The quantization of the reduced phase-space of the Einstein-Hilbert action for gravity in $2+1D$ has been shown to bring about the emergence, at the quantum level, of a topological quantum field theory endowed with an $SU_q(2)$ quantum group symmetry structure. We hereby tackle the same problem, but start from the kinematical $SU(2)$ (quantum) Hilbert space of the theory of $2+1D$ gravity with non-zero cosmological constant in the Palatini formalism, and subsequently impose the constraints. We hence show the dynamical emergence of the $SU_q(2)$ quantum group at the quantum level within the spin-foam framework. The regularized curvature constraint is responsible for the effective representations of $SU_q(2)$ that are recovered for any Wilson loop evaluated at the $SU(2)$ group element that encodes the discretization of the space-time curvature induced by the cosmological constant. The extension to the spin-network basis, and consequently to any transition amplitude between its generic states, enables us to derive in full generality the recoupling theory of $SU_q(2)$. We provide constructive examples for the scalar product of two loop states and spin-networks encoding trivalent vertices. We further comment on the diffeomorphism symmetry generated by the implementation of the curvature constraint, and finally derive explicitly the partition function amplitude of the Turaev-Viro model.
We investigate anisotropic fluid cosmology in a situation where the spacetime metric back-reacts in a local, time-dependent way to the presence of inhomogeneities. We derive exact solutions to the Einstein field equations describing Friedmann-Lemaitre-Robertson-Walker (FLRW) large scale cosmological evolution in the presence of local inhomogeneities and time-dependent back reaction. We use our derivation to tackle the cosmological constant problem. A cosmological constant emerges by averaging the back reaction term on spatial scales of the order of $100 \ \text{Mpc}$, at which our universe beg…
The concepts of Lorentz invariance of local (flat space) physics, and unitarity of time evolution and the S-matrix, are famously rigid and robust, admitting no obvious consistent theoretical deformations, and confirmed to incredible accuracy by experiments. But neither of these notions seem to appear directly in describing the spatial correlation functions at future infinity characterizing the "boundary" observables in cosmology. How then can we see them emerge as {\it exact} concepts from a possible ab-initio theory for the late-time wavefunction of the universe? In this letter we examine thi…
The Hamiltonian of Intrinsic Time Gravity is elucidated. The theory describes Schrodinger evolution of our universe with respect to the fractional change of the total spatial volume. Gravitational interactions are introduced by extending Klauder's momentric variable with similarity transformations, and explicit spatial diffeomorphism invariance is enforced via similarity transformation with exponentials of spatial integrals. In analogy with Yang-Mills theory, a Cotton-York term is obtained from the Chern-Simons functional of the affine connection. The essential difference is the fundamental va…
In this paper we address the issue of exploring some cosmological scenarios in modified Einstein gravity through non-dynamical (auxiliary) fields. We found that all scenarios are controlled by a specific parameter associated with an auxiliary field. We explore the emergence of inflationary, radiation, matter and dark energy dominated regimes. Furthermore, an interesting possibility such as the emergence of a self-tuning mechanism to the cosmological constant problem in the radiation dominated era is also discussed.
We study the deep connections between the concepts of quantum information theory and cosmology. Employing Fermi normal coordinates and conformal Fermi coordinates, we construct a relation between Friedmann equations of Friedmann-Lemaitre-Robertson-Walker universe and entanglement. Friedmann equations are derived with the first law of entanglement under the assumption that entanglement entropy in a geodesic balls is maximized at fixed volume.
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful in the Lambda=0 case and widely applied in four dimensional LQG) lead to a deformation of the classical constraint algebra (or anomaly) proportional to the local strength of the curvature squared. We argue that this is an unavoidable consequence of the non-local nature of generalized connections.
The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that when the background metric possesses an isometry, like stationary or spherically symmetric black holes, the method can be upgraded into a pragmatic procedure of renormalization that produces efficient numerical calculations. In this note we show that when the background enjoys three-dimensional spatial symmetries, like homogeneous expanding universes, the abov…
In the Palatini action of general relativity the connection and the metric are treated as independent dynamical variables. Instead of assuming a relation between these quantities, the desired relation between them is derived through the Euler-Lagrange equations of the Palatini action. In this manuscript we construct an extended Palatini action, where we do not assume any a priori relationship between the connection, the covariant metric tensor, and the contravariant metric tensor. Instead we treat these three quantities as independent dynamical variables. We show that this action reproduces th…
We regard the Wheeler-De Witt equation as a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The used method to study such a problem is a variational approach with Gaussian trial wave functionals. We approximate the equation to one loop in a Schwarzschild background. A zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities together …
In this paper we consider a scalar field system with a class of potentials given by the expression, $V(ϕ)\propto ϕ^m {\rm exp}({-λϕ^n/{M^n_{Pl}}})$; $m\geqslant 0, n>1$ for which $Γ=V_{ϕϕ}V/V^2_ϕ\to 1 $ as $|ϕ|\to \infty$. We carry out dynamical analysis for the underlying system choosing a suitable set of autonomous variables and find all the fixed points. In particular, we show that the scaling solution is an attractor of the system in the asymptotic regime. We indicate the application of the solution to models of quintessential inflation.
We consider one loop graviton corrections to scalar field Green's functions in the de Sitter phase of an inflationary space-time, a topic relevant to the computation of cosmological observables beyond linear order. By embedding de-Sitter space into an ultraviolet complete theory such as M-theory we argue that the ultraviolet (UV) cutoff of the effective field theory should be taken to be fixed in physical coordinates, whereas the infrared (IR) cutoff is expanding as space expands. In this context, we demonstrate how to implement three different regularization schemes -- the brute force cutoff …
Many studies have been carried out since T.Padmanabhan proposed that the cosmic acceleration can be understood from the perspective that spacetime dynamics is an emergent phenomenon. Motivated by such a new paradigm, we firstly study the de Sitter universe from emergence of space. After that we investigate the universes in general cases and then narrow down our discussions into one of them with a detailed discussion of the possibility in describing our real universe classically. Furthermore, a constraint on $Ht$ and a estimated value of $\tildeΩ_Λ$ (caused by $ρ_{vac}$) can be derived from our…
Considering the Barrett-Crane spin foam model for quantum gravity with (positive) cosmological constant, we show that speeds must be quantized and we investigate the physical implications of this effect such as the emergence of an effective deformed Poincare symmetry.
An one-parameter regularization freedom of the Hamiltonian constraint for loop quantum gravity is analyzed. The corresponding spatially flat, homogenous and isotropic model includes the two well-known models of loop quantum cosmology as special cases. The quantum bounce nature is tenable in the generalized cases. For positive value of the regularization parameter, the effective Hamiltonian leads to an asymptotic de-Sitter branch of the Universe connecting to the standard Friedmann branch by the quantum bounce. Remarkably, by suitably choosing the value of the regularization parameter, the obse…
Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic four-dimensional world emerges from this theory dynamically.
A time-varying cosmological "constant" Lambda is consistent with Einstein's equation, provided matter and/or radiation is created or destroyed to compensate for it. Supposing an empty primordial universe endowed with a very large cosmological term, matter will emerge gradually as Lambda decays. Provided only radiation or ultrarelativistic matter is initially created, the universe starts in a nearly de Sitter phase, which evolves towards a FRW regime as expansion proceeds. If, at some cosmological time, the cosmological term begins increasing again, as presently observed, expansion will acceler…
The way physics of loop quantum gravity is affected by the underlying quantization ambiguities is an open question. We address this issue in the context of loop quantum cosmology using gauge-covariant fluxes. Consequences are explored for two choices of regularization parameters: $μ_0$ and $\bar μ$ in presence of a positive cosmological constant, and two choices of regularizations of the Hamiltonian constraint in loop quantum cosmology: the standard and the Thiemann regularization. We show that novel features of singularity resolution and bounce, occurring due to gauge-covariant fluxes, exist …
Recent astronomical observations strongly indicate that the current Universe is undergoing an accelerated phase of expansion. The discovery of this fact was unexpected and resulted in the comeback of cosmological constant. The conception of standard cosmological model has its roots in this context. The paper relates to the methodological status of effective theories in the context of cosmological investigations. We argue that the standard cosmological model (LCDM model) as well as the CDM have a status of effective theories only, similarly to the standard model of particle physics. The LCDM mo…
The cosmological constant induced by quantum fluctuation of the graviton on a given background is considered as a tool for building a spectrum of different geometries. In particular, we apply the method to the Schwarzschild background with positive and negative mass parameter. In this way, we put on the same level of comparison the related naked singularity (-M) and the positive mass wormhole. We use the Wheeler-De Witt equation as a basic equation to perform such an analysis regarded as a Sturm-Liouville problem . The cosmological constant is considered as the associated eigenvalue. The used …
We have shown how the quantization of two-dimensional quantum gravity with an action which contains only a positive cosmological constant and boundary cosmological constants leads to the emergence of a spacetime which can be described as a constant negative curvature spacetime with superimposed quantum fluctuations.
We show that the Stephenson-Kilmister-Yang (SKY) equation combined with Camenzind's matter current term naturally provides the cosmological constant and dark radiation as integration constants of the SKYC field equation. To characterize the property of the dark radiation, we develop a method to separate it from the ordinary radiation. We found a special property of Camenzind's matter current, namely that the solution space for radiation in fact belongs to that of the vacuum solution of SKY equation. We also found that his matter current does not obey the conservation condition suggested by Kil…
In this work, we compute the time-dependent masses that govern the dynamics of scalar and tensor perturbations propagating on an effective flat, homogeneous, and isotropic background within the framework of loop quantum cosmology, regularized according to the procedure put forward by Dapor and Liegener. To do so, we follow the two main approaches that, in the field of loop quantum cosmology, lead to hyperbolic equations for the perturbations in the ultraviolet sector: the hybrid and dressed metric formalisms. This allows us to compare the masses resulting from both proposals and analyze their …
Casimir energy is calculated for the 5D electromagnetism in the warped geometry. It is compared with the flat case(arXiv:0801.3064). A new regularization, called sphere lattice regularization, is taken. It is based on the minimal area principle and is a direct realization of the geometrical approach to the renormalization group. The properly regularized form of Casimir energy, is expressed in a closed form. We numerically evaluate $\La$(4D UV-cutoff), $\om$(5D bulk curvature, warp parameter) and $T$(extra space IR parameter) dependence of the Casimir energy. The warp parameter $\om$ suffers fr…
As previously discussed in (D. Sudarsky, Int.J.Mod.Phys.D20:509-552, (2011); [arXiv:0906.0315]), the inflationary account for the emergence of the seeds of cosmic structure falls short of actually explaining the generation of primordial anisotropies and inhomogeneities. This description starts from a symmetric background, and invokes symmetric dynamics, so it cannot explain asymmetries. To generate asymmetries, we present an application of the Continuous Spontaneous Localization (CSL) model of wave function collapse (P. Pearle, Phys. Rev. A 39, 2277, (1989); G. C. Ghirardi, P. Pearle and A. Ri…
It has recently been speculated that the end state of a collapsing universe is a tachyonic big crunch. The time reversal of this process would be the emergence of an expanding universe from a tachyonic big bang. In this framework, we study the emergence of cosmological fluctuations. In particular, we compare the amplitude of the perturbations at tne end of the tachyon phase with what would be obtained assuming the usual vacuum initial conditions. We find that cosmological fluctuations emerge in a thermal state. We comment on the relation to the trans-Planckian problem of inflationary cosmology…
According to the principle of emergence, the expansion of the universe can be explained as the emergence of space with the progress of cosmic time. We have analytically solved the equation of emergence proposed by Padmanabhan by assuming the Komar energy density $ρ+3P$ as a function of the Hubble parameter. The resulting model describes the evolution of the universe, which proceeds towards a final de Sitter state. Model parameters have been extracted using the cosmological observational data. Further, the horizon entropy evolution of the model has been studied. The model predicts a universe ha…
We extend the adiabatic regularization method by introducing an arbitrary mass scale $μ$ in the construction of the subtraction terms. This allows us to obtain, in a very robust way, the running of the coupling constants by demanding $μ$-invariance of the effective semiclassical (Maxwell-Einstein) equations. In particular, we get the running of the electric charge of perturbative quantum electrodynamics. Furthermore, the method brings about a renormalization of the cosmological constant and the Newtonian gravitational constant. The running obtained for these dimensionful coupling constants has…
We reexamine the regularization of the two-point function of a scalar field in a Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. Adiabatic regularization provides a set of subtraction terms in momentum space that successfully remove its ultraviolet divergences at coincident points, but can significantly distort the power spectrum at infrared scales, especially for light fields. In this work we propose, by using the intrinsic ambiguities of the renormalization program, a new set of subtraction terms that minimize the distortions for scales $k \lesssim M$, with $M$ an arbitrary mass scale.…
We express the in-in functional determinant giving the one-loop effective potential for a scalar field propagating in a cosmological spacetime in terms of the mode functions specifying the vacuum of the theory and then apply adiabatic regularization to make this bare potential finite. In this setup, the adiabatic regularization offers a particular renormalization prescription that isolates the effects of the cosmic expansion. We apply our findings to determine the radiative corrections to the classical inflaton potentials in scalar field inflationary models and also we derive an effective pote…
We use the $ζ$-function regularization method to evaluate the finite temperature 1-loop effective potential for $ϕ^4$ theory in the Godel spacetime. It is used to study the effects of temperature and curvature coupling on the cosmological phase transition in the rotational spacetime. From our results the critical temperature of symmetry restoration, which is a function of curvature coupling and magnitude of spacetime rotation, can be determined.
In this paper, we consider a high-curvature limit of the varying fundamental constants toy model in which both the value of the speed of light and the value of the gravitational constant are related to the values of the two non-minimally coupled scalar fields. The high-curvature limit motivates the application of the third quantization procedure to such a toy model which results in a theory that describes bosonic massive particles that move freely in the three-dimensional minisuperspace associated with the degrees of freedom of the original model. Motivated by the idea that in the quantum cosm…
We present and discuss an asynchronous coordinate system covering de Sitter spacetime, notably in a complete way in 1+1 dimensions. The new coordinates have several interesting cosmological properties: the worldlines of comoving ($x^i=const$) observers are geodesics, cosmic time is finite in the past, and the coordinates asymptotically tend to that of a flat Robertson & Walker model at large times. This analysis also provides an argument in favor of the natural emergence of an equation of state of the type $p=-ρ$ in the context of the standard cosmological model.
To derive loop quantum cosmology from loop quantum gravity, I apply the model given in \cite{lin1} to a system with coupled gravitational and matter fields. The matter sector consists of a scalar field $phi$ serving as a cosmological clock, and other fields ${psi}$ providing physical spatial coordinates and frames. The physical Hilbert space of the model is constructed from the kinematical Hilbert space of loop quantum gravity, and the local observables in the physical Hilbert space are constructed using the matter coordinates and frames. A specific coherent physical state is then chosen, whos…
We regard the Casimir energy of the universe as the main contribution to the cosmological constant. Using 5 dimensional models of the universe, the flat model and the warped one, we calculate Casimir energy. Introducing the new regularization, called {\it sphere lattice regularization}, we solve the divergence problem. The regularization utilizes the closed-string configuration. We consider 4 different approaches: 1) restriction of the integral region (Randall-Schwartz), 2) method of 1) using the minimal area surfaces, 3) introducing the weight function, 4) {\it generalized path-integral}. We …
We discuss the case of massive gravitons and their relation with the cosmological constant, considered as an eigenvalue of a Sturm-Liouville problem. A variational approach with Gaussian trial wave functionals is used as a method to study such a problem. We approximate the equation to one loop in a Schwarzschild background and a zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormalization procedure is introduced to remove the infini…
The loop quantum dynamics of Kantowski-Sachs spacetime and the interior of higher genus black hole spacetimes with a cosmological constant has some peculiar features not shared by various other spacetimes in loop quantum cosmology. As in the other cases, though the quantum geometric effects resolve the physical singularity and result in a non-singular bounce, after the bounce a spacetime with small spacetime curvature does not emerge in either the subsequent backward or the forward evolution. Rather, in the asymptotic limit the spacetime manifold is a product of two constant curvature spaces. …
The spacial expansion of the universe could be described as a tendency for satisfying holographic equipartition which inevitably demands the presence of dark energy. We explore whether this novel idea proposed by Padmanabhan give any additional insights into the nature of dark energy. In particular, we obtain the constraints imposed by the law of emergence on the equation of state parameter, $ω$. We also present a thermodynamic motivation for the obtained constraints on $ω$. Further, we explicitly prove the feasibility of describing a dynamic dark energy model through the law of emergence. Int…
Using the coherent-state representation we show that the classical Einstein equation for the FRW cosmological model with a general minimal scalar field can be derived from the semiclassical quantum Einstein equation.
Evolution of life on earth was governed, primarily, by natural selection, with major contribution of other evolutionary processes, such as neutral variation, exaptation, and gene duplication. However, for biological evolution to take off, a certain minimal degree of complexity is required such that a replicating genome encodes means for its own replication with sufficient rate and fidelity. In all existing life forms, this is achieved by dedicated proteins, polymerases (replicases), that are produced by the elaborate translation system. However, evolution of the coupled system of replication a…
An effective cosmological constant as black hole primary hair
Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎萨克雷大学）；Institut für Theoretische Physik, Universität Heidelberg（海德堡大学）；Instituto de Matemáticas, Universidad de Talca（塔尔卡大学）
This article concerns the problems regarding different lattice regularization techniques for the matter fields of Hamiltonian constraints defined in the framework of loop quantum gravity. The analysis is formulated in the phase space-reduced cosmological model of the hypothetical theory of canonical quantum general relativity. This article explains why a different than links-related lattice smearing of fields leads to a local violation of general covariance. This happens by assuming, for instance, the nodes-related smearing. Therefore, this problem occurs in the case of any polymerlike scalar …
Intrigued by the holographic principle, Padmanabhan recently proposed a novel idea, saying that our cosmic space is emergent as cosmic time progresses. In particular, the expansion rate of the Universe is related to the difference between the surface degrees of freedom on the holographic horizon and the bulk degrees of freedom inside. In this note, we generalize this interesting paradigm to brane world, scalar-tensor gravity, and f(R) theory, respectively, and find that in the cosmological setting the Friedmann equations can be successfully derived.
We study a consistent infrared and ultraviolet regularization scheme for the cosmological perturbations. The infrared divergences are cured by assuming that the Universe undergoes a transition between a non-singular pre-inflationary, radiation-dominated phase and a slow-roll inflationary evolution. The ultraviolet divergences are eliminated via adiabatic subtraction. A consistent regularization of the field fluctuations through this transition is obtained by performing a mode matching for both the gauge invariant Mukhanov variable and its adiabatic expansion. We show that these quantities do n…
It is shown that the Cotton tensor can describe the effects of gravity beyond general relativity. Any solution of the Einstein equations with or without the cosmological constant satisfies the field equations described by the Cotton tensor. It implies that the cosmological constant is an integration constant. A vacuum of a theory is represented by the vanishing of the Cotton tensor, rather than the vanishing of the Ricci tensor. An exact Schwarzschild-like solution for a static and spherically symmetric source is discovered. Although the field equations involve the third order of derivative, i…
We complete the proof of Weinberg's no-go theorem on the cosmological constant problem in classical gravity when the theory has a (global) scale symmetry. Stimulated with this proof, we explore a solution to the cosmological constant problem by the help of renormalization group equations. We find that the manifestly scale invariant regularization method provides a physically plausible solution to the cosmological constant problem, in particular, to the issue of radiative instability of the cosmological constant.
In the present paper, we investigate regularization of the one-loop quantum corrections with infinite Kaluza-Klein (KK) states and evaluate Casimir vacuum energy from extra dimensions. The extra dimensional models always involve the infinite massless or massive Kaluza-Klein states, and therefore, the regularization of the infinite KK corrections is highly problematic. In order to avoid the ambiguity, we adopt the proper time integrals and the Riemann zeta function regularization in evaluating the summations of infinite KK states. In the calculation, we utilize the KK regularization method with…
