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We propose a new method to investigate signatures of a quantum gravity phase in the primordial state of cosmological perturbations. We formulate and study a quantum model of a perturbed Friedmann-Lemaitre-Robertson-Walker universe beyond a tensor-product Born-Oppenheimer-like factorization, that is, without restricting the wave function of the universe to the product of the background and perturbation wave functions. We show that the quantum dynamics generically does not preserve the product form of the universe's wave function, which spontaneously evolves into a more general entangled state. Upon expanding this state in a suitable basis of background wave functions and setting Gaussian initial conditions for the perturbations, we numerically find that each of these wave functions becomes associated with a non-Gaussian state of an inhomogeneous perturbation., Comment: 10 pages, 7 figures

Primordial black holes (PBHs) are hypothetical objects that could have originated from density fluctuations in a very early phase of our Universe. Recent observations restrict the masses that such PBHs could have, if they are to constitute all of dark matter today: $10^{17} \, {\rm g} \leq m \leq 10^{23} \, {\rm g}$. With such low masses, general relativity predicts that the corresponding radii for the PBHs would be atomic or subatomic in size. When captured by a star, such a tiny PBH could exhibit an orbit completely or partially inside the body of the star, without significantly changing its mass for quite a long time. Here we examine the possible trajectories of a PBH that is captured by a Sun-like star. When in motion in the interior of the star, the amount of stellar mass that effectively interacts with the PBH will be a function of its distance to the center of the star. As a consequence, a strong effect on the shape of the orbits emerges, leading to PBH trajectories that could be open or closed, and exhibiting a rich variety of patterns., Comment: 11 pages, 15 figures

We continue our studies of the evolution and cosmological consequences of current-carrying cosmic string networks, described by a charge-velocity-dependent one scale (CVOS) model. We present a detailed calculation of the effects of these networks on the cosmic microwave background (CMB), in the context of this model, and specifically discuss how such current-carrying strings may be distinguished from their uncharged (Nambu-Goto) counterparts by current or forthcoming CMB data. We find that, under the CVOS hypothesis, the constraints on current-carrying strings should not differ much from those of their structureless counterparts in that the impact on the CMB can at most be reduced by a factor of ~25%. Nevertheless, the presence of a current and charge affects the distribution of power among scalar, vector and tensor modes, and also its distribution between small and large scales. It should therefore be possible for future high-sensitivity CMB experiments to distinguish between the two types of strings., Comment: 16 pages, 16 figures

We study the non-unitary relation between quantum gravitational models defined using different internal times. We show that despite the non-unitarity, it is possible to provide a prescription for making unambiguous, though restricted, physical predictions independent of specific clocks. To illustrate this result, we employ a model of quantum gravitational waves in a quantum Friedmann universe., Comment: Corrected typos

We have discovered a class of dynamically stable coherent states for motion on the half-line. The regularization of the half-line boundary and the consequent quantum motion are expounded within the framework of covariant affine quantization, although alternative approaches are also feasible. The former approach is rooted in affine coherent states and offers a consistent semiclassical representation of quantum motion. However, this method has been known to possess two shortcomings: (a) the dependence of affine coherent states on the choice of a vector, denoted as 'fiducial vector' (which remains unspecified), introduces significant arbitrariness in boundary regularization, and (b) regardless of the choice of 'fiducial vector,' affine coherent states fail to evolve parametrically under the Schr\"odinger equation, thus limiting the accuracy of the semiclassical description. This limitation, in particular, hampers their suitability for approximating the evolution of compound observables. We demonstrate that a distinct and more refined definition of affine coherent states can simultaneously address both of these issues. In other words, these new affine coherent states exhibit parametric evolution only when the 'fiducial vector,' denoted as $|\psi_0>$, possesses a highly specific character, such as being an eigenstate of a well-defined Hamiltonian. Our discovery holds significant relevance in the field of quantum cosmology, particularly in scenarios where the positive variable is the scale factor of the universe, and its regularized motion plays a crucial role in avoiding the big-bang singularity., Comment: 15 pages, 3 figures

We consider the evolution of current-carrying cosmic string networks described by the charge-velocity-dependent one scale (CVOS) model beyond the linear equation of state regime, specifically focusing on the Witten superconducting model. We find that, generically, for almost chiral currents, the network evolution reduces dynamically to that of the linear case, which has been discussed in our previous work. However, the Witten model introduces a maximum critical current which constrains the network scaling behaviour during the radiation era when currents can grow and approach this limit. Unlike the linear model, only if the energy density in the critical current is comparable to the bare string tension will there be substantial backreaction on the network evolution, thus changing the observational predictions of superconducting strings from those expected from a Nambu-Goto network. During the matter era, if there are no external sources, then dynamical effects dilute these network currents and they disappear at late times., Comment: 10 pages, 5 figures

A quantum cosmological bouncing model may exhibit an ambiguity stemming from the nonclassical nature of the background evolution: two classically equivalent theories can produce two qualitatively different potentials sourcing the perturbations. We derive explicitly the quantum canonical transformation involving the quantum background to show how it leads to inequivalent theories. We identify the relevant quantum parameter describing the difference and expand upon the ambiguity by calculating the expected power spectra produced for initial quantum vacuum fluctuations in the contracting phase of both potentials. We find that one spectral index corresponds to all values of this parameter but one, while the other thus represents a set of measure zero., Comment: 16 pages, 7 figures, follow-up article to gr-qc 2111.02963, matching published version

General relativity and its cosmological solution predicts the existence of tensor modes of perturbations evolving on top of our Friedman-Lema\^itre-Robertson-Walker expanding Universe. Being gauge invariant and not necessarily coupled to other quantum sources, they can be seen as representing pure gravity. Unambiguously showing they are indeed to be quantised would thus provide an unquestionable proof of the quantum nature of gravitation. This review will present a summary of the various theoretical issues that could lead to this conclusion., Comment: Invited chapter for the Section "Perturbative Quantum Gravity" of the "Handbook of Quantum Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer Singapore, expected in 2023). New version matches the accepted version

We consider a simple cosmological model consisting of an empty Bianchi I Universe, whose Hamiltonian we deparametrise to provide a natural clock variable. The model thus effectively describes an isotropic universe with an induced clock given by the shear. Quantising this model, we obtain various different possible bouncing trajectories (semiquantum expectation values on coherent states or obtained by the de Broglie-Bohm formulation) and explicit their clock dependence, specifically emphasising the question of symmetry across the bounce., Comment: 13 pages, 4 figures, for Universe special issue on quantum cosmology

Time in quantum gravity is not a well-defined notion, despite its central role in the very definition of dynamics. Using the formalism of quantum geometrodynamics, we shortly review the problem and illustrate it with two proposed solutions. Our main application is quantum cosmology -- the application of quantum gravity to the Universe as a whole., Comment: 18 pages, 3 figures

By quantising the background as well as the perturbations in a simple one fluid model, we show that there exists an ambiguity in the choice of relevant variables, potentially leading to incompatible observational physical predictions. In a classical or quantum inflationary background, the exact same canonical transformations lead to unique predictions, so the ambiguity we put forward demands a semiclassical background with a sufficiently strong departure from classical evolution. The latter condition happens to be satisfied in bouncing scenarios, which may thus be having predictability issues. Inflationary models could evade such a problem because of the monotonic behavior of their scale factor; they do, however, initiate from a singular state which bouncing scenarios aim at solving., Comment: 13 pages, 7 figures

We apply a recently developed formalism to study the evolution of a current-carrying string network under the simple but generic assumption of a linear equation of state. We demonstrate that the existence of a scaling solution with non-trivial current depends on the expansion rate of the universe, the initial root mean square current on the string, and the available energy loss mechanisms. We find that the fast expansion rate after radiation-matter equality will tend to rapidly dilute any pre-existing current and the network will evolve towards the standard Nambu-Goto scaling solution (provided there are no external current-generating mechanisms). During the radiation era, current growth is possible provided the initial conditions for the network generate a relatively large current and/or there is significant early string damping. The network can then achieve scaling with a stable non-trivial current, assuming large currents will be regulated by some leakage mechanism. The potential existence of current-carrying string networks in the radiation era, unlike the standard Nambu-Goto networks expected in the matter era, could have interesting phenomenological consequences., Comment: 21 pages, 9 figures

We develop an analytic model to quantitatively describe the evolution of superconducting cosmic string networks. Specifically, we extend the velocity-dependent one-scale (VOS) model to incorporate arbitrary currents and charges on cosmic string worldsheets under two main assumptions, the validity of which we also discuss. We derive equations that describe the string network evolution in terms of four macroscopic parameters: the mean string separation (or alternatively the string correlation length) and the root mean square (RMS) velocity which are the cornerstones of the VOS model, together with parameters describing the averaged timelike and spacelike current contributions. We show that our extended description reproduces the particular cases of wiggly and chiral cosmic strings, previously studied in the literature. This VOS model enables investigation of the evolution and possible observational signatures of superconducting cosmic string networks for more general equations of state, and these opportunities will be exploited in a companion paper., Comment: 17 pages, 6 figures

The existence of a scaling network of current-carrying cosmic strings in our Universe is expected to continuously create loops endowed with a conserved current during the cosmological expansion. These loops radiate gravitational waves and may stabilise into centrifugally supported configurations. We show that this process generates an irreducible population of vortons which has not been considered so far. In particular, we expect vortons to be massively present today even if no loops are created at the time of string formation. We determine their cosmological distribution, and estimate their relic abundance today as a function of both the string tension and the current energy scale. This allows us to rule out new domains of this parameter space. At the same time, given some conditions on the string current, vortons are shown to provide a viable and original dark matter candidate, possibly for all values of the string tension. Their mass, spin and charge spectrum being broad, vortons would have an unusual phenomenology in dark matter searches., Comment: 27 pages, 6 figures, uses jcappub. Discussions and references added, matches published version

We discuss the question of time in a Bianchi I quantum cosmology in the framework of singularity avoidance. We show that time parameters fall into two distinct classes, that are such that the time development of the wave function either always leads to the appearance of a singularity (fast-gauge time) or that always prevents it from occurring (slow-gauge time). Furthermore, we find that, in the latter case, there exists an asymptotic regime, independent of the clock choice. This may point to a possible solution of the clock issue in quantum cosmology if there exists a suitable class of clocks all yielding identical relevant physical consequences., Comment: 16 pages, 13 figures, matches version to appear in Phys. Rev. D

Quantum cosmology based on the Wheeler De Witt equation represents a simple way to implement plausible quantum effects in a gravitational setup. In its minisuperspace version wherein one restricts attention to FLRW metrics with a single scale factor and only a few degrees of freedom describing matter, one can obtain exact solutions and thus acquire full knowledge of the wave function. Although this is the usual way to treat a quantum mechanical system, it turns out however to be essentially meaningless in a cosmological framework. Turning to a trajectory approach then provides an effective means of deriving physical consequences., Comment: 6 pages, 6 figures, conference "Estate Quantistica" report

We investigate a set of cosmological models for which the primordial power spectrum has a large-scale power deficit. The standard power-law spectrum is subject to long-wavelength modifications described by some new parameters, resulting in corrections to the anisotropies in the cosmic microwave background. The new parameters are fitted to different data sets: temperature only, temperature and polarization, the low-redshift determination of $H_0$, and baryonic acoustic oscillations. We discuss the statistical significance of the modified spectra, from both frequentist and Bayesian perspectives. Our analysis suggests motivations for considering models that break scalar-tensor consistency, or models with negligible power in the far super-Hubble limit. We present what appears to be substantial evidence for a new scale around 350 Mpc above which the primordial (scalar) power spectrum is sharply reduced by about 20%., Comment: 25 pages, 7 figures

It is known that the perturbative instability of tensor excitations in higher derivative gravity may not take place if the initial frequency of the gravitational waves are below the Planck threshold. One can assume that this is a natural requirement if the cosmological background is sufficiently mild, since in this case the situation is qualitatively close to the free gravitational wave in flat space. Here, we explore the opposite situation and consider the effect of a very far from Minkowski radiation-dominated or de Sitter cosmological background with a large Hubble rate, e.g., typical of an inflationary period. It turns out that, then, for initial Planckian or even trans-Planckian frequencies, the instability is rapidly suppressed by the very fast expansion of the universe., Comment: 12 pages, 9 figures

We present a detailed analysis of {\it excited} cosmic string solutions which possess superconducting currents. These currents can be excited inside the string core, and - if the condensate is large enough - can lead to the excitations of the Higgs field. Next to the case with global unbroken symmetry, we discuss also the effects of the gauging of this symmetry and show that excited condensates persist when coupled to an electromagnetic field. The space-time of such strings is also constructed by solving the Einstein equations numerically and we show how the local scalar curvature is modified by the excitation. We consider the relevance of our results on the cosmic string network evolution as well as observations of primordial gravitational waves and cosmic rays., Comment: 20 pages; v2: matches version accepted for publication in Phys. Rev. D

We analyze the Galileon ghost condensate implementation of a bouncing cosmological model in the presence of a non negligible anisotropic stress. We exhibit its structure, which we find to be far richer than previously thought. In particular, even restricting attention to a single set of underlying microscopic parameters, we obtain, numerically, many qualitatively different regimes: depending on the initial conditions on the scalar field leading the dynamics of the universe, the contraction phase can evolve directly towards a singularity, avoid it by bouncing once, or even bounce many times before settling into an ever-expanding phase. We clarify the behavior of the anisotropies in these various situations., Comment: 11 pages, 9 figures, minor corrections

Following previous works on generalized Abelian Proca theory, also called vector Galileon, we investigate the massive extension of an SU(2) gauge theory, i.e., the generalized SU(2) Proca model, which could be dubbed non-Abelian vector Galileon. This particular symmetry group permits fruitful applications in cosmology such as inflation driven by gauge fields. Our approach consists in building, in an exhaustive way, all the Lagrangians containing up to six contracted Lorentz indices. For this purpose, and after identifying by group theoretical considerations all the independent Lagrangians which can be written at these orders, we consider the only linear combinations propagating three degrees of freedom and having healthy dynamics for their longitudinal mode, i.e., whose pure St\"uckelberg contribution turns into the SU(2) multi-Galileon dynamics. Finally, and after having considered the curved space-time expansion of these Lagrangians, we discuss the form of the theory at all subsequent orders., Comment: LaTeX file in Revtex4 style, 25 pages in single column, no figures. v2: miscellaneous changes. Version to be published in Physical Review D

We report on the existence of a new type of cosmic string solutions in the Witten model with U(1)xU(1) symmetry. These solutions are superconducting with radially excited condensates that exist for both gauge and ungauged currents. Our results suggest that these new configurations can be macroscopically stable, but microscopically unstable to radial perturbations. Nevertheless, they might have important consequences for the network evolution and particle emission. We discuss these effects and their possible signatures. We also comment on analogies with non-relativistic condensed matter systems where these solutions may be observable., Comment: v2: 6 pages, 5 figures, discussion on stability and connection to condensed matter systems added, title of paper changed; v3: matched version accepted for publication in Phys. Lett. B

We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated St\"uckelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the St\"uckelberg field describing the longitudinal mode, which is in agreement with the results of JCAP 1405, 015 (2014) and Phys. Lett. B 757, 405 (2016) and complements those of JCAP 1602, 004 (2016). We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field $A_\mu$, the Faraday tensor $F_{\mu \nu}$ and its Hodge dual $\tilde{F}_{\mu \nu}$., Comment: LaTeX file in jcappub style, 11 pages, no figures. v2: Minor changes according to the referee requirements. A new parity-violating term in the Lagrangian has been uncovered and the text has been changed accordingly. The conclusions are, essentially, unchanged. v3: Miscellaneous changes. Version to be published in Journal of Cosmology and Astroparticle Physics

We review the status of bouncing cosmologies as alternatives to cosmological inflation for providing a description of the very early universe, and a source for the cosmological perturbations which are observed today. We focus on the motivation for considering bouncing cosmologies, the origin of fluctuations in these models, and the challenges which various implementations face., Comment: 30 pages, 6 figures; references added

We present and expand the simplest possible quantum cosmological bouncing model already discussed in previous works: the trajectory formulation of quantum mechanics applied to cosmology (through the Wheeler-De Witt equation) in the FLRW minisuper- space without spatial curvature. The initial conditions that were previously assumed were such that the wave function would not change its functional form but instead provide a dynamics to its parameters. Here, we consider a more general situation, in practice con- sisting of modified Gaussian wave functions, aiming at obtaining a non singular bounce from a contracting phase. Whereas previous works consistently obtain very symmetric bounces, we find that it is possible to produce highly non symmetric solutions, and even cases for which multiple bounces naturally occur. We also introduce a means of treating the shear in this category of models by quantizing in the Bianchi I minisuperpace., Comment: 10 pages, proceeding of the workshop "Current challenges in cosmology" held in Cali, Colombia, May 18 to 22, 2015

We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the flat spacetime (Minkowski) case, we obtain all the possible terms containing products of up to five first-order derivatives of the vector field, and provide a conjecture about higher-order terms. Rendering the metric dynamical, we covariantize the results and add all possible terms implying curvature., Comment: LaTeX file, 15 pages, no figures. v2: some typos have been fixed. A couple of references added. Version to be published in Journal of Cosmology and Astroparticle Physics

The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and momenta leading to the quadratic Hamiltonian describing linear perturbations. The final Hamiltonian is obtained without assuming any equations of motions for the background variables. This general formalism is applied to the special case of two fluids, having in mind the usual radiation and matter mix which made most of our current Universe history. Quantization is achieved using an adiabatic expansion of the basis functions. This allows for an unambiguous definition of a vacuum state up to the given adiabatic order. Using this basis, we show that particle creation is well defined for a suitable choice of vacuum and canonical variables, so that the time evolution of the corresponding quantum fields is unitary. This provides constraints for setting initial conditions for an arbitrary number of fluids and background time evolution. We also show that the common choice of variables for quantization can lead to an ill-defined vacuum definition. Our formalism is not restricted to the case where the coupling between fields is small, but is only required to vary adiabatically with respect to the ultraviolet modes, thus paving the way to consistent descriptions of general models not restricted to single-field (or fluid)., Comment: 20 pages, matches PRD published version

Although the inflationary paradigm is the most widely accepted explanation for the current cosmological observations, it does not necessarily correspond to what actually happened in the early stages of our Universe. To decide on this issue, two paths can be followed: first, all the possible predictions it makes must be derived thoroughly and compared with available data, and second, all imaginable alternatives must be ruled out. Leaving the first task to all other contributors of this volume, we concentrate here on the second option, focusing on the bouncing alternatives and their consequences., Comment: 11 pages, 3 figures, submitted as a contribution to the French 'Comptes Rendus de l'Academie des Sciences' on Inflation

The simplest possible classical model leading to a cosmological bounce is examined in the light of the non-Gaussianities it can generate. Concentrating solely on the transition between contraction and expansion, and assuming initially purely Gaussian perturbations at the end of the contracting phase, we find that the bounce acts as a source such that the resulting value for the post-bounce $f_{\mathrm{NL}}$ may largely exceed all current limits, to the point of potentially casting doubts on the validity of the perturbative expansion. We conjecture that if one can assume that the non-Gaussianity production depends only on the bouncing behavior of the scale factor and not on the specifics of the model examined, then many realistic models in which a nonsingular classical bounce takes place could exhibit a generic non-Gaussianity excess problem that would need to be addressed for each case., Comment: 7 pages, 2 figures. Inclusion of additional results (equations and plots) and more detailed discussion in the introduction and main body. Accepted for publication in Physical Review D

Given the proliferation of bouncing models in recent years, we gather and critically assess these proposals in a comprehensive review. The Planck data shows an unmistakably red, quasi scale-invariant, purely adiabatic primordial power spectrum and no primary non-Gaussianities. While these observations are consistent with inflationary predictions, bouncing cosmologies aspire to provide an alternative framework to explain them. Such models face many problems, both of the purely theoretical kind, such as the necessity of violating the NEC and instabilities, and at the cosmological application level, as exemplified by the possible presence of shear. We provide a pedagogical introduction to these problems and also assess the fitness of different proposals with respect to the data. For example, many models predict a slightly blue spectrum and must be fine-tuned to generate a red spectral index; as a side effect, large non-Gaussianities often result. We highlight several promising attempts to violate the NEC without introducing dangerous instabilities at the classical and/or quantum level. If primordial gravitational waves are observed, certain bouncing cosmologies, such as the cyclic scenario, are in trouble, while others remain valid. We conclude that, while most bouncing cosmologies are far from providing an alternative to the inflationary paradigm, a handful of interesting proposals have surfaced, which warrant further research. The constraints and lessons learned as laid out in this review might guide future research., Comment: 60 pages, 20 figures, review article

We compute the level of non-gaussianities produced by a cosmological bouncing phase in the minimal non-singular setup that lies within the context of General Relativity when the matter content consists of a simple scalar field with a standard kinetic term. Such a bouncing phase is obtained by requiring that the spatial sections of the background spacetime be positively curved. We restrict attention to the close vicinity of the bounce by Taylor expanding the scale factor, the scalar field and its potential in powers of the conformal time around the bounce. We find that possibly large non-gaussianities are generically produced at the bounce itself and also discuss which shapes of non-gaussianities are mostly likely to be produced., Comment: Matches published version