes. The fundamental description ought to be stages of inflation? This is a question that one might expect always quantum mechanical; the so-called classical regimes should be addressed, at least, in principle, by any theory that are those in which certain quantities can be described to a deals with the emergence of cosmic structure. Yet in the sufficient accuracy by their classical counterparts represent- standard inflationary account [ 1], which is nowadays re- ing the corresponding quantum expectation values. The garded as a remarkable success, the context in which such paradigmatic example of this classical regime is provided issues can be addressed seems to be simply absent [ 2]. That by the coherent states of a harmonic oscillator, which cor- is, within the orthodox accounts, one cannot identify the respond to minimal wave packets with expectation values of physical process responsible for the generation of those position and momentum that follow the classical equations features in our Universe. In fact, according to the infla- of motion (Ehrenfest theorem). In any case, it seems clear tionary paradigm, from a relatively wide initial set of pos- that from a situation corresponding to a H&I background, sibilities marking the end of the mysterious quantum gravity and quantum fields characterized by a H&I state, one cannot era, the accelerated inflationary burst leads to a homoge- end up—in the absence of something else, which in other neous and isotropic (H&I) Universe where the quantum circumstances would be identified as a measurement, but fields are all characterized by the equally homogeneous which clearly cannot be invoked in the present setting 3—in a and isotropic vacuum states (usually taken specifically to situation that is characterized, at any level, as containing be the so-called Bunch-Davies vacuum). From these con- actual inhomogeneities and anisotropies. It is clear that, in 2 ditions, it is usually argued, in a rather unclear although terms of the standard dynamics, such a transition cannot strongly image-evoking manner, that the ‘‘quantum fluctua- be accounted for by anything that relies just on the tions’’ present in such a quantum state morph into the seeds gravity/inflaton action, 4 which is known to preserve such *[email protected] †[email protected] 3Observers and measuring apparatuses are only possible well ‡[email protected] after the H&I has been broken, so those can hardly be part of the 1The level of inhomogeneity that might still be present at any cause of the breakdown. point during inflation is expected to be of order eÀN, where N is 4In fact, even the interaction with other fields, controlled by the number of e-folds of inflation occurred up to that point. the usual symmetry preserving dynamics, cannot account for the 2Acknowledgments that this is an unclear aspect of the stan- emergence of inhomogeneities and anisotropies, since, accord- dard approach can be seen, for instance, in the book Cosmology ing to the inflationary paradigm, the state for all fields should by Weinberg [ 3], where the author explicitly states his view on correspond to a homogenous and isotropic state such as the the subject. Bunch-Davies vacuum. 1550-7998 =2013 =88(2) =023526(27) 023526-1 Ó 2013 American Physical Society SUSANA LANDAU, GABRIEL LEO ´ N, AND DANIEL SUDARSKY PHYSICAL REVIEW D 88, 023526 (2013) symmetries. Simply put, if the initial state is H&I and the the standard inflationary paradigm, which we have been Schro¨dinger evolution is tied to a Hamiltonian that preserves advocating in previous works [ 4,8–11 ]. The basis of that these symmetries, the resulting state cannot be anything but proposal is to modify the standard inflationary paradigm a H&I state (see Appendix A). Nonetheless, various types of with the incision of a modified quantum mechanics that arguments are often put forward in attempts to bypass the involves the spontaneous collapse of the wave function. above conclusion. Most cosmologists adopt a posture that We should note, however, that we cannot escape from attributes to decoherence the role of explaining the emer- the related problems, even if we choose to adopt a very gence of inhomogeneities and anisotropies from the H&I ‘‘pragmatic position’’: Assume, that one chooses to ignore state. This approach faces several problems: the shortcomings of the standard accounts [ 5] and accepts (i) The decoherence program is based on partitioning that, say, decoherence addresses somehow the issue at hand the degrees of freedom in two categories—The de- and that the mystery lies ‘‘only’’ in the question concerning grees of freedom of the environment and the degrees the precise mechanism that lies behind the fact that, from of freedom of the system of interest. In the cosmo- the options exhibited in those analyses (i.e., the options logical case however, in which one cannot evoke displayed in the diagonal reduced-density matrix; see observers or measurements, the way to do the sepa- Appendix D), one single realization seems to be selected ration of the degrees of freedom is rather ad hoc . [12 ] for our Universe. In adopting such a point of view, one (ii) In order to argue that the symmetry was broken, would be assuming that the initial symmetry has been lost one needs to assume that the world is suddenly (at least for practical purposes) in association with that represented by one of the elements appearing in particular ‘‘realization’’ or ‘‘actualization’’ (represented by the diagonal of the deciphering density matrix, a particular element in the density matrix). Thus, it seems and it is not clear how to argue for that. clear that, for the sake of self-consistency, one should (iii) Sometimes people evoke the many worlds interpre- consider, when studying aspects of the inhomogeneity tation of quantum theory in order to deal with the and anisotropies in the cosmic microwave background previous point but seem to ignore that, in order to (CMB) we observe, the state corresponding to such real- do that, one needs to choose a privileged basis ization or actualization, and not the complete vacuum state, which describes the H&I state of affairs previous to the associated with the world splittings, and that choice, 5 in practice, is tied to the notion of conscience, again actualization. In following such views, the discussion that a notion that cannot be invoked in the context at we are presenting in this paper would have to be taken to hand. Another popular posture is to rely on the represent the effective description corresponding to ‘‘our consistent histories approach, ignoring the problem- perceived Universe’’ (in a context in which one puts atic issues afflicting that proposal. In particular, we together something like the many worlds interpretation, with the arguments based on decoherence). Although we should note that the usage of the formalism requires definitely do not adhere to such a view for the reasons a choice of realm, a choice that in the current context explained in Ref. [ 5], it is clear that when accepting a seems completely arbitrary. In fact, one can make description, such as the one presented above, one would one such choice when one is led to the conclusion have to use the characteristics of the selected state in order that the Universe is, even today, perfectly homoge- to estimate the details of the inhomogeneities and anisot- nous and isotropic (see Appendix D).
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