Abstract

The inflationary paradigm is extremely successful regarding predictions of temperature anisotropies in the CMB. However, inflation also makes predictions for a CMB B-mode polarization, which has not been detected. Moreover, the standard inflationary paradigm is unable to accommodate the evolution from the initial state, which is assumed to be symmetric, into a non-symmetric aftermath. In Phys. Rev. D 96, 101301(R), we show that the incorporation of an element capable of explaining such a transition drastically changes the prediction for the shape and size of the B-mode spectrum. In particular, employing a realistic objective collapse model in a well-defined semiclassical context, we find that, while predictions of temperature anisotropies are nor altered (with respect to standard predictions), the B-mode spectrum gets strongly suppressed--in accordance with observations. Here we present an in-depth discussion of that analysis, together with the details of the calculation.

Highlights

  • The measurement problem has bothered physicists since the birth of quantum theory

  • The problem consists of the fact that the standard formalism crucially depends on notions such as measurement or observer, but such notions are never formally defined within the theory [1,2,3]

  • Since the construction of quantum field theory is based on standard quantum mechanics, a modification of the latter, such as the one proposed by continuous spontaneous localization (CSL), clearly affects the former

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Summary

INTRODUCTION

The measurement problem has bothered physicists since the birth of quantum theory. In short, the problem consists of the fact that the standard formalism crucially depends on notions such as measurement or observer (to decide when to use the unitary evolution and when the collapse postulate), but such notions are never formally defined within the theory (i.e., the formalism fails to offer a detailed and unambiguous prescription identifying the interactions and objects that should be taken as playing such roles) [1,2,3]. The initial state of this field is assumed to be the homogeneous and isotropic Bunch-Davies vacuum and the quantum fluctuations of this state are regarded as seeds for the anisotropic and inhomogeneous cosmic structures of the present Universe. As we discussed above, no measurements can happen in this setting, clearly there is something missing in the inflationary account of the emergence of seeds of cosmic structure This issue can be taken care of by employing an objective collapse model, such as CSL. In [37], we put such a result on an even stronger ground by obtaining analogous results with the adaptation of a realistic objective collapse model to the situation at hand In this manuscript, we present an in-depth discussion of that analysis, together with the details of the calculation. VI, we provide a brief summary of the results and our conclusions (we include an Appendix where the details of the calculations can be found)

OBJECTIVE
SCALAR AND TENSOR PERTURBATIONS DURING INFLATION
First-order perturbations
Second-order perturbations
THE TENSOR POWER SPECTRUM WITHIN THE OBJECTIVE COLLAPSE FRAMEWORK
The tensor power spectrum in the CSL inflationary model
The tensor power spectrum in the Newtonian collapse scheme
M4Pq61 π 2
MZ4Pq81
M4Pq31
M2Pε cos z sin z z2 : ð72Þ
The magnitude of the B-mode polarization spectrum
The shape of the B-mode polarization spectrum
CONCLUSIONS

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