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 by Planck temperature and polarization in combination with the BICEP2/Keck Array data in which $ζ= 12κ/k_*$ with pivot scale $k_*$. The spectral index of scalar perturbations is determined to be $n_{\rm Bs}=0.9623\pm0.0055$ which lies 7$σ$ away from the scale-invariant primordial spectrum. We find scale dependency for $n_{\rm s}$ at the $1σ$ confidence level and a tighter constraint on the running of the spectral index compared to $Λ$CDM+$α_s$ cosmology. The running of the spectral index in quasi-matter bounce cosmology is $α_{\rm Bs}= πζ/2 c_{\rm s} = -\hspace{.5mm}0.0021 \pm 0.0016$ which is nonzero at the $1.3σ$ level, whereas in $Λ$CDM+$α_{\rm s}$ it is nonzero at the $0.8σ$ level for Planck temperature and polarization data. The sound speed of density fluctuations of the quasi-matter field at the crossing time is $c_{\rm s} = 0.097^{+0.037}_{-0.023}$, which is not a very small value in the contracting phase.
A Bianchi IX Mixmaster spacetime is the most general spatially homogeneous solution of Einstein's equations and it can represent the space-averaged Universe. We introduce two novel mechanisms resulting in a Mixmaster Universe with non-singular bounces which are quasi-isotropic. A fluid with a non-linear equation of state allows non-singular bounces. Using negative anisotropic stresses successfully isotropises this Universe and mitigates the well known Mixmaster chaotic behaviour. Thus the Universe can be an eternal Mixmaster, going through an infinite series of different cycles separated by bo…
We analyze the dynamics of a homogeneous and isotropic universe in the Einstein--Cartan theory of gravity. The spin of fermions produces spacetime torsion that prevents gravitational singularities and replaces the big bang with a nonsingular big bounce. We show that a closed universe exists only when a particular function of its scale factor and temperature is higher than some threshold value, whereas an open and a flat universes do not have such a restriction. We also show that a bounce of the scale factor is double: as the temperature increases and then decreases, the scale factor decreases,…
Cosmological bounces occur in many gravity theories. We define singularity scattering maps relating large scale geometries before and after the bounce (assuming no BKL oscillations) and encoding microscopic details of the theory. By classifying all suitably local maps we uncover three universal laws: scaling of Kasner exponents, canonical transformation of matter, directional metric scaling. These are indeed obeyed by Bianchi I bounces in string theory, loop quantum cosmology and modified matter models; our classification then determines how inhomogeneities and anisotropies traverse bounces, a…
We consider the most general quadratic in curvature stringy motivated non-local action for the modified Einstein's gravity. We present exact analytic cosmological solutions including the bouncing ones and develop the relevant techniques for the further study of this type of models. We also elaborate on the perturbation formalism and argue that the found bouncing solution is stable during the bounce phase.
We argue that the anomalous power asymmetry observed in the cosmic microwave background (CMB) may have originated in a cosmic bounce preceding inflation. In loop quantum cosmology (LQC) the big bang singularity is generically replaced by a bounce due to quantum gravitational effects. We compute the spectrum of inflationary non-Gaussianity and show that strong correlation between observable scales and modes with longer (super-horizon) wavelength arise as a consequence of the evolution of perturbations across the LQC bounce. These correlations are strongly scale dependent and induce a dipole-dom…
We study the bounce and cyclicity realization in the framework of new gravitational scalar-tensor theories. In these theories the Lagrangian contains the Ricci scalar and its first and second derivatives, in a specific combination that makes them free of ghosts, and transformed into the Einstein frame they are proved to be a subclass of bi-scalar extensions of general relativity. We present analytical expressions for the bounce requirements, and we examine the necessary qualitative behavior of the involved functions that can give rise to a given scale factor. Having in mind these qualitative f…
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.
We investigate the bounce realization in the framework of generalized modified gravities arising from Finsler and Finsler-like geometries. In particular, the richer intrinsic geometrical structure is reflected in the appearance of extra degrees of freedom in the Friedmann equations that can drive the bounce. We examine various Finsler and Finsler-like constructions. In the cases of general very special relativity as well as of Finsler-like gravity on the tangent bundle we show that a bounce cannot be easily obtained. However, in the Finsler-Randers space the induced scalar anisotropy can fulfi…
We show that a nonsingular bounce, free of ghosts and gradient instabilities, can be realized in the framework of Horndeski or generalized Galileon cosmology. In particular, we first review that the theoretical no-go theorem, which states that the above is impossible, is based on two very strong assumptions, namely that a particular quantity cannot be discontinuous during the bounce, and that there is only one bounce. However, as we show in the present work, the first assumption not only can be violated in a general Horndeski/Galileon scenario, but also it is necessarily violated at the bounce…
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）
In this work we investigate which Loop Quantum Cosmology corrected Gauss-Bonnet $F(\mathcal{G})$ gravity can realize two singular cosmological scenarios, the intermediate inflation and the singular bounce scenarios. The intermediate inflation scenario has a Type III sudden singularity at $t=0$, while the singular bounce has a soft Type IV singularity. By using perturbative techniques, we find the holonomy corrected $F(\mathcal{G})$ gravities that generate at leading order the aforementioned cosmologies and we also argue that the effect of the holonomy corrections is minor to the power spectrum…
We develop a non-singular bouncing cosmology using a non-trivial coupling of general relativity to fermionic fields. The usual Big Bang singularity is avoided thanks to a negative energy density contribution from the fermions. Our theory is ghost-free since the fermionic operator that generates the bounce is equivalent to torsion, which has no kinetic terms. The physical system consists of standard general relativity plus a topological sector for gravity, and fermionic matter described by Dirac fields with a non-minimal coupling. We show that a scale invariant power-spectrum generated in the c…
We provide an $F(R)$ gravity description of a $Λ$CDM bouncing model, without the need for matter fluids or for cosmological constant. As we explicitly demonstrate, the two cosmological eras that constitute the $Λ$CDM bouncing model, can be generated by $F(R)$ gravity which can lead to accelerating cosmologies. The resulting F(R) gravity has Einstein frame inflationary properties that have concordance to the latest Planck observational data. Both the $F(R)$ gravity stability properties are thoroughly investigated and also, the gravitational particle production, a feature necessary for the viabi…
We investigate the bounce and cyclicity realization in the framework of weakly broken galileon theories. We study bouncing and cyclic solutions at the background level, reconstructing the potential and the galileon functions that can give rise to a given scale factor, and presenting analytical expressions for the bounce requirements. We proceed to a detailed investigation of the perturbations, which after crossing the bouncing point give rise to various observables, such as the scalar and tensor spectral indices and the tensor-to-scalar ratio. Although the scenario at hand shares the disadvant…
It is of great interest to connect cosmology in the early universe to the Standard Model of particle physics. In this paper, we try to construct a bounce inflation model with the standard model Higgs boson, where the one loop correction is taken into account in the effective potential of Higgs field. In this model, a Galileon term has been introduced to eliminate the ghost mode when bounce happens. Moreover, due to the fact that the Fermion loop correction can make part of the Higgs potential negative, one naturally obtains a large equation of state(EoS) parameter in the contracting phase, whi…
We study a nonsingular bounce inflation model, which can drive the early universe from a contracting phase, bounce into an ordinary inflationary phase, followed by the reheating process. Besides the bounce that avoided the Big-Bang singularity which appears in the standard cosmological scenario, we make use of the Horndesky theory and design the kinetic and potential forms of the lagrangian, so that neither of the two big problems in bouncing cosmology, namely the ghost and the anisotropy problems, will appear. The cosmological perturbations can be generated either in the contracting phase or …
Smoking-gun signatures of bounce cosmology from echoes of relic gravitational waves
College of Physics, Sichuan University（四川大学物理学院）；Department of Astronomy, School of Physical Sciences, University of Science and Technology of China（中国科学技术大学物理科学学院天文学系）；CAS Key Laboratory for Researches in Galaxies and Cosmology, School of Astronomy and Space Science, University of Science and Technology of China（中国科学院星系与宇宙学重点实验室，中国科学技术大学天文与空间科学学院）
The matter bounce scenario allows for a sizable parameter space where cosmological fluctuations originally exited the Hubble radius when the background energy density was small. In this scenario and its extended versions, the low energy degrees of freedom are likely responsible for the statistical properties of the cosmic microwave background power spectrum at large length scales. An interesting consequence is that these modes might be observable only at relatively late times. Therefore low redshift observations could provide evidence for, or even falsify, various bouncing models. We provide a…
We discuss the asymmetry of cosmic background evolution in time with respect to the quantum bounce in the Loop Quantum Cosmology (LQC), employing the value of scalar field at the bounce $ϕ_{\rm B}$. We use the Chaotic and the $R^2$ potentials to demonstrate that a possible deflation before the bounce may counteract the inflation that is needed for resolving the cosmological conundrums, so a certain level of time asymmetry is required for the models in LQC. This $ϕ_{\rm B}$ is model dependent and closely related to the amounts of deflation and inflation, so we may use observations to confine $ϕ…
We investigate the bounce realization in the framework of DHOST cosmology, focusing on the relation with observables. We perform a detailed analysis of the scalar and tensor perturbations during the Ekpyrotic contraction phase, the bounce phase, and the fast-roll expansion phase, calculating the power spectra, the spectral indices, and the tensor to-scalar ratio. Furthermore, we study the initial conditions, incorporating perturbations generated by Ekpyrotic vacuum fluctuations, by matter vacuum fluctuations, and by thermal fluctuations. The scale invariance of the scalar power spectrum can be…
It is shown that teleparallel $F({\mathcal T})$ theories of gravity combined with Loop Quantum Cosmology support a Matter Bounce Scenario which is an alternative to the inflation scenario in the Big Bang paradigm. It is checked thatthese bouncing models provide theoretical data that fits well with the current observational data, allowing the viability of the Matter Bounce Scenario.
Using the reconstruction technique with an auxiliary field, we investigate which $F(R)$ gravities can produce the matter bounce cosmological solutions. Owing to the specific functional form of the matter bounce Hubble parameter, the reconstruction technique leads, after some simplifications, to the same Hubble parameter as in the matter bounce scenario. Focusing the study to the large and small cosmic time $t$ limits, we were able to find which $F(R)$ gravities can generate the matter bounce Hubble parameter. In the case of small cosmic time limit, which corresponds to large curvature values, …
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…
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…
Torsion is a geometrical object, required by quantum mechanics in curved spacetime, which may naturally solve fundamental problems of general theory of relativity and cosmology. The black-hole cosmology, resulting from torsion, could be a scenario uniting the ideas of the big bounce and inflation, which were the subject of a recent debate of renowned cosmologists.
We extend the phenomenology of loop quantum cosmology (LQC) to second order in perturbations. Our motivation is twofold. On the one hand, since LQC predicts a cosmic bounce that takes place at the Planck scale, the second order contributions could be large enough to jeopardize the validity of the perturbative expansion on which previous results rest. On the other hand, the upper bounds on primordial non-Gaussianity obtained by the Planck Collaboration are expected to play a significant role on explorations of the LQC phenomenology. We find that the bounce in LQC produces an enhancement of non-…
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, …
Using the reconstruction method, we investigate which $F(R)$ theories, with or without the presence of matter fluids, can produce the matter bounce scenario of holonomy corrected Loop Quantum Cosmology. We focus our study in two limits of the cosmic time, the large cosmic time limit and the small cosmic time limit. For the former, we found that, in the presence of non-interacting and non-relativistic matter, the $F(R)$ gravity that reproduces the late time limit of the matter bounce solution is actually the Einstein-Hilbert gravity plus a power law term. In the early time limit, since it corre…
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…
