Bounce and stability in the early cosmology with anomaly-induced corrections
Wagno Cesar e Silva, Ilya L. Shapiro
备注：
22 pages, 12 figures. Extended version, added more details concerning phase diagrams, many new references and a few comments. Article written by invitation for the Special Issue "Physics and Mathematics of the Dark Universe" in Symmetry (Editor Sergei Ketov)
An extremely fast exponential expansion of the Universe is typical for the stable version of the inflationary model, based on the anomaly-induced action of gravity. The total amount of exponential $e$-folds could be very large, before the transition to the unstable version and the beginning of the Starobinsky inflation. Thus, the stable exponential expansion can be seen as a pre-inflationary semiclassical cosmological solution. We explore whether this stable phase could follow after the bounce, subsequent to the contraction of the Universe. Extending the previous consideration of the bounce, we explore both stable expansion and the bounce solutions in the models with non-zero cosmological constant and the presence of background radiation. The critical part of the analysis concerns stability for small perturbations of the Hubble parameter. It is shown that the stability is possible for the variations in the bounce region, but not in the sufficiently distant past in the contraction phase.
We derive the cosmological Big Bounce scenario from the dipole approximation of Loop Quantum Gravity. We show that a non-singular evolution takes place for any matter field and that, by considering a massless scalar field as a relational clock for the dynamics, the semi-classical proprieties of an initial state are preserved on the other side of the bounce. This model thus enhances the relation between Loop Quantum Cosmology and the full theory.
Within the context of the Fermi-bounce curvaton mechanism, we analyze the one-loop radiative corrections to the four fermion interaction, generated by the non-dynamical torsion field in the Einstein-Cartan-Holst-Sciama-Kibble theory. We show that contributions that arise from the one-loop radiative corrections modify the energy-momentum tensor, {\it mimicking} an effective Ekpyrotic fluid contribution. For these reasons, we call this effect {\it quantum Ekpyrotic} mechanism. This leads to the dynamical washing out of anisotropic contributions to the energy-momentum tensor, without introducing …
In this paper, we analyze the modified $f(\mathcal{R})$ gravity models in Friedmann--Lema\^ıtre--Robertson--Walker (FLRW) background. The actions of bouncing cosmology are studied under consideration of different viable models in $f(\mathcal{R})$ gravity theory that can resolve the difficulty of singularity in standard Big-Bang cosmology. Under different viable models in $f(\mathcal{R})$ gravity theory, the cosmological constraints are plotted in provisions of cosmic-time, then investigated the bounce circumstance. In addition, the red-shift parameter is used to reconstruct the modified gravit…
The propagation of a scalar field in an open FLRW bounce-type quantum spacetime is examined, which arises within the framework of the IKKT matrix theory. In the first part of the paper, we employ general-relativity tools to study null and timelike geodesics at the classical level. This analysis reveals that massless and massive non-interacting particles can travel across the big bounce. We then exploit quantum-field-theory techniques to evaluate the scalar field propagator. In the late-time regime, we find that it resembles the standard Feynman propagator of flat Minkowski space, whereas for e…
We give a prescription to define in Loop Quantum Gravity the electric field operator related to the scale factor of an homogeneous and isotropic cosmological space-time. This procedure allows to link the fundamental theory with its cosmological implementation. In view of the conjugate relation existing between holonomies and fluxes, the edge length and the area of surfaces in the fiducial metric satisfy a duality condition. As a consequence, the area operator has a discrete spectrum also in Loop Quantum Cosmology. This feature makes the super-Hamiltonian regularization an open issue of the who…
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.
This brief article sums up the possible imprints of loop quantum gravity effects on the cosmological microwave background. We focus on semi-classical terms and show that "Big Bounce" corrections, together with the "pre Big Bounce" state, could modify the observed spectrum.
The absence of isotropic singularity in loop quantum cosmology can be understood in an effective classical description as the universe exhibiting a Big Bounce. We show that with scalar matter field, the big bounce is generic in the sense that it is independent of quantization ambiguities and details of scalar field dynamics. The volume of the universe at the bounce point is parametrized by a single parameter. It provides a minimum length scale which serves as a cut-off for computations of density perturbations thereby influencing their amplitudes.
We consider the process of magnetogenesis in the context of nonsingular bounce cosmology. We show that large primordial magnetic fields can be generated during contraction without encountering strong coupling and backreaction issues. The fields may seed large-scale magnetic fields with observationally interesting strengths. This result leads to a theoretical constraint on the relation of the energy scale of the bounce cosmology to the number of effective e-folding of the contracting phase in the case of scale invariance for the power spectrum of primordial magnetic fields. We show that this co…
In this work, we analyzed the improved Deser-Woodard non-local gravity over the background of five different bouncing cosmologies, whose premise is avoid the initial singular state of the universe. We developed the numerical solution for the non-local distortion function, which encompass the modifications to the Einstein-Hilbert action, using the reconstruction procedure and we have found that they have a viable cosmological solution. Afterwards, we discussed the physical aspects and outcomes of the evolution of the distortion function throughout the bouncing point for these models, specifical…
We develop a Gauss-Bonnet extension of Loop Quantum Cosmology, by introducing holonomy corrections in modified $F(\mathcal{G})$ theories of gravity. Within the context of our formalism, we provide a perturbative expansion in the critical density, a parameter characteristic of Loop Quantum Gravity theories, and we result in having leading order corrections to the classical $F(\mathcal{G})$ theories of gravity. After extensively discussing the formalism, we present a reconstruction method that makes possible to find the Loop Quantum Cosmology corrected $F(\mathcal{G})$ theory that can realize va…
Horava-Lifshitz gravity, a recent proposal for a UV-complete renormalizable gravity theory, may lead to a bouncing cosmology. In this note we argue that Horava-Lifshitz cosmology may yield a concrete realization of the matter bounce scenario, and thus give rise to an alternative to inflation for producing a scale-invariant spectrum of cosmological perturbations. In this scenario, quantum vacuum fluctuations exit the Hubble radius in the pre-bounce phase and the spectrum is transformed into a scale-invariant one on super-Hubble scales before the bounce because the long wavelength modes undergo …
In the matter bounce scenario, a dust-dominated contracting space-time generates scale-invariant perturbations that, assuming a nonsingular bouncing cosmology, propagate to the expanding branch and set appropriate initial conditions for the radiation-dominated era. Since this scenario depends on the presence of a bounce, it seems appropriate to consider it in the context of loop quantum cosmology where a bouncing universe naturally arises. For a pressureless collapsing universe in loop quantum cosmology, the predicted power spectrum of the scalar perturbations after the bounce is scale-invaria…
In the loop approach to the quantisation of gravity, one uses a Hilbert space which is too singular for some operators to be realised as derivatives. This is usually addressed by instead using finite difference operators at the Planck scale, a process known as ``polymerisation''. In the symmetry reduced example of loop cosmology, we study an ambiguity in the regularisation which we relate to the ambiguity of fixing the coefficients of infinitely many higher curvature counter terms augmenting the Einstein-Hilbert action. Thus the situation is comparable to he one in a naive perturbative treatme…
A bouncing cosmology with an initial matter-dominated phase of contraction during which scales which are currently probed with cosmological observations exit the Hubble radius provides a mechanism alternative to inflation for producing a nearly scale-invariant spectrum of cosmological perturbations. In this review article I first discuss the evolution of cosmological fluctuations in the matter bounce scenario, and then discuss various attempts at realizing such a scenario. Observational signatures which will allow the matter bounce to be distinguished from the inflationary paradigm are also di…
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…
An oscillating universe cycles through a series of expansions and contractions. We propose a model in which ``phantom'' energy with a supernegative pressure ($p < - ρ$) grows rapidly and dominates the late-time expanding phase. The universe's energy density is then so large that the effects of quantum gravity are important at both the beginning and the end of each expansion (or contraction). The bounce can be caused by high energy modifications to the Friedmann equation governing the expansion of the universe, which make the cosmology nonsingular. The classic black hole overproduction of oscil…
We present exact non-singular bounce solutions of general relativity in the presence of a positive cosmological constant and an electromagnetic field, without any exotic matter. The solutions are distinguished by being spatially inhomogeneous in one direction, while they can also contain non-trivial electromagnetic field lines. The inhomogeneity may be substantial, for instance, there can be one bounce in one region of the universe and two bounces elsewhere. Since the bounces are followed by a phase of accelerated expansion, the metrics described here also permit the study of (geodesically com…
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）
We investigate non-singular bounce and cyclic cosmological evolutions in a universe governed by the extended nonlinear massive gravity, in which the graviton mass is promoted to a scalar-field potential. The extra freedom of the theory can lead to certain energy conditions violations and drive cyclicity with two different mechanisms: either with a suitably chosen scalar-field potential under a given Stuckelberg-scalar function, or with a suitably chosen Stuckelberg-scalar function under a given scalar-field potential. Our analysis shows that extended nonlinear massive gravity can alter signifi…
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…
A nonsingular bouncing cosmology can be achieved by introducing a fermion field with BCS condensation occurring at high energy scales. In this paper we are able to dilute the anisotropic stress near the bounce by means of releasing the gap energy density near the phase transition between the radiation and condensate states. In order to explain the nearly scale-invariant CMB spectrum, another fermion field is required. We investigate one possible curvaton mechanism by involving one another fermion field without condensation where the mass is lighter than the background field. We show that, by v…
We examine the nature of the cosmological Big Bounce transition within the loop geometry underlying loop quantum cosmology at classical and quantum levels. Our canonical quantization method is an alternative to the standard loop quantum cosmology. An evolution parameter we use has a clear interpretation. Our method opens the door for analyses of spectra of physical observables like the energy density and the volume operator. We find that one cannot determine the energy scale specific to the Big Bounce by making use of the loop geometry without an extra input from observational cosmology.
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…
We consider the ekpyrotic paradigm in the context of loop quantum cosmology. In loop quantum cosmology the classical big-bang singularity is resolved due to quantum gravity effects, and so the contracting ekpyrotic branch of the universe and its later expanding phase are connected by a smooth bounce. Thus, it is possible to explicitly determine the evolution of scalar perturbations, from the contracting ekpyrotic phase through the bounce and to the post-bounce expanding epoch. The possibilities of having either one or two scalar fields have been suggested for the ekpyrotic universe, and both c…
We show that the f(T) gravitational paradigm, in which gravity is described by an arbitrary function of the torsion scalar, can provide a mechanism for realizing bouncing cosmologies, thereby avoiding the Big Bang singularity. After constructing the simplest version of an f(T) matter bounce, we investigate the scalar and tensor modes of cosmological perturbations. Our results show that metric perturbations in the scalar sector lead to a background-dependent sound speed, which is a distinguishable feature from Einstein gravity. Additionally, we obtain a scale-invariant primordial power spectrum…
The implications of a deformed Heisenberg algebra on the Friedmann-Robertson-Walker cosmological models are investigated. We consider the Snyder non-commutative space in which the translation group is undeformed and the rotational invariance preserved. When this framework is implemented to one-dimensional systems (which is this case) the modifications are uniquely fixed up to a sign. A cosmological quantum bounce à la loop quantum cosmology is then obtained. We also get the Randall-Sundrum braneworld scenario and this way a Snyder-deformed quantum cosmology can be considered as a common phenom…
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…
A non-singular bouncing cosmology is generically obtained in loop quantum cosmology due to non-perturbative quantum gravity effects. A similar picture can be achieved in standard general relativity in the presence of a scalar field with a non-standard kinetic term such that at high energy densities the field evolves into a ghost condensate and causes a non-singular bounce. During the bouncing phase, the perturbations can be stabilized by introducing a Horndeski operator. Taking the matter content to be a dust field and an ekpyrotic scalar field, we compare the dynamics in loop quantum cosmolog…
Among many models which can describe the bouncing cosmology, A matter bounce scenario that is deformed by a running vacuum model of dark energy (RVM-DE) has been interested. In this research, I show that a class of RVM-CDM (cold dark matter) model can also describe a cyclical cosmology in which the universe undergoes cycles of expansion to the contraction phase and vice versa. To this end, following our previous work, I consider one of the most successful class of RVM-CDM model in bouncing cosmology, $ρ_x=n_0+n_2 H^2 +n_4 H^4$, in which the power spectral index gets a red tilt and the running …
One of the greatest problems of primordial inflation is that the inflationary space-time is past-incomplete. This is mainly because Einstein's GR suffers from a space-like Big Bang singularity. It has recently been shown that ghost-free, non-local higher-derivative ultra-violet modifications of Einstein's gravity may be able to resolve the cosmological Big Bang singularity via a non-singular bounce. Within the framework of such non-local cosmological models, we are going to study both sub- and super-Hubble perturbations around an inflationary trajectory which is preceded by the Big Bounce in t…
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 …
We investigate non-singular bounce realizations in the framework of ghost-free generalized Galileon cosmology, which furthermore can be free of the anisotropy problem. Considering an Ekpyrotic-like potential we can obtain a total Equation-of-State (EoS) larger than one in the contracting phase, which is necessary for the evolution to be stable against small anisotropic fluctuations. Since such a large EoS forbids the Galileon field to generate the desired form of perturbations, we additionally introduce the curvaton field which can in general produce the observed nearly scale-invariant spectru…
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…
The occurrence of a bounce in the FRW cosmology requires modifications of General Relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a "dark radiation" term with a negative coefficient in the analog of the Friedmann equation. A modification of the HL gravity, relaxing the "detailed balance" condition, brings additional terms to the equations of motion, corresponding to stiff matter. This paper presents comparison of the phase structure of the original and modified Horava cosmology. Special attention is paid to the analysis o…
The occurrence of a bounce in FRW cosmology requires modifications of general relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a ``dark radiation'' term with a negative coefficient in the analog of the Friedmann equation. This paper describes a phase space analysis of models of this sort with the aim of determining to what extent bouncing solutions can occur. A simplification, valid in the relevant region, allows a reduction of the dimension of phase space so that visualization in three dimensions is possible. It is found …
We study the dynamics of states perturbatively expanded about a harmonic system of loop quantum cosmology, exhibiting a bounce. In particular, the evolution equations for the first and second order moments of the system are analyzed. These moments back-react on the trajectories of the expectation values of the state and hence alter the energy density at the bounce. This analysis is performed for isotropic loop quantum cosmology coupled to a scalar field with a small but non-zero constant potential, hence in a regime in which the kinetic energy of matter dominates. Analytic restrictions on the …
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…
The big bang singularity of the expanding-universe Friedmann solution of the Einstein gravitational field equation can be regularized by the introduction of a degenerate metric and a nonzero length scale $b$. The result is a nonsingular bounce of the cosmic scale factor with a contracting prebounce phase and an expanding postbounce phase. The corresponding maximum values of the curvature and the energy density occur at the moment of the bounce and are proportional to powers of $1/b$. This article presents a detailed calculation of the dynamics of such a nonsingular bounce. In addition, a compa…
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, …
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…
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, …
The FRW model with non-minimally coupled massive scalar field has been investigated in LQC framework. Considered form of the potential and coupling allows applications to Higgs driven inflation. Out of two frames used in the literature to describe such systems: Jordan and Einstein frame, the latter one is applied. Specifically, we explore the idea of the Einstein frame being the natural 'environment' for quantization and the Jordan picture having an emergent nature. The resulting dynamics qualitatively modifies the standard bounce paradigm in LQC in two ways: (i) the bounce point is no longer …
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 reconstruct $F(R)$ gravity models with exponential and power-law forms of the scale factor in which bounce cosmology can be realized. We explore the stability of the reconstructed models with analyzing the perturbations from the background solutions. Furthermore, we study an $F(R)$ gravity model with a sum of exponentials form of the scale factor, where the bounce in the early universe as well as the late-time cosmic acceleration can be realized in a unified manner. As a result, we build a second order polynomial type model in terms of $R$ and show that it could be stable. Moreover, when th…
We re-examine the non-singular Matter Bounce scenario first developed in [arXiv:1206.2382], which starts with a matter-dominated period of contraction and transitions into an Ekpyrotic phase of contraction. We consider both matter fields, the first of which plays the role of regular matter, and the second of which is responsible for the non-singular bounce. Since the dominant matter field is massive, the induced curvature fluctuations are initially not scale-invariant, whereas the fluctuations of the second scalar field (which are initially entropy fluctuations) are scale-invariant. We study t…
We study a cosmological scenario in which inflation is preceded by a bounce. In this scenario, the primordial singularity, one of the major shortcomings of inflation, is replaced by a non-singular bounce, prior to which the universe undergoes a phase of contraction. Our starting point is the bouncing cosmology investigated in Falciano et al. (2008), which we complete by a detailed study of the transfer of cosmological perturbations through the bounce and a discussion of possible observational effects of bouncing cosmologies. We focus on a symmetric bounce and compute the evolution of cosmologi…
Loop quantum cosmology predicts that, in simple models, the big bang singularity of classical general relativity is replaced by a quantum bounce. Because of the extreme physical conditions near the bounce, a natural question is whether the universe can retain, after the bounce, its memory about the previous epoch. More precisely, does the universe retain various properties of the state after evolving unitarily through the bounce or does it suffer from some cosmic amnesia as has been recently suggested? Here we show that this issue can be answered unambiguously at least within an exactly solvab…
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…
