We study the implementation of Polymer Quantum Mechanics (PQM) to a system decomposed into a quasi-classical background and a small quantum subsystem, according to the original Vilenkin proposal. We develop the whole formalism in the momentum representation that is the only viable in the continuum limit of the polymer paradigm and we generalize the fundamental equations of the original Vilenkin analysis in the considered context. Then, we provide a Minisuperspace application of the theory, first considering a Bianchi I cosmology and then extending the analysis to a Bianchi IX model in the limit of small anisotropies. In both these cases, the quasi-classical background is identified with an isotropic bouncing Universe whereas the small quantum subsystem contains the anisotropic degrees of freedom. When the Big Bounce scenario is considered, we obtain that in the Bianchi I model the anisotropies standard deviation is regular at $t=0$ but still increases indefinitely, whereas in the presence of the harmonic Bianchi IX potential such same quantity is bounded and oscillate around a constant value. As a consequence, we demonstrate that the picture of a semiclassical isotropic Bounce can be extended to more general cosmological settings if the spatial curvature becomes relevant when the anisotropic degrees of freedom are still small quantum variables.
In homogeneous and isotropic loop quantum cosmology, gravity can behave repulsively at Planckian energy densities leading to the replacement of the big bang singularity with a big bounce. Yet in any bouncing scenario it is important to include non-linear effects from anisotropies which typically grow during the collapsing phase. We investigate the dynamics of a Bianchi I anisotropic model within the framework of loop quantum cosmology. Using effective semi-classical equations of motion to study the dynamics, we show that the big bounce is still predicted with only differences in detail arising…
We study the dynamics of perturbations representing deviations from perfect isotropy in the context of the emergent cosmology obtained from the group field theory formalism for quantum gravity. Working in the mean field approximation of the group field theory formulation of the Lorentzian EPRL model, we derive the equations of motion for such perturbations to first order. We then study these equations around a specific simple isotropic background, characterised by the fundamental representation of $\mbox{SU(2)}$, and in the regime of the effective cosmological dynamics corresponding to the bou…
We investigate the classical and quantum behavior of a Bianchi I model in the presence of a stiff matter contribution when the Vilenkin interpretation of the wave function of the Universe is taken into account. We study its evolution in the so-called polymer representation of quantum mechanics, in order to characterize the modifications that a discrete nature in the isotropic variable of the Universe induces on the morphology of the cosmological singularity. We demonstrate that in such a model the Big-Bang singularity is removed at a semiclassical level in favor of a Big-Bounce when a lattice …
Following recent claims relative to the question of large anisotropy production in regular bouncing scenarios, we study the evolution of such anisotropies in a model where an Ekpyrotic phase of contraction is followed by domination of a Galileon-type Lagrangian which generates a non-singular bounce. We show that the anisotropies decrease during the phase of Ekpyrotic contraction (as expected) and that they can be constrained to remain small during the non-singular bounce phase (a non-trivial result). Specifically, we derive the e-folding number of the phase of Ekpyrotic contraction which leads…
Constraining a de Broglie--Bohm quantum bounce cosmology with Planck data
Scuola Superiore Meridionale（南方高等学院）；INFN Sez. di Napoli（那不勒斯 INFN 分部）；Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）；Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro（里约热内卢州立大学技术学院）
It is commonly assumed that the stochastic background of gravitational waves on cosmological scales follows an almost scale-independent power spectrum, as generically predicted by the inflationary paradigm. However, it is not inconceivable that the spectrum could have strongly scale-dependent features, generated, e.g., via transient dynamics of spectator axion-gauge fields during inflation. Using the temperature and polarisation maps from the \textit{Planck} and BICEP/Keck datasets, we search for such features, taking the example of a log-normal bump in the primordial tensor spectrum at CMB sc…
We introduce an extension of the standard inflationary paradigm on which the big bang singularity is replaced by an anisotropic bounce. Unlike in the big bang model, cosmological perturbations find an adiabatic regime in the past. We show that this scenario accounts for the observed quadrupolar modulation in the temperature anisotropies of the cosmic microwave background (CMB), and we make predictions for the remaining angular correlation functions E-E, B-B and T-E, together with non-zero temperature-polarization correlations T-B and E-B, that can be used to test our ideas. We base our calcula…
The baryon-antibaryon asymmetry (excess of matter over antimatter in our Universe), indicated by observational data from the Cosmic Microwave Background anisotropies, predictions of primordial Nucleosynthesis, and the absence of intense radiation from matter-antimatter annihilation, constitutes an unsolved puzzle in cosmology. Two mechanisms for baryon asymmetry have been proposed as extensions of the Standard Model of Particle Physics at high energies. They rely on new couplings involving the baryon number current, one with a scalar field, called Spontaneous Baryogenesis, and the other with s…
Due to non-perturbative quantum gravitational effects, the classical big bang singularity is replaced by a quantum big bounce of the mean scale factor in loop quantization of Bianchi-I spacetime. An important issue is to understand various differences in the physical properties of the spacetime across the bounce. We investigate this issue in the context of various geometrical structures, identified by Kasner exponents of the metric, which arise on approach to the singularity in the classical theory. Using effective spacetime description of Bianchi-I model in loop quantum cosmology with dust, r…
We present a complete analysis of the imprint of tensor anisotropies on the Cosmic Microwave Background for a class of f(R) gravity theories within the PPF-CAMB framework. We derive the equations, both for the cosmological background and gravitational wave perturbations, required to obtain the standard temperature and polarization power spectra, taking care to include all effects which arise from f(R) modifications of both the background and the perturbation equations. For R^n gravity, we show that for n different from 2, the initial conditions in the radiation dominated era are the same as th…
The cosmological magnetic field is one of the important physical quantities which affect strongly the cosmic microwave background (CMB) power spectrum. Recent CMB observations have been extended to higher multipoles $l\gtrsim$1000, and they resultantly exhibit an excess power than the standard model prediction in cosmological theory which best fits the Wilkinson Microwave Anisotropy Probe (WMAP) data at lower multipoles $l\lesssim$900. We calculate the CMB temperature anisotropies generated by the power-law magnetic field at the last scattering surface (LSS) in order to remove the tension betw…
If the spatial sections of the Universe are positively curved, extrapolating the inflationary stage backward in time inevitably leads to a classical bounce. This simple scenario, non-singular and free of exotic physics, deserves to be investigated in details. The background dynamics exhibits interesting features and is shown to be mostly insensitive to initial conditions as long as observational consequences are considered. The primordial scalar power spectrum is explicitly computed, for different inflaton potentials, and the subsequent CMB temperature anisotropies are calculated. The results …
We calculate new corrections to the Brane-world dynamics, lying in a 5D Schwarzschild-De Sitter black hole, generalizing the result of Nojiri, Odintsov and Ogushi (NOO) in Ref.\cite{Nojiri:2002vu}, The NOO entropy effect is based on the Logharitmic correction to the bulk entropy firstly calculated by Mukherji and Pal in Ref.\cite{Mukherji:2002de}. We calculate higher order contributions to the brane worldsheet. The extra terms obtained lead to interesting implications in brane-cosmology. In particular, new entropic terms rapidly disappear in the late Universe while exploding in the very Early …
We consider a modified gravity model with a massive graviton, but which nevertheless only propagates two gravitational degrees of freedom and which is free of ghosts. We show that non-singular bouncing cosmological background solutions can be generated. In addition, the mass term for the graviton prevents anisotropies from blowing up in the contracting phase and also suppresses the spectrum of gravitational waves compared to that of the scalar cosmological perturbations. This addresses two of the main problems of the matter bounce scenario.
We numerically investigate the solutions to the effective equations of the Bianchi II model within the "improved" Loop Quantum Cosmology (LQC) dynamics. The matter source is a massless scalar field. We perform a systematic study of the space of solutions, and focus on the behavior of several geometrical observables. We show that the big-bang singularity is replaced by a bounce and the point-like singularities do not saturate the energy density bound. There are up to three directional bounces in the scale factors, one global bounce in the expansion, the shear presents up to four local maxima an…
We calculate how primordial anisotropies in the background space-time affect the evolution of cosmological perturbations for bouncing alternatives to inflation, like ekpyrosis and the matter bounce scenario. We find that the leading order effect of anisotropies in the contracting phase of the universe is to induce anisotropies in the cosmic microwave background with a very concrete form: a scale-invariant quadrupolar angular distribution. Sub-leading effects are the generation of higher-order moments in the angular distribution, as well as cross-correlations between scalar and tensor modes. We…
We present a nonsingular scenario in which an inflation era goes after a bounce from a contracting scenario in the early universe. The contracting of the universe is supposed to be slow, such that the initial anisotropies will not grow too fast to become dominant and destroy the bounce. After the bounce, the universe enters into an inflationary region and reheating phase, where primordial perturbations are generated. The tensor-to-scalar ratio of the perturbations are expected to be consistent with the newly released data, $r=0.2^{+0.07}_{-0.05}$. The addition of the bounce process is aimed at…
This article addresses the issue of estimating the duration in inflation in bouncing cosmology when anisotropies, inevitably playing an important role, are taken into account. It is shown that in Bianchi-I loop quantum cosmology, the higher the shear, the shorter the period of inflation. In a range of parameters, the probability distribution function of the duration of inflation is however peaked at values compatible with data, but not much higher. This makes the whole bounce/inflationary scenario consistent and phenomenologically appealing as all the information from the bounce might then not…
The Deser-Woodard (DW) nonlocal gravity model has been proposed in order to describe the late-time acceleration of the universe without introducing dark energy. In this paper we focus, however, on the early stage of the universe and demonstrate how a primordial bounce in the vacuum spacetime can be realized in the framework of the DW nonlocal model. We reconstruct the nonlocal distortion function, which encodes all the modifications to the Einstein-Hilbert action, in order to generate bouncing solutions to solve the initial singularity problem. We show that the initial conditions can be chosen…
The Continuous Spontaneous Localization (CSL) model has been proposed as a possible solution to the quantum measurement problem by modifying the Schrödinger equation. In this work, we apply the CSL model to two cosmological models of the early Universe: the matter bounce scenario and slow roll inflation. In particular, we focus on the generation of the classical primordial inhomogeneities and anisotropies that arise from the dynamical evolution, provided by the CSL mechanism, of the quantum state associated to the quantum fields. In each case, we obtained a prediction for the shape and the par…
In this paper we consider realistic model of inflation embedded in the framework of loop quantum cosmology. Phase of inflation is preceded here by the phase of a quantum bounce. We show how parameters of inflation depend on the initial conditions established in the contracting, pre-bounce phase. Our investigations indicate that phase of the bounce easily sets proper initial conditions for the inflation. Subsequently we study observational effects that might arise due to the quantum gravitational modifications. We perform preliminary observational constraints for the Barbero-Immirzi parameter $…
The Bianchi IX cosmological model (through Bianchi I and II) is analyzed in the framework of a generalized uncertainty principle. In particular, the anisotropies of the Universe are described by a deformed Heisenberg algebra. Three main results are in order. (i) The Universe can not isotropize because of the deformed Kasner dynamics. (ii) The triangular allowed domain is asymptotically stationary with respect to the particle (Universe) and its bounces against the walls are not interrupted by the deformed effects. (iii) No reflection law can be in obtained since the Bianchi II model is no longe…
We examine reheating in the two-field matter bounce cosmology. In this model, the universe evolves from a matter-dominated phase of contraction to an Ekpyrotic phase of contraction before the nonsingular bounce. The Ekpyrotic phase frees the model from unwanted anisotropies, but leaves the universe cold and empty of particles after the bounce. For this reason, we explore two particle production mechanisms which take place during the course of the cosmological evolution: Parker particle production where the matter field couples only to gravity and particle creation via interactions between the …
We analyze the semiclassical polymer dynamics of the inhomogeneous Mixmaster model by choosing the cubed scale factor as the discretized configurational variable, while the anisotropies remain pure Einsteinian variables. Such a modified theory of gravity should be regarded as the appropriate framework to describe the behavior of quantum mean values, both in polymer quantum mechanics and in Loop Quantum Cosmology. We first construct the generalized Kasner solution, including a massless scalar field and a cosmological constant in the dynamics. They account for a quasi-isotropization, inflationar…
We provide a quantum picture for the emergence of a bouncing cosmology, according to the idea that a semiclassical behavior of the Universe towards the singularity is not available in many relevant Minisuperspace models. In particular, we study the Bianchi I model in vacuum adopting the isotropic Misner variable as an internal clock for the quantum evolution. The isomorphism between the Wheeler-DeWitt equation in this Minisuperspace representation and the Klein-Gordon one for a relativistic scalar field allows to identify the positive and negative frequency solutions as associated to the colla…
We constrain the deviation of adiabatic evolution of the Universe using the data on the Cosmic Microwave Background (CMB) temperature anisotropies measured by the {\it Planck} satellite and a sample of 481 X-ray selected clusters with spectroscopically measured redshifts. To avoid antenna beam effects, we bring all the maps to the same resolution. We use a CMB template to subtract the cosmological signal while preserving the Thermal Sunyaev-Zeldovich (TSZ) anisotropies; next, we remove galactic foreground emissions around each cluster and we mask out all known point sources. If the CMB black-b…
We revisit the predictions for the duration of the inflationary phase after the bounce in loop quantum cosmology. We present our analysis for different classes of inflationary potentials that include the monomial power-law chaotic type of potentials, the Starobinsky and the Higgs-like symmetry breaking potential with different values for the vacuum expectation value. Our setup can easily be extended to other forms of primordial potentials than the ones we have considered. Independently on the details of the contracting phase, if the dynamics starts sufficiently in the far past, the kinetic ene…
We analyze the dynamics of the Bianchi I model in the presence of stiff matter, an ultrarelativistic component and a small negative cosmological constant. We quantize this model in the framework of the polymer quantum mechanics, in order to introduce cut-off features in the minisuperspace dynamics. We then apply to the polymer Wheeler-DeWitt equation, emerging from the Dirac constraint, an adiabatic approximation a la Vilenkin, which treats the Universe volume as a quasi-classical variable, becoming de facto the dynamical clock for the pure quantum degrees of freedom, here identified in the Un…
Anisotropies generically dominate the earliest stages of expansion of a homogeneous universe. They are particularly relevant in bouncing models, since shears grow in the contracting phase of the cosmos, making the isotropic situation unstable. This paper extends the study of cosmological perturbations in loop quantum cosmology (LQC) to anisotropic Bianchi I models that contain a bounce followed by a phase of slow-roll inflation. We show that, although the shear tensor dilutes and the universe isotropizes soon after the bounce, cosmic perturbations retain memory of this short anisotropic phase.…
We study the behaviour of Bianchi class A universes containing an ultra-stiff isotropic ghost field and a fluid with anisotropic pressures which is also ultra-stiff on the average. This allows us to investigate whether cyclic universe scenarios, like the ekpyrotic model, do indeed lead to isotropisation on approach to a singularity (or bounce) in the presence of dominant ultra-stiff pressure anisotropies. We specialise to consider the closed Bianchi type IX universe and show that when the anisotropic pressures are stiffer on average than any isotropic ultra-stiff fluid then, if they dominate o…
Quantum Damping of Cosmological Shear: A New Prediction from Loop Quantum Cosmologies
Jiangxi Normal University（江西师范大学）；Universidade Federal Fluminense（巴西联邦弗鲁米嫩塞大学）；Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）；Baylor University（贝勒大学）
A stochastic gravitational wave background (SGWB) will affect the CMB anisotropies via weak lensing. Unlike weak lensing due to large scale structure which only deflects photon trajectories, a SGWB has an additional effect of rotating the polarization vector along the trajectory. We study the relative importance of these two effects, deflection \& rotation, specifically in the context of E-mode to B-mode power transfer caused by weak lensing due to SGWB. Using weak lensing distortion of the CMB as a probe, we derive constraints on the spectral energy density ($Ω_{GW}$) of the SGWB, sourced at …
We theoretically and observationally investigate different choices of initial conditions for the primordial mode function that are imposed during an epoch preceding inflation. By deriving predictions for the observables resulting from several alternate quantum vacuum prescriptions we show some choices of vacua are theoretically observationally distinguishable from others. Comparing these predictions to the Planck 2018 observations via a Bayesian analysis shows no significant evidence to favour any of the quantum vacuum prescriptions over the others. In addition we consider frozen initial condi…
The curl (B) modes of cosmic microwave background (CMB) polarization anisotropies are a unique probe of the primordial background of inflationary gravitational waves (IGWs). Unfortunately, the B-mode polarization anisotropies generated by gravitational waves at recombination are confused with those generated by the mixing of gradient-mode (E-mode) and B-mode polarization anisotropies as CMB photons propagate through the Universe and are gravitationally lensed. We describe here a method for delensing CMB polarization anisotropies using observations of anisotropies in the cosmic 21-cm radiation …
We analyze the phase space of Bianchi I cosmologies filled by a spin fluid in the framework of $f(R)$-gravity with torsion using a combination of the dynamical systems approach and the 1+3 covariant formalism. In the simple case of $f(R)=R^n$ our results allow a quantification of the role of torsion and the spin of the cosmic fluid in the evolution of the cosmology. While torsion is able to modify the cosmological dynamics with respect to the purely metric case, the spin has little influence on the cosmology. We argue that this is due to the different symmetries of the tensor characterizing th…
Genericness of quantum damping of cosmological shear in modified loop quantum cosmology
Jiangxi Normal University（江西师范大学）；Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）；Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）；Baylor University（贝勒大学）
The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show it is natural to extend the scale factor to negative values, allowing a large, collapsing Universe to evolve across a quantum "bounce" into an expanding Universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the ope…
We analyse the clustering of matter on large scales in an extension of the concordance model that allows for spatial curvature. We develop a consistent approach to curvature and wide-angle effects on the galaxy 2-point correlation function in redshift space. In particular we derive the Alcock-Paczynski distortion of $fσ_{8}$, which differs significantly from empirical models in the literature. A key innovation is the use of the `Clustering Ratio', which probes clustering in a different way to redshift-space distortions, so that their combination delivers more powerful cosmological constraints.…
The Bianchi IX cosmological model is analyzed in a generalized uncertainty principle framework. The Arnowitt-Deser-Misner reduction of the dynamics is performed and a time-coordinate, namely the volume of the Universe, naturally arises. Such a variable is treated in the ordinary way while the anisotropies (the physical degrees of freedom) are described by a deformed Heisenberg algebra. The analysis of the model (passing through Bianchi I and II) is performed at classical level by studying the modifications induced on the symplectic geometry by the deformed algebra. We show that, the Universe c…
By quantizing the background as well as the perturbations in a simple one fluid cosmological model, we show that there exists an ambiguity in the choice of relevant variables, potentially leading to incompatible observational physical predictions. In a classical 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 is clearly satisfied by bouncing models. We propose coherent states as the tool for introduc…
We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function $f(\Boxϕ)$ implementing the limiting curvature hypothesis. We show how relevant physical information can be extracted from power law expansions of $f$ in different regimes, corresponding e.g. to the very early universe or to late times. Our results are then applied to two specific models reproducing the cosmological background dynamics obtained in group field theory and in loop quantum cosmology, and we discuss…
We investigate the $ϕ^2$ inflationary model in the Bianchi-I spacetime using effective spacetime description of loop quantum cosmology to understand the issues of the resolution of initial singularity, isotropization, effect of anisotropies on amount of inflation, and the phase space attractors in the presence of non-perturbative quantum gravitational modifications. A comparative analysis with the classical theory by including more general initial conditions than the ones previously considered in the latter is also performed. We show that, in general, the classical singularity is replaced by a…
Loop quantum cosmology is a tentative approach to model the universe down to the Planck era where quantum gravity settings are needed. The quantization of the universe as a dynamical space-time is inspired by Loop Quantum Gravity ideas. In addition, loop quantum cosmology could bridge contact with astronomical observations, and thus potentially investigate quantum cosmology modellings in the light of observations. To do so however, modelling both the background evolution and its perturbations is needed. The latter describe cosmic inhomogeneities that are the main cosmological observables. In t…
