We formulate the transition from decelerated to accelerated expansion as a bounce in connection space and study its quantum cosmology, knowing that reflections are notorious for bringing quantum effects to the fore. We use a formalism for obtaining a time variable via the demotion of the constants of Nature to integration constants, and focus on a toy Universe containing only radiation and a cosmological constant $Λ$ for its simplicity. We find that, beside the usual factor ordering ambiguities, there is an ambiguity in the order of the quantum equation, leading to two distinct theories: one second, the other first order. In both cases two time variables may be defined, conjugate to $Λ$ and to the radiation constant of motion. We make little headway with the second-order theory, but are able to produce solutions to the first-order theory. They exhibit the well-known "ringing" whereby incident and reflected waves interfere, leading to oscillations in the probability distribution even for well-peaked wave packets. We also examine in detail the probability measure within the semiclassical approximation. Close to the bounce, the probability distribution becomes double-peaked, with one peak following a trajectory close to the classical limit but with a Hubble parameter slightly shifted downwards, and the other with a value of $b$ stuck at its minimum. An examination of the effects still closer to the bounce, and within a more realistic model involving matter and $Λ$, is left to future work.
In this paper we put forward the idea that the comoving Hubble horizon undergoes multiple stages of contraction (a.k.a. inflationary phase) and expansion. The observable inflation, that produces the CMB anisotropies and generates primordial gravitational waves, follows and is followed by multiple early and late inflations. The trans-Planckian censorship conjecture restricts the duration of each inflationary phases and determines their Hubble rates. Early inflations could start immediately after the universe emerges from the Planck era. It alleviates the initial condition problem for the lower-…
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, …
In this paper we study the evolution of cosmological perturbations through a nonsingular bouncing universe using covariant perturbation theory and examine the validity of linear perturbation theory. The bounce is modeled by a two component perfect fluid. Gauge invariant perturbations are defined in terms of the comoving observers. The scalar and vector perturbations become singular at the turning point, which is the boundary of the spacetime region where the null energy condition is violated. Nonadiabatic modes of comoving curvature perturbation diverge at the turning point. The gravitational …
String-inspired cosmologies, whereby a non-singular curvature bounce is induced by a general-covariant, $T$-duality-invariant, non-local dilaton potential, are used to study numerically how inhomogeneities evolve and to compare the outcome with analytic expressions obtained through different matching conditions across the bounce. Good agreement is found if continuity across the bounce is assumed to hold for $\cal{R}$, the curvature perturbation on comoving hypersurfaces, rather than for the Bardeen potential.
In the context of a ghost free $f(R,\mathcal{G})$ model, we present a non-singular cosmological scenario in which the universe initially contracts through an ekpyrotic phase having a bouncing like behaviour, and following the bounce, it smoothly transits to a matter or radiation like deceleration era which is further smoothly connected to the dark energy era at present epoch. We consider the Gauss-Bonnet (GB) coupling function in such a way that it gets compatible with the event GW170817. Using suitable reconstruction technique, we obtain the non-trivial scalar field potential as well as the G…
We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. As is well known from standard cosmological perturbation theory, under the assumption of initial quantum vacuum fluctuations the Fourier modes of the comoving curvature perturbation that exit the (sound) Hubble radius in such a contracting universe at a time of matter-domination will be nearly scale-invariant. Furthermore, the modes that exit the (sound) Hubble radius when the effective equation of state is slightly negative due to the cosmological constant will have a slight …
We study the dynamics of gauge-invariant scalar perturbations in cosmological scenarios with a modified Friedmann equation, such as quantum gravity bouncing cosmologies. We work within a separate universe approximation which captures wavelengths larger than the cosmological horizon; this approximation has been successfully applied to loop quantum cosmology and group field theory. We consider two variables commonly used to characterise scalar perturbations: the curvature perturbation on uniform-density hypersurfaces $ζ$ and the comoving curvature perturbation $\mathcal{R}$. For standard cosmolo…
We derive explicit and exact expressions for the physical velocity of a free particle comoving with the Hubble flow as measured by a static observer, and for the frequency shift of light emitted by a comoving source and received, again, by a static observer. The expressions make it clear that an interpretation of the redshift as a kind of Doppler effect only makes sense when the distance between the observer and the source vanishes exactly.
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…
We propose a new five-parameter entropy function that proves to be singular-free during the entire cosmic evolution of the universe, and at the same time, also generalizes the Tsallis, Barrow, Rényi, Sharma-Mittal, Kaniadakis and Loop Quantum Gravity entropies for suitable limits of the parameters. In particular, all the above mentioned known entropies become singular (or diverge) when the Hubble parameter vanishes in course of the universe's evolution (for instance, in bounce cosmology at the instant of bounce), while the newly proposed entropy function seems to be singular-free even at $H = …
As a deformed matter bounce scenario with a dark energy component we propose a deformed one with running vacuum model (RVM) in which the dark energy density is written as a power series of $H^2$ and $\dot H$ with a constant equation of state parameter same as the cosmological constant. Our results in analytical and numerical point of views show that in some cases same as LCDM bounce scenario, although the spectral index may achieve a good consistency with observations, a positive value of running of spectral index is obtained which is not compatible with inflationary paradigm where it predicts…
Assuming the existence of a scalar field which undergoes "ghost condensation" and which has a suitably chosen potential, it is possible to obtain a non-singular bouncing cosmology in the presence of regular matter and radiation. The potential for the ghost condensate field can be chosen such that the cosmological bounce is stable against the presence of anisotropic stress. Cosmological fluctuations on long wavelengths relevant to current cosmological observations pass through the bounce unaffected by the new physics which yields the bounce. Thus, this model allows for the realization of the "m…
We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models that contain the Hilbert-Einstein curvature term, the induced gravity term with a negative coupled constant, and even polynomial potentials of the scalar field. Bounce solutions with non-monotonic Hubble parameters have been obtained and analyzed. The case when the scalar field has the conformal coupling and the Higgs-like potential with an opposite sign is studied in detail. In this model the evolution of the Hubble param…
We extend the Loop Quantum Cosmology matter bounce scenario in order to include a dark energy era, which ends abruptly at a Rip singularity where the scale factor and the Hubble rate diverge. In the "deformed matter bounce scenario", the Universe is contracting from an initial non-causal matter dominated era until it reaches a minimal radius. After that it expands in a decelerating way, until at late times, where it expands in an accelerating way, thus the model is described by a dark energy era that follows the matter dominated era. Depending on the choice of the free parameters of the model,…
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 identify a signature of quantum gravitational effects that survives from the early universe to the current era: Fluctuations of quantum fields as seen by comoving observers are significantly influenced by the history of the early universe. In particular we show how the existence (or not) of a quantum bounce leaves a trace in the background quantum noise that is not damped and would be non-negligible even nowadays. Furthermore, we estimate an upper bound for the typical energy and length scales where quantum effects are relevant. We discuss how this signature might be observed and therefore …
We study the background conditions for a bounce uniquely driven by a single scalar field model with a generalized kinetic term $K(X)$, without any additional matter field. At the background level we impose the existence of two turning points where the derivative of the Hubble parameter $H$ changes sign and of a bounce point where the Hubble parameter vanishes. We find the conditions for $K(X)$ and the potential which ensure the above requirements. We then give the examples of two models constructed according to these conditions. One is based on a quadratic $K(X)$, and the other a $K(X)$ which …
An alternative to the Big Bang cosmologies is obtained by the Big Bounce cosmologies. In this paper, we study a bounce cosmology with a Type IV singularity occurring at the bouncing point, in the context of $F(R)$ modified gravity. We investigate the evolution of the Hubble radius and we examine the issue of primordial cosmological perturbations in detail. As we demonstrate, for the singular bounce, the primordial perturbations originating from the cosmological era near the bounce, do not produce a scale invariant spectrum and also the short wavelength modes, after these exit the horizon, do n…
The ekpyrotic and cyclic universe scenarios have revived the idea that the density perturbations apparent in today's universe could have been generated in a `pre-singularity' epoch before the big bang. These scenarios provide explicit mechanisms whereby a scale invariant spectrum of adiabatic perturbations may be generated without the need for cosmic inflation, albeit in a phase preceding the hot big bang singularity. A key question they face is whether there exists a unique prescription for following perturbations through the bounce, an issue which is not yet definitively settled. This goal o…
In this paper we investigate how to realize various quite well known cosmological bouncing models in the context of the recently developed unimodular $F(R)$ gravity. Particularly, we shall study the matter bounce scenario, the singular bounce, the superbounce and a symmetric bounce scenario. We present the behavior of the Hubble radius for each of the bouncing models we shall take into account and we investigate which era of the bouncing model is responsible for the cosmological perturbations. As we shall demonstrate, the various bouncing models do not behave in the same way, so the cosmologic…
We analyze whether a black hole can exist and survive in a universe that goes through a cosmological bounce. To this end, we investigate a central inhomogeneity embedded in a bouncing cosmological background modeled by the comoving generalized McVittie metric. Contrary to other dynamical metrics available in the literature, this solution allows for the interaction of the central object with the cosmological fluid. We show that the horizons associated with this metric change with cosmic time because they are coupled to the cosmic evolution as the mass of the central object is always proportiona…
Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of c…
We present a detailed study of a simple scalar field model that yields non-singular cosmological solutions. We study both the qualitative dynamics of the homogeneous and isotropic background and the evolution of inhomogeneous linear perturbations. We calculate the spectrum of perturbations generated on super-Hubble scales during the collapse phase from initial vacuum fluctuations on small scales and then evolve these numerically through the bounce. We show there is a gauge in which perturbations remain well-defined and small throughout the bounce, even though perturbations in other commonly us…
The recent transition from decelerated to accelerated expansion can be seen as a reflection (or "bounce") in the connection variable, defined by the inverse comoving Hubble length ($b=\dot a$, on-shell). We study the quantum cosmology of this process. We use a formalism for obtaining relational time variables either through the demotion of the constants of Nature to integration constants, or by identifying fluid constants of motion. We extend its previous application to a toy model (radiation and $Λ$) to the realistic setting of a transition from dust matter to $Λ$ domination. In the dust and …
We demonstrate how pulsar timing arrays (PTAs) can, in principle, yield a purely gravitational wave (GW) measurement of the luminosity distance and comoving distance to a supermassive black hole binary source, hence providing an estimate of the source redshift and the Hubble constant. The luminosity distance is derived through standard measurement of the chirp mass, which for the slowly evolving binary sources in the PTA band can be found by comparing the frequency of GW-timing residuals at the Earth compared to those at distant pulsars in the array. The comoving distance can be measured from …
The existence of cosmological perturbations of wavelength larger than the Hubble radius is a generic prediction of the inflationary paradigm. We provide the derivation beyond perturbation theory of a conserved quantity which generalizes the linear comoving curvature perturbation. As a by-product, we show that super-Hubble-radius (super-Hubble) perturbations have no physical influence on local observables e.g., the local expansion rate) if cosmological perturbations are of the adiabatic type.
We study the classical dynamics of black holes during a nonsingular cosmological bounce. Taking a simple model of a nonsingular bouncing cosmology driven by the combination of a ghost and ordinary scalar field, we use nonlinear evolutions of the Einstein equations to follow rotating and non-rotating black holes of different sizes through the bounce. The violation of the null energy condition allows for a shrinking black hole event horizon and we find that for sufficiently large black holes (relative to the minimum Hubble radius) the black hole apparent horizon can disappear during the contract…
We implement Polymer Quantum Mechanics on the Hamiltonian formulation of the isotropic Universe in both the representations of the standard Ashtekar-Barbero-Immirzi connection and of a new generalized coordinate conjugate to the Universe volume. The resulting dynamics is a bouncing cosmology; when quantizing the volume-like variable the Big Bounce is an intrinsic cut-off on the cosmological dynamics, while when using the standard connection the Bounce density results to be dependent on the initial conditions of the prepared wave packet. Then we compare the nature of the resulting Bounce with w…
We construct two reduced quantum theories for the Oppenheimer-Snyder model, respectively taking the point of view of the comoving and the exterior stationary observer, using affine coherent states quantization. Investigations of the quantum corrected dynamics reveal that both observers can see a bounce, although for the exterior observer certain quantization ambiguities have to be chosen correctly. The minimal radius for this bounce as seen from the stationary observer is then shown to always be outside of the photon sphere. Possible avenues to lower this minimal radius and reclaim black holes…
We develop the formalism for computing gravitational corrections to vacuum decay from de Sitter space as a sub-Planckian perturbative expansion. Non-minimal coupling to gravity can be encoded in an effective potential. The Coleman bounce continuously deforms into the Hawking-Moss bounce, until they coincide for a critical value of the Hubble constant. As an application, we reconsider the decay of the electroweak Higgs vacuum during inflation. Our vacuum decay computation reproduces and improves bounds on the maximal inflationary Hubble scale previously computed through statistical techniques.
Bouncing Cosmological Models and Energy Conditions in $f(Q, L_m)$ gravity
Centre for Interdisciplinary Studies and Research, D Y Patil International University（D Y Patil国际大学跨学科研究与中心）；JSPM’s Bhivarabai Sawant Institute of Technology and Research（JSPM Bhivarabai Sawant技术与研究所）；Department of Mathematics, SR University（SR大学数学系）
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, w…
The Riccati equation for the Hubble parameter H of barotropic FRW cosmologies in conformal time for κ\neq 0 spatial geometries and in comoving time for the κ=0 geometry, respectively, is generalized to odd Grassmannian time parameters. We obtain a system of simple differential equations for the four supercomponents (two of even type and two of odd type) of the Hubble superfield function {\cal H} that is explicitly solved. The second even Hubble component does not have an evolution governed by general relativity although there are effects of the latter upon it
We consider cosmological evolution from the perspective of quantum information. We present a quantum circuit model for the expansion of a comoving region of space, in which initially-unentangled ancilla qubits become entangled as expansion proceeds. We apply this model to the comoving region that now coincides with our Hubble volume, taking the number of entangled degrees of freedom in this region to be proportional to the de Sitter entropy. The quantum circuit model is applicable for at most 140 $e$-folds of inflationary and post-inflationary expansion: we argue that no geometric description …
We discuss the effect of super-Hubble cosmological fluctuations on the locally measured Hubble expansion rate. We consider a large bare cosmological constant in the early universe in the presence of scalar field matter (the dominant matter component), which would lead to a scale-invariant primordial spectrum of cosmological fluctuations. Using the leading order gradient expansion we show that the expansion rate measured by a (secondary) clock field which is not comoving with the dominant matter component obtains a negative contribution from infrared fluctuations, a contribution whose absolute …
In the context of the late time cosmic acceleration phenomenon, many geometrically modified theories of gravity have been proposed in recent times. In this paper, we have investigated the role of a recently proposed extension of symmetric teleparallel gravity dubbed as f(Q,T) gravity in getting viable cosmological models, where Q and T respectively denote the non-metricity and the trace of energy momentum tensor. We stress upon the mathematical simplification of the formalism in the f(Q,T) gravity and derived the dynamical parameters in more general form in terms of the Hubble parameter. We co…
We state a condition for an observer to be comoving with another observer in general relativity, based on the concept of lightlike simultaneity. Taking into account this condition, we study relative velocities, Doppler effect and light aberration. We obtain that comoving observers observe the same light ray with the same frequency and direction, and so gravitational redshift effect is a particular case of Doppler effect. We also define a distance between an observer and the events that it observes, that coincides with the known affine distance. We show that affine distance is a particular case…
We present a consistent canonical formulation of the flat Oppenheimer-Snyder model, including the Schwarzschild exterior. The switching between comoving and stationary observer is realized by promoting the coordinate transformation between dust proper time and Schwarzschild-Killing time to a canonical one. This leads to two different forms of the Hamiltonian constraint, both (almost) deparameterizable with regard to one of these times. A preliminary quantization of these constraints reveals a consistent picture for both observers: the singularity is avoided by a bounce.
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…
In this Letter, we study analytically the evolutions of the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe and its linear perturbations in the framework of {\em the dressed metric approach} in loop quantum cosmology (LQC). Assuming that the evolution of the background is dominated by the kinetic energy of the inflaton at the quantum bounce, we find that both evolutions of the background and its perturbations are independent of the inflationary potentials during the pre-inflationary phase. During this period the effective potentials of the perturbations can be well approximated by a P…
We study cosmological solutions of Einstein gravity with a positive cosmological constant in diverse dimensions. These include big-bang models that re-collapse, big-bang models that approach de Sitter acceleration at late times, and bounce models that are both past and future asymptotically de Sitter. The re-collapsing and the bounce geometries are all tall in the sense that entire spatial slices become visible to a comoving observer before the end of conformal time, while the accelerating big-bang geometries can be either short or tall. We consider the interpretation of these cosmological sol…
The purpose of this short review is to describe cosmological models with a linear inhomogeneous time-dependent equation of state (EoS) for the dark energy, when the dark fluid is coupled with dark matter. This may lead to a bounce cosmology. We consider equivalent descriptions in terms of the EoS parameters for an exponential, a power-law, or a double-exponential law for the scale factor $a$. Stability issues are discussed by considering small perturbations around the critical points for the bounce, in the early as well as in the late, universe. The latter part of the paper is concerned with d…
Cosmological bouncing solutions and their stability in teleparallel gravity
University of South China（南华大学）；University of Management and Technology（管理科技大学）；Khazar University（哈扎尔大学）；Fukushima University（福岛大学）；Princess Nourah Bint Abdulrahman University（公主努拉·宾特·阿卜杜勒·拉赫曼大学）
In loop quantum cosmology (LQC) the big bang is replaced by a quantum bounce which is followed by a robust phase of super-inflation. Rather than growing unboundedly in the past, the Hubble parameter \emph{vanishes} at the bounce and attains a \emph{finite universal maximum} at the end of super-inflation. These novel features lead to an unforeseen implication: in presence of suitable potentials all LQC dynamical trajectories are funneled to conditions which virtually guarantee slow roll inflation with more than 68 e-foldings, {without any input from the pre-big bang regime}. This is in striking…
Explicit Fermi coordinates are given for geodesic observers comoving with the Hubble flow in expanding Robertson-Walker spacetimes, along with exact expressions for the metric tensors in Fermi coordinates. For the case of non inflationary cosmologies, it is shown that Fermi coordinate charts are global, and space-time is foliated by space slices of constant Fermi (proper) time that have finite extent. A universal upper bound for the proper radius of any leaf of the foliation, i.e., for the proper radius of the spatial universe at any fixed time of the geodesic observer, is given. A general exp…
We analyze the semiclassical and quantum polymer dynamics of the isotropic Universe in terms of both the standard Ashtekar-Barbero-Immirzi connection and its conjugate momentum and also of the new generalized coordinate conjugate to the Universe volume. We study the properties of the resulting bouncing cosmology that emerges in both the representations and we show that the Big Bounce is an intrinsic cut-off on the cosmological dynamics only when the volume variable is implemented, while in terms of the standard connection the Universe Bounce energy density is fixed by the initial conditions on…
Assuming the Hubble parameter is a continuous and differentiable function of comoving time, we investigate necessary conditions for quintessence to phantom phase transition in quintom model. For power-law and exponential potential examples, we study the behavior of dynamical dark energy fields and Hubble parameter near the transition time, and show that the phantom-divide-line w=-1 is crossed in these models.
In this paper, in an extended theory of gravity, we have presented bouncing cosmological model at the backdrop of an isotropic, homogeneous space-time, in presence of general relativistic hydrodynamics (GRH). The scale factor has been chosen in such a manner that with appropriate normalization, the quintom bouncing scenario can be assessed. Accordingly, the bounce occurs at $t=0$ and the corresponding Hubble parameter vanishes at the bounce epoch. The equation of state (EoS) parameter and the energy conditions of the model have been analysed. The violation of strong energy condition further su…
