Loop quantum cosmology is a tentative approach to model the universe down to the Planck era where quantum gravity settings are needed. The quantization of the universe as a dynamical space-time is inspired by Loop Quantum Gravity ideas. In addition, loop quantum cosmology could bridge contact with astronomical observations, and thus potentially investigate quantum cosmology modellings in the light of observations. To do so however, modelling both the background evolution and its perturbations is needed. The latter describe cosmic inhomogeneities that are the main cosmological observables. In this context, we present the so-called deformed algebra approach implementing the quantum corrections to the perturbed universe at an effective level by taking great care of gauge issues. We particularly highlight that in this framework, the algebra of hypersurface deformation receives quantum corrections, and we discuss their meaning. The primordial power spectra of scalar and tensor inhomogeneities are then presented, assuming initial conditions are set in the contracting phase preceding the quantum bounce and the well-known expanding phase of the cosmic history. These spectra are subsequently propagated to angular power spectra of the anisotropies of the cosmic microwave background. It is then shown that regardless of the choice for the initial conditions inside the effective approach for the background evolution (except that they are set in the contracting phase), the predicted angular power spectra of the polarized B-modes exceed the upper bound currently set by observations. The exclusion of this specific version of loop quantum cosmology establishes the falsifiability of the approach, though one shall not conclude here that either loop quantum cosmology or loop quantum gravity is excluded.
The effects of phase space deformations on Kalutza-Klein cosmology are studied. The deformation is introduced by modifying the symplectic structure of the minisuperspace variables. In the deformed model, we find an accelerating scale factor and therefore infer the existence of an effective cosmological constant from the phase space deformation parameter $β$.
The effects of phase space deformations in standard scalar field cosmology are studied. The deformation is introduced by modifying the symplectic structure of the minisuperspace variables to have a deformed Poisson algebra among the coordinates and the canonical momenta. It is found that in the deformed minisuperspace model the volume of the universe is non singular. Finally, the late time evolution gives rise to an accelerating scale factor, this acceleration is a consequence of the noncommutative deformation.
Loop quantum cosmology tries to capture the main ideas of loop quantum gravity and to apply them to the Universe as a whole. Two main approaches within this framework have been considered to date for the study of cosmological perturbations: the dressed metric approach and the deformed algebra approach. They both have advantages and drawbacks. In this article, we accurately compare their predictions. In particular, we compute the associated primordial tensor power spectra. We show -- numerically and analytically -- that the large scale behavior is similar for both approaches and compatible with…
Scalar cosmological perturbations in loop quantum cosmology (LQC) is revisited in a covariant manner, using self dual Ashtekar variables. For real-valued Ashtekar-Barbero variables, this `deformed algebra' approach has been shown to implement holonomy corrections from loop quantum gravity (LQG) in a consistent manner, albeit deforming the algebra of modified constraints in the process. This deformation has serious conceptual ramifications, not the least of them being an effective `signature-change' in the deep quantum regime. In this paper, we show that working with self dual variables lead to…
The noncommutativity of the space-time had important implications for the very early Universe, when its size was of the order of the Planck length. An important implication of this effect is the deformation of the standard dispersion relation of special relativity. Moreover, in the Planck regime gravity itself must be described by a quantum theory. We consider the implications of the modified dispersion relations for a photon gas, filling the early Universe, in the framework of Loop Quantum Cosmology, a theoretical approach to quantum gravity. We consider three types of deformations of the dis…
In this paper, we use the WKB approximation method to approximately solve a deformed Schrodinger-like differential equation: $\left[ -\hbar^{2} \partial_ξ^{2}g^{2}\left( -i\hbarα\partial_ξ\right) -p^{2}\left( ξ\right) \right] ψ\left( ξ\right) =0$, which are frequently dealt with in various effective models of quantum gravity, where the parameter $α$ characterizes effects of quantum gravity. For an arbitrary function $g\left( x\right) $ satisfying several properties proposed in the paper, we find the WKB solutions, the WKB connection formulas through a turning point, the deformed Bohr--Sommerfe…
In this paper, by establishing a Brans-Dicke (BD) cosmology by means of a deformed phase space, in the absence of any scalar potential, cosmological constant and ordinary matter, we show that it is feasible to overcome obstacles reported in the corresponding commutative (non-deformed) frameworks. More concretely, by applying the Hamiltonian formalism and introducing a dynamical deformation, between the momenta associated to the FLRW scale factor and the BD scalar field, we obtain the modified equations of motion. In particular, these equations reduce to their standard counterparts when the non…
Stability of the Einstein static universe versus the linear scalar, vector and tensor perturbations is investigated in the context of deformed Hořava-Lifshitz cosmology inspired by entropic force scenario. A general stability condition against the linear scalar perturbations is obtained. Using this general condition, it is shown that there is no stable Einstein static universe for the case of flat universe, $k=0$. For the the special case of large values of running parameter of HL gravity $ω$, in a positively curved universe $k>0$, the domination of the quintessence and phantom matter fields w…
Considering Verlinde's entropic gravity proposal, we focus the effects of fermionic $q$ deformation on the Einstein's field equations and Friedmann equations. For this purpose, we represent the thermodynamical properties of the deformed fermion gas model in two-dimensional space. To describe the behavior of the quantum black holes, deformed Einstein field equations are derived with the help of deformed entropy function. Moreover, deformed Friedmann equations are investigated by using Friedmann-Robertson-Walker (FRW) metric. We also present the effective ones of the energy density, the pressure…
Anomaly-free perturbations of loop quantum cosmology with holonomy corrections reveal an $Ω$ -deformed spacetime structure, $Ω:=1-2ρ/ρ_c$, where $Ω<0$ indicates a Euclidean-like space and $Ω>0$ indicates a Lorentz-like space. It would be reasonable to give the initial value at the spacetime transition point, $ρ=ρ_c/2$, but we find that it is impossible to define a Minkowski-like vacuum even for large $k$ modes at that time. However, if we loosen the condition and give the initial value slightly after $Ω=0$, e.g., $Ω\simeq 0.2$, the vacuum state can be well defined and, furthermore the slow rol…
The cosmology of $f(R, L_m)$ gravity: constraining the background and perturbed dynamics
North-West University（西北大学）；Wolkite University（沃尔基特大学）；Entoto Observatory and Research Center, Space Science and Geospatial Institute（恩托托观测与研究中心，空间科学与地理信息研究所）；Imam Mohammad Ibn Saud Islamic University (IMSIU)（伊马姆穆罕默德·本·沙特伊斯兰大学）；University of Khartoum（喀土穆大学）；National Institute for Theoretical and Computations Sciences (NITheCS)（国家理论与计算科学研究所）
In this paper we study the effects of noncommutative phase space deformations on the Schwarzschild black hole. This idea has been previously studied in {Friedmann-Robertson-Walker (FRW)} cosmology, where this "noncommutativity" provides a simple mechanism that can explain the origin of the cosmological constant. In this paper we obtain the same relationship between the cosmological constant and the deformation parameter that appears in deformed phase space cosmology, but in the context of the deformed phase space black holes. This was achieved by comparing the entropy of the deformed Schwarzsc…
In this work, we focus on the collapse of a spherically symmetric perturbation, with a classical top-hat profile, to study the nonlinear evolution of only viscous modified Chaplygin gas (VMCG) perturbations in Einstein's gravity as well as in loop quantum Cosmology (LQC). In the perturbed region, we have investigated the natures of equation of state parameter, square speed of sound and another perturbed quantities. The results have been analyzed by numerical and graphical investigations.
An integral kernel representation for the commutative $\star$-product on curved classical spacetime is introduced. Its convergence conditions and relationship to a Drin'feld differential twist are established. A $\star$-Einstein field equation can be obtained, provided the matter-based twist's vector generators are fixed to self-consistent values during the variation in order to maintain $\star$-associativity. Variations not of this type are non-viable as classical field theories. $\star$-Gauge theory on such a spacetime can be developed using $\star$-Ehresmann connections. While the theory pr…
Cosmology with minimal length uncertainty relations
我们研究了经典和量子de Sitter（dS）和Anti de Sitter（AdS）宇宙学相空间中存在最小可观测长度的影响。由于这个长度已经在量子引力和弦论中提出，它在早期宇宙中的影响是可以预期的。采用这样的最小长度的存在导致广义不确定原理（GUP），这是一个变形的海森堡代数之间的小超空间变量和他们的动量算子。我们将这些变形的交换关系推广到相应的变形Poisson代数的经典极限。使用由此产生的泊松和海森堡关系，然后，我们构建了经典和量子宇宙学的dS和广告模型的规范框架。我们表明，在经典的dS宇宙学中，这种效应产生了一个暴胀宇宙，其中的膨胀率大于通常的dS宇宙。此外，对于AdS模型，它表明，GUP可能会改变相应的宇宙学的振荡性质。我们还研究了量子化模型中GUP的影响，通过近似的Wheeler-DeWitt（WD）方程的解析解，在小尺度因子的限制下的宇宙，并比较结果与普通的量子宇宙学在每种情况下。
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,…
Whenever the condition of anomaly freedom is imposed within the framework of effective approaches to loop quantum cosmology, one seems to conclude that a deformation of general covariance is required. Here, starting from a general deformation we regain an effective gravitational Lagrangian including terms up to fourth order in extrinsic curvature. We subsequently constrain the form of the corrections, and then investigate the conditions for the occurrence of a big bounce and the realisation of an inflationary era, in the presence of a perfect fluid or scalar field.
Based on the assumptions of the standard model of cosmology, a phase transition associated with chiral symmetry breaking after the electroweak transition has occurred at approximately $10μ$ seconds after the Big Bang to convert a plasma of free quarks and gluons into hadrons. We consider such a phase transition in the context of a deformed Horava-Lifshitz cosmology. The Friedmann equation for the deformed Horava-Lifshitz universe is obtained using the entropic interpretation of gravity, proposed by Verlinde. We investigate the effects of the parameter $ω$ appearing in the theory on the evoluti…
This article is devoted to the study of scalar perturbations in loop quantum cosmology. It aims at clarifying the situation with respect to the way initial conditions are set and to the specific choice of an inflaton potential. Several monomial potentials are studied. Both the dressed metric and deformed algebra approaches are considered. We show that the calculation of the ultraviolet part of the spectrum, which is the physically relevant region for most background trajectories, is reliable, whereas the infrared and intermediate parts do depend on some specific choices that are made explicit.
The relativistic restricted three-body problem: geometry and motion around tidally perturbed black holes
Sapienza Università di Roma（罗马第一大学）；INFN, Sezione di Roma（意大利国家核物理研究所罗马分部）；Niels Bohr Institute（尼尔斯·玻尔研究所）；Instituto Superior Técnico – IST, Universidade de Lisboa – UL（里斯本大学高等技术学院）
It is often argued that inflation erases all the information about what took place before it started. Quantum gravity, relevant in the Planck era, seems therefore mostly impossible to probe with cosmological observations. In general, only very ad hoc scenarios or hyper fine-tuned initial conditions can lead to observationally testable theories. Here we consider a well-defined and well motivated candidate quantum cosmology model that predicts inflation. Using the most recent observational constraints on the cosmic microwave background B modes, we show that the model is excluded for all its para…
In the last years, we saw more and more attempts to explain dark matter as a general relativistic effect, at least for some fraction. Following this philosophy, we considered the gravitational distortions due to the inhomogeneous distribution of matter in the universe, which we know from general relativity to be retarded distortions. This provides a magnification effect, since the distortions we feel now depend not on the present matter density, but on the past one, which is greater. The expansion rate of the universe is perturbed as well, in a not negligible way, despite matter inhomogeneitie…
Deformed Schwarzschild horizons in second-order perturbation theory: mass, geometry, and teleology
Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen（格罗宁根大学伯努利数学、计算机科学与人工智能研究所）；School of Mathematical Sciences and STAG Research Centre, University of Southampton（南安普顿大学数学科学学院和STAG研究中心）；Institute for Physics and Astronomy, University of Potsdam（波茨坦大学物理与天文学研究所）
We investigate the phase space of a scalar field theory obtained by minisuperspace deformation. We consider quintessence or phantom scalar fields in the action which arise from minisuperspace deformation on the Einstein-Hilbert action. We use a modified Poisson Algebra where Poisson brackets are the $α$-deformed ones and are related to the Moyal-Weyl star product. We discuss early and late-time attractors, and we reconstruct the cosmological evolution. We show that the model can have $Λ$CDM model as a future attractor if we initially consider a massless scalar field without a cosmological cons…
Considering as usual that the underlying geometry of our universe is well described by the spatially flat Friedmann-Lemaitre-Robertson-Walker line element, we review how the background of holonomy corrected Loop Quantum Cosmology (LQC) could be obtained as a simple modified version of the mimetic gravity. We also analyze the scalar and tensor perturbations of this modified mimetic model, from which we find that at the level of tensor perturbations it is indistinguishable from General Relativity while at the level of scalar perturbations, the modified mimetic model, which has the same backgroun…
In this paper, we have studied the bouncing behavior of the cosmological models formulated at the background of the Hubble function in the F(R, G) theory of gravity, where R and G denote the Ricci scalar and Gauss-Bonnet invariant. The actions of bouncing cosmology are studied under consideration of different viable models and can resolve the difficulty of singularity in standard Big-Bang cosmology. Both models show bouncing behavior and satisfy the bouncing cosmological properties. Models based on dynamical, deceleration, and energy conditions indicate the accelerating behavior at the late ev…
Anomaly-free perturbations of loop quantum cosmology reveal a deformed space-time structure, in which the signature changes when the energy density is $ρ=ρ_c/2$. Furthermore, in loop quantum cosmology, one can obtain an effective causal structure only for a low density region ($ρ\leqρ_c/2$), which gives a natural initial condition to consider the horizon problem. Choosing the initial value at $ρ(0)=ρ_c/2$ in this paper, we investigate the horizon problem and the probability of inflation in the framework of loop quantum cosmology. Two models are considered: the quadratic inflation and the natur…
The applicability of a linearized perturbed FLRW metric to the late, lumpy universe has been subject to debate. We consider in an elementary way the Newtonian limit of the Einstein equations with this ansatz for the case of structure formation in late-time cosmology, on small and large scales, and argue that linearizing the Einstein tensor produces only a small error down to arbitrarily small, decoupled scales (e.g. Solar system scales). On subhorizon patches, the metric scale factor becomes a coordinate choice equivalent to choosing the spatial curvature, and not a sign that the FLRW metric c…
We calculate the emission of gravitational waves, gravitons, photons and neutrinos from a perturbed Schwarzschild blackhole (BH). The perturbation can be due to either classical or quantum sources and therefore the injected energy can be either positive or negative. The emission can be classical in nature, as in the case of gravitational waves, or of quantum nature, for gravitons and the additional fields. We first set up the theoretical framework for calculating the emission by treating the case of a minimally coupled scalar field and then present the results for the other fields. We perform …
