We introduce analytic solutions for a class of two components bouncing models, where the bounce is triggered by a negative energy density perfect fluid. The equation of state of the two components are constant in time, but otherwise unrelated. By numerically integrating regular equations for scalar cosmological perturbations, we find that the (would be) growing mode of the Newtonian potential before the bounce never matches with the the growing mode in the expanding stage. For the particular case of a negative energy density component with a stiff equation of state we give a detailed analytic study, which is in complete agreement with the numerical results. We also perform analytic and numerical calculations for long wavelength tensor perturbations, obtaining that, in most cases of interest, the tensor spectral index is independent of the negative energy fluid and given by the spectral index of the growing mode in the contracting stage. We compare our results with previous investigations in the literature.
We quantise and solve the dynamics of gravitational waves in a quantum Friedmann-Lemaitre-Robertson-Walker spacetime filled with perfect fluid. The classical model is formulated canonically. The Hamiltonian constraint is de-parametrised by setting a fluid variable as the internal clock. The obtained reduced (i.e. physical) phase space is then quantised. Our quantisation procedure is implemented in accordance with two different phase space symmetries, namely, the Weyl-Heisenberg symmetry for the perturbation variables, and the affine symmetry for the background variables. As an appealing outcom…
We derive in detail the equations of motion for the tensorial modes of primordial metric perturbations in the Coupled-Scalar-Tachyon Bounce Universe. We solve for the gravitational wave equations in the pre-bounce contraction and the post-bounce expansion epochs. To match the solutions of the tensor perturbations, we idealise the bounce process yet retaining the essential physical properties of the bounce universe. We put forward two matching conditions: one ensures the continuity of the gravitational wave functions and the other respects the symmetric nature of the bounce dynamics. The matchi…
Recent data suggest that the Universe could be positively curved. Combined with an inflationary stage, this might lead to a curvature bounce instead of the Big Bang. The background evolution is presented, as a function of the parameters controlling the cosmic evolution. The primordial tensor spectrum is also calculated and possible observational footprints of the model are underlined. Several potentials are considered and general remarks are made about "naturalness" in this context.
Certain features in the primordial scalar power spectrum are known to improve the fit to the cosmological data. We examine whether bouncing scenarios can remain viable if future data confirm the presence of such features. In inflation, the fact that the trajectory is an attractor permits the generation of features. However, bouncing scenarios often require fine tuned initial conditions, and it is only the ekpyrotic models that allow attractors. We demonstrate, for the first time, that ekpyrotic scenarios can generate specific features that have been considered in the context of inflation.
In this work we examine the effects of a pre-inflationary de Sitter bounce on the energy spectrum of the primordial gravitational waves. Specifically we assume that the Universe is described by several evolution patches, starting with a de Sitter pre-inflationary bounce which is followed by an quasi-de Sitter slow-roll inflationary era, followed by a constant equation of state parameter abnormal reheating era, which is followed by the radiation and matter domination eras and the late-time acceleration eras. The bounce and the inflationary era can be realized by vacuum $f(R)$ gravity and the ab…
Robustness of the primordial power spectrum in hybrid loop quantum cosmology to approximations near the bounce
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Instituto de Estructura de la Materia, IEM-CSIC（物质结构研究所）；Università degli Studi di Roma “La Sapienza”（罗马第一大学）
It has been pointed out that matter bounce cosmology driven by a k-essence field cannot satisfy simultaneously the observational bounds on the tensor-to-scalar ratio and non-Gaussianity of the curvature perturbation. In this paper, we show that this is not the case in more general scalar-tensor theories. To do so, we evaluate the power spectra and the bispectra of scalar and tensor perturbations on a general contracting background in the Horndeski theory. We then discuss how one can discriminate contracting models from inflation based on non-Gaussian signatures of tensor perturbations.
While loop quantum cosmology (LQC) predicts a robust quantum bounce of the background evolution of a Friedmann-Robertson-Walker (FRW) spacetime prior to the standard slow-roll inflation, whereby the big bang singularity is resolved, there are several different quantization procedures to cosmological perturbations, for instance, {\em the deformed algebra, dressed metric, and hybrid quantizations}. This paper devotes to study the quantum bounce effects of primordial perturbations in the hybrid approach. The main discrepancy of this approach is the effective positive mass at the quantum bounce fo…
In this paper we construct a bounce model that mimics the Starobinsky inflationary model. Our construction relies on Wands' duality, which shows that the Mukhanov-Sasaki equation has a symmetry transformation by changing appropriately its time-dependent mass term. One of the advantages of this constructive method is that one can control every contribution to the primordial power spectrum and check how far we can emulate a given primordial model with a different scenario. In particular, we show that mapping the Starobinsky inflation into a quasi-matter bounce gives the correct relation between …
A bounce universe model, known as the coupled-scalar-tachyon bounce (CSTB) universe, has been shown to solve the Horizon, Flatness and Homogeneity problems as well as the Big Bang Singularity problem. Furthermore a scale invariant spectrum of primordial density perturbations generated from the phase of pre-bounce contraction is shown to be stable against time evolution. In this work we study the detailed dynamics of the bounce and its imprints on the scale invariance of the spectrum. The dynamics of the gravitational interactions near the bounce point may be strongly coupled as the spatial cur…
In this work we shall study a possible pre-inflationary scenario for our Universe and how this might be realized by $f(R)$ gravity. Specifically, we shall introduce a scenario in which the Universe in the pre-inflationary era contracts until it reaches a minimum magnitude, and subsequently expands, slowly entering a slow-roll quasi-de Sitter inflationary era. This pre-inflationary bounce avoids the cosmic singularity, and for the eras before and after the quasi-de Sitter inflationary stage, approximately satisfies the string theory motivated scale factor duality $a(t)=a^{-1}(-t)$. We investiga…
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…
A union of matter bounce and Ekpyrotic scenarios is often studied in an attempt to combine the most promising features of these two models. Since non-perturbative quantum geometric effects in loop quantum cosmology (LQC) result in natural bouncing scenarios without any violation of energy conditions or fine tuning, an investigation of matter-Ekpyrotic bounce scenario is interesting to explore in this quantum gravitational setting. In this work, we explore this unified phenomenological model for a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe in LQC filled with dust and a s…
In this work we study non-singular{ bounce cosmology} in the context of the Lagrange multiplier generalized $F(R)$ gravity theory of gravity. We specify our study by using a specific variant form of the well known matter{ bounce cosmology}, with scale factor $a(t) = \left(a_0t^2 + 1 \right)^n$, and we demonstrate that for $n < 1/2$, the primordial curvature perturbations are generated deeply in the contraction era. Particularly, we show explicitly that the perturbation modes exit the horizon at a large negative time during the contraction era, which in turn makes the ``low-curvature'' regime, …
In this work we shall demonstrate that it is possible to describe in a unified way a primordial bounce with the dark energy era, in the context of Gauss-Bonnet modified gravity. Particularly, the early time bounce has a nearly scale invariant power spectrum of primordial scalar curvature perturbations, while the dark energy era is a viable one, meaning that it mimics the $Λ$-Cold-Dark-Matter model and also is compatible with the Planck 2018 data on cosmological parameters. In addition, our analysis indicates that the dark energy era is free from dark energy oscillations, which occur in the con…
We study quasi-matter bounce cosmology in light of Planck cosmic microwave background (CMB) angular anisotropy measurements along with the BICEP2/Keck Array data. We propose a new primordial scalar power spectrum by considering a linear approximation of the equation of state $w\cong w_0+κ(η-η_0)$ for quasi-matter field in the contracting phase of the universe. Using this new primordial scalar power spectrum, we constrain the zeroth-order approximation of the equation of state $w_0= -\,0.00340\pm 0.00044$ and first-order correction $10^{4} ζ= -1.67^{+1.50}_{-0.83}$ at the $1σ$ confidence level …
Quantum cosmological models are commonly described by means of semiclassical approximations in which a smooth evolution of the expectation values of elementary geometry operators replaces the classical and singular dynamics. The advantage of such descriptions is that they are relatively simple and display the classical behavior for large universes. However, they may smooth out an important inner structure and to include it a more detailed treatment is needed. The purpose of the present work is to investigate quantum uncertainty in the basic background variables and its influence on primordial …
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…
Primordial Gravitational waves leave polarization imprints on the Cosmic Microwave Background (CMB). In this article, we investigate polarization bispectrum, which is also referred to as the B-mode auto bispectrum, due to a matter bounce Universe. For simplicity, we consider a minimally coupled Einstein frame and obtain an analytical integral expression for the bispectrum and numerically perform the integration. We find that the signal-to-noise ratio is small, when compared with the same in the inflationary paradigm and hence quite difficult to detect in the future experiments. Thus a detectio…
In this work we consider a cosmological scenario in which the Universe contracts initially having a bouncing-like behavior, and accordingly after it bounces off, it decelerates following a matter dominated like evolution and at very large positive times it undergoes through an accelerating stage. Our aim is to study such evolution in the context of $F(R)$ gravity theory, and confront quantitatively the model with the recent observations. Using several reconstruction techniques, we analytically obtain the form of $F(R)$ gravity in two extreme stages of the universe, particularly near the bounce…
We propose a cosmological scenario in which the universe undergoes through a non-singular bounce, and after the bounce, it decelerates having a matter-like dominated evolution during some regime of the deceleration era, and finally at the present epoch it evolves through an accelerating stage. Our aim is to study such evolution in the context of Chern-Simons corrected F(R) gravity theory and confront the model with various observational data. Using the reconstruction technique, and in addition by employing suitable boundary conditions, we determine the form of F(R) for the entire possible rang…
We investigate the role played by the vacuum of the primordial fluctuations in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton potential is a mass term and the unperturbed quantum geometry is governed by the effective dynamics of Loop Quantum Cosmology. In this situation, the phenomenologically interesting solutions have a preinflationary regime where the kinetic energy of the inflaton dominates over the potential. For these kind of solutions, we show that the primordial power spectra depend strongly on the choice of vacuum. We study in detail the case of adiabatic stat…
Matter bounces refer to scenarios wherein the universe contracts at early times as in a matter dominated epoch until the scale factor reaches a minimum, after which it starts expanding. While such scenarios are known to lead to scale invariant spectra of primordial perturbations after the bounce, the challenge has been to construct completely symmetric bounces that lead to a tensor-to-scalar ratio which is small enough to be consistent with the recent cosmological data. In this work, we construct a model involving two scalar fields (a canonical field and a non-canonical ghost field) to drive t…
With the observational advance in recent years, primordial gravitational waves (GWs), known as the tensor-mode cosmic perturbations, in the Loop Quantum Cosmology (LQC) are becoming testable and thus require better framework through which to bridge between the observations and the theories. In this work we present a new formalism that employs the transfer functions to bring the GWs from any epoch, even before the quantum bounce, to a later time, including the present. The evolutionary epochs considered here include the possible deflation, quantum bounce, and inflation. This formalism enables u…
Evolution of cosmological perturbations and the production of non-Gaussianities through a nonsingular bounce: Indications for a no-go theorem in single field matter bounce cosmologies
This work investigates the formation of primordial black holes within a radiation fluid with an anisotropic pressure. We focus our attention on the initial conditions describing cosmological perturbations in the super horizon regime, using a covariant form of the equation of state in terms of pressure and energy density gradients. The effect of the anisotropy is to modify the initial shape of the cosmological perturbations with respect to the isotropic case. Using the dependence of the threshold $δ_\mathrm{c}$ for primordial black holes with respect to the shape of cosmological perturbations, …
Matter and quasi-matter bounce scenarios are studied for an F(R) gravity model with holonomy corrections and a Lagrange multiplier, with a scale factor $a(t) = \left(a_0t^2 + 1 \right)^n$, where the Hubble parameter squared has a linear and a quadratic dependence on the effective energy density. Provided $n < 1/2$, it is shown that the primordial curvature perturbations are generated deeply into the contracting era, at large negative time, which makes the low-curvature limit a good approximation for calculating the perturbation power spectrum. Moreover, it is shown that, for $n$ within this ra…
