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A biggest challenge for today’s astrophysicist is to solve the mystery of primordial evolution of the universe. This is also known as belongs to Planck’s era. In this stage space-time singularity and inflationary phase all occur when universe was just of the size 10-5m. All this evolution occurs in a tiny fraction of a second. This description is made by joining the cosmological principle of isotropy and homogeneity, the Hubble law, and the Einstein’s field equations of General Relativity in the Big Bang Theory or Standard Cosmological Model (SCM). The SCM is failed to describe first moment in which universe emerges out in presence of singularity. Due to failure of above model quantum theory of gravitation is needed to understand the evolution of early universe. Quantum gravity (QG) is a field of theoretical physics that need to describe gravity by the principles of quantum mechanics, and where quantum effects cannot be ignored, such as in the vicinity of black holes or similar compact astrophysical objects where the effects of gravity are strong(such as neutron stars). Though the theory is able to unfold many mystery but the observational results to prove it are still not exist. The Quantum Cosmology provides some simulating models to understand the primordial evolution by adding some hypothesis. The SCM well explain the observational data with consistency but have some limitations. In present paper Anti de Sitter and Conformal Field Theory are combined together to study condensed matter made up of extra dimensional particles like Dilaton and Strings which are going to decide ultimate fate; the Big Crunch of our Universe. The AdS/CFT correspondence is used to understand the transition from expanding universe to non relativistic transformation to obtain Big Crunch.

The present work shows that the mathematical equivalence of the Jordan frame and its conformally transformed version, the Einstein frame, so as far as Brans–Dicke theory is concerned, survives a quantization of cosmological models, arising as solutions to the Brans–Dicke theory. We work with the Wheeler–deWitt quantization scheme and take up quite a few anisotropic cosmological models as examples. We effectively show that the transformation from the Jordan to the Einstein frame is a canonical one and hence two frames furnish equivalent description of same physical scenario.

Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing canonical treatments. In particular, a successful transition through a turning point is provided in the model system, together with a new definition of such a transition in general terms. Some of the results rely on a fruitful relation between the problem of time and general Gribov problems., Comment: 19 pages, v2: additional remarks on topological turning points

We endorse the context that the cosmological constant problem is a quantum cosmology issue. Therefore, in this paper we investigate the $q$-deformed Wheeler-DeWitt equation of a spatially closed homogeneous and isotropic Universe in the presence of a conformally coupled scalar field. Specifically, the quantum deformed Universe is a quantized minisuperspace model constructed from quantum Heisenberg-Weyl $\mathcal U_q(h_4)$ and $\mathcal U_q(su(1, 1))$ groups. These intrinsic mathematical features allow to establish that ($i$) the scale factor, the scalar field and corresponding momenta are quantized and ($ii$) the phase space has a non-equidistance lattice structure. On the other hand, such quantum group structure provides us a new framework to discuss the cosmological constant problem. Subsequently, we show that a ultraviolet cutoff can be obtained at $10^{-3} eV$, i.e., at a scale much larger than the expected Planck scale. In addition, an infrared cutoff, at the size of the observed Universe, emerges from within such quantum deformation of Universe. In other words, the spectrum of the scale factor is upper bounded. Moreover, we show that the emerged cosmological horizon is a quantum sphere $S^2_q$ or, alternatively, a fuzzy sphere $S^2_F$ which explicitly exhibits features of the holographic principle. The corresponding number of fundamental cells equals the dimension of the Hilbert space and hence, the cosmological constant can be presented as a consequence of the quantum deformation of the FLRW minisuperspace., 14 pages, to appear in Physics of Dark Universe

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\"oschl-Teller (PT) potential, from which we find analytically the mode functions and then calculate the corresponding Bogoliubov coefficients at the onset of the slow-roll inflation, valid for any inflationary model with a single scalar field. Imposing the Bunch-Davies (BD) vacuum in the contracting phase prior to the bounce when the modes are all inside the Hubble horizon, we show that particles are generically created due to the pre-inflation dynamics. Matching them to those obtained in the slow-roll inflationary phase, we investigate the effects of the pre-inflation dynamics on the scalar and tensor power spectra and find features that can be tested by current and forthcoming observations. In particular, to be consistent with the Planck 2015 data, we find that the universe must have expanded at least $141$ e-folds since the bounce., Comment: revtex4, 7 figures, 1 table. Further corrected some typos. Phys. Lett. B773 (2017) 196-202

The paper puts forward a modification of the no-boundary Hartle–Hawking wave function in which, in the general case, the Euclidean functional integral can be described by an inhomogeneous universe. The regularization of this integral is achieved in arbitrary canonical calibration by abandoning integration over the lapse and shift functions. This makes it possible to ‘correct’ the sign of the Euclidean action corresponding to the scale factor of geometry. An additional time parameter associated with the canonical calibration condition then emerges. An additional condition for the stationary state of the wave function's phase after returning to the Lorentzian signature, serving as the quantum equivalent of the classical principle of the least action, was used to find this time parameter. We have substantiated the interpretation of the modified wave function as the amplitude of the universe's birth from ‘nothing’ with the additional parameter as the time of this process. A homogeneous model of the universe with a conformally invariant scalar field has been considered. In this case, two variants of the no-boundary wave function which are solutions of the Wheeler–DeWitt equation have been found.

This is an introduction to the approach to the extraction of cosmological dynamics from full quantum gravity based on group field theory condensates. We outline its general perspective, which sees cosmology as the hydrodynamics of the fundamental quantum gravity degrees of freedom, as well as its concrete implementation within the group field theory formalism. We summarise recent work showing the emergence of a bouncing cosmological dynamics from a fundamental group field theory model, and provide a brief but complete survey of other results in the literature. Finally, we discuss open issues and directions for further research., Comment: 20 pages; extended version of the invited contribution to the special issue "Testing Quantum Gravity with Cosmology" of Comptes rendus Physique, Acad\'emie des sciences, Paris, edited by A. Barrau

In the approach of Causal Dynamical Triangulations (CDT), quantum gravity is obtained as a scaling limit of a non-perturbative path integral over space-times whose causal structure plays a crucial role in the construction. After some general considerations about the relation between quantum gravity and cosmology, we examine which aspects of CDT are potentially interesting from a cosmological point of view, focussing on the emergence of a de Sitter universe in CDT quantum gravity., Comment: 14 pages, invited review for a special issue of Compte Rendus Physique

The causal set approach to the problem of quantum gravity is based on the hypothesis that spacetime is fundamentally discrete. Spacetime discreteness opens the door to novel types of dynamical law for cosmology and the Classical Sequential Growth (CSG) models of Rideout and Sorkin form an interesting class of such laws. It has been shown that a renormalisation of the dynamical parameters of a CSG model occurs whenever the universe undergoes a Big Crunch–Big Bang bounce. In this paper we propose a way to model the creation of a new universe after the singularity of a black hole. We show that renormalisation of dynamical parameters occurs in a CSG model after such a creation event. We speculate that this could realise aspects of Smolin's Cosmological Natural Selection proposal.

This paper provides a prospectus for a new way of thinking about the wavefunction of the universe: a $\Psi$-epistemic quantum cosmology. We present a proposal that, if successfully implemented, would resolve the cosmological measurement problem and simultaneously allow us to think sensibly about probability and evolution in quantum cosmology. Our analysis draws upon recent work on the problem of time in quantum gravity, upon causally-symmetric local hidden variable theories, and upon a dynamical origin for the cosmological arrow of time. Our conclusion weighs the strengths and weaknesses of the approach and points towards paths for future development., Comment: 33 pre-print pages

In this paper, we study the classical limit and unitary evolution of quantum cosmology by applying the Weyl--Wigner--Groenewold--Moyal formalism of deformation quantization to quantum cosmology of a homogeneous and isotropic universe with positive spatial curvature and conformally coupled scalar field. The corresponding quantum cosmology (similar to the Schr\"{o}dinger interpretation in canonical quantization scheme of quantum cosmology) is described by the Moyal--Wheeler--DeWitt equation which has an exact solution in Moyal phase space, resulting in Wigner quasiprobability distribution function, peaking over the classical solutions. We show that for a large value of the quantum number $n$, the emerged classical universe is filled with radiation with quantum mechanical origin. Also, we introduce a canonical transformation on the scalar field sector of the model such that the conjugate momenta of the new canonical variable appear linearly in the transformed total Hamiltonian. Using this canonical transformation, we show that, it may lead to disentangle the time from the true dynamical variables. We obtain the time-dependent Wigner function for a coherent as well as for squeezed states. We show that the peak of these Wigner functions follows the classical trajectory in the phase space., Comment: 11 pages, 3 figure, to appear in Physics of the Dark Universe

Quantizing a flat FLRW cosmology in the context of the different modified gravities by Noether symmetry approach is one of the viable ways to consider modified gravity theories. In this context, we explicitly calculate the form of f ( T ) for which symmetries exist, and is shown that the existence of Noether symmetry yields a general solution of the Wheeler–DeWitt equation where can be expressed as a superposition of states of the form e i S . This type of wave function exhibits classical correlations, i.e. the emergent of classical universe is expected due to the oscillating behavior of the solutions of Wheeler–DeWitt equation in terms of Hartle criterion. Hence, we also provide the Noether symmetric classical solutions of f ( T ) cosmological model. According to quantum investigation the square of wave equation loses its energy for expanding universe which satisfies energy conservation law.

We solve a general equation describing the lowest order corrections arising from quantum gravitational effects to the spectrum of cosmological fluctuations. The spectra of scalar and tensor perturbations are calculated to first order in the slow roll approximation and the results are compared with the most recent observations. The slow roll approximation gives qualitatively new quantum gravitational effects with respect to the pure de Sitter case., Comment: 19 pages, 2 figures; final version accepted for publication in PLB

Studying astroparticle physics sheds new light on scientific explanation and on the ways in which cosmology is empirically underdetermined or not. Astroparticle physics extends the empirical domain of cosmology from purely astronomical data to “multi-messenger astrophysics”, i.e., measurements of all kinds of cosmic rays including very high energetic gamma rays, neutrinos, and charged particles. My paper investigates the ways in which these measurements contribute to cosmology and compares them with philosophical views about scientific explanation, the relation between theory and data, and scientific realism. The “standard models” of cosmology and particle physics lack of unified foundations. Both are “piecemeal physics” in Cartwright's sense, but contrary to her metaphysics of a “dappled world” the work in both fields of research aims at unification. Cosmology proceeds “top-down”, from models to data and from large scale to small-scale structures of the universe. Astroparticle physics proceeds “bottom-up”, from data taking to models and from subatomic particles to large-scale structures of the universe. In order to reconstruct the causal stories of cosmic rays and the nature of their sources, several pragmatic unifying strategies are employed. Standard views about scientific explanation and scientific realism do not cope with these “bottom-up” strategies and the way in which they contribute to cosmology. In addition it has to be noted that the shift to “multi-messenger astrophysics” transforms the relation between cosmological theory and astrophysical data in a mutually holistic way.

This paper gives an overview of significant issues in the philosophy of cosmology, starting off by emphasizing the uniqueness of the universe and the way models are used in description and explanation. It then considers, basic limits on observations; the need to test alternatives; ways to test consistency; and implications of the uniqueness of the universe as regards distinguishing laws of physics from contingent conditions. It goes on to look at the idea of a multiverse as a scientific explanation of facts about fine-tuning, in particular considering criteria for a scientific theory and for justifying unseen entities. It considers the relation between physical laws and the natures of existence, and emphasizes limits on our knowledge of the physics relevant to the early universe (the physics horizon), and the non-physical nature of some claimed infinities. The final section looks briefly at deeper issues, commenting on the scope of enquiry of cosmological theory and the limits of science in relation to the creation of the universe.

We study the quantum avoidance of the big rip singularity in the Eddington-inspired-Born–Infeld (EiBI) phantom model. Instead of considering a simple phantom dark energy component, which is described by a perfect fluid, we consider a more fundamental degree of freedom corresponding to a phantom scalar field with its corresponding potential, which would lead the classical universe to a big rip singularity. We apply a quantum geometrodynamical approach by performing an appropriate Hamiltonian study including an analysis of the constraints of the system. We then derive the Wheeler–DeWitt (WDW) equation and see whether the solutions to the WDW equation satisfy the DeWitt boundary condition. We find that by using a suitable Born–Oppenheimer (BO) approximation, whose validity is proven, the DeWitt condition is satisfied. Therefore, the big rip singularity is expected to be avoided in the quantum realm.

We study the classical and quantum models of a scalar field Friedmann-Robertson-Walker (FRW) cosmology with an eye to the issue of time problem in quantum cosmology. We introduce a canonical transformation on the scalar field sector of the action such that the momentum conjugate to the new canonical variable appears linearly in the transformed Hamiltonian. Using this canonical transformation, we show that, it may lead to the identification of a time parameter for the corresponding dynamical system. In the cases of flat, closed and open FRW universes the classical cosmological solutions are obtained in terms of the introduced time parameter. Moreover, this formalism gives rise to a Schr\"{o}dinger-Wheeler-DeWitt equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave functions in order to investigate the possible corrections to the classical cosmologies due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology., Comment: 12 pages, 13 figures, minor changes. arXiv admin note: text overlap with arXiv:1104.1163, arXiv:1004.0306

We give a short description of the qBounce-experiment. The dynamics of the wavefunction of a neutron in the gravity potential has been observed and transitions between discrete energy level have been realized. The experiment allows to test Newton's inverse-square law of gravity with quantum objects by means of quantum interference at short distances.

We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the scalar-metric gravity. Using the Schutz' representation for the perfect fluid, we show that, under a particular gauge choice, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that the evolution of the universe based on the classical cosmology represents a late time power law expansion coming from a big-bang singularity in which the scale factor goes to zero while the scalar field blows up. Moreover, this formalism gives rise to a Schr\"{o}dinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology., Comment: 14 pages, 8 figures, to appear in PLB, Refs. added, This work is dedicated to the revered memory of Prof. Masoud Alimohammadi

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities. In this Letter, we quantize the Lorentz term of the gravitational Hamiltonian constraint in the spatially flat FRW model by two approaches different from that of the Euclidean term. One of the approaches is very similar to the treatment of the Lorentz part of Hamiltonian in loop quantum gravity and hence inherits more features from the full theory. Two symmetric Hamiltonian constraint operators are constructed respectively in the improved scheme. Both of them are shown to have the correct classical limit by the semiclassical analysis. In the loop quantum cosmological model with a massless scalar field, the effective Hamiltonians and Friedmann equations are derived. It turns out that the classical big bang is again replaced by a quantum bounce in both cases. Moreover, there are still great possibilities for the expanding universe to recollapse due to the quantum gravity effect.

Loop quantum cosmology (LQC) is used to provide concrete evidence in support of the general paradigm underlying spin foam models (SFMs). Specifically, it is shown that: i) the physical inner product in the timeless framework equals the transition amplitude in the deparameterized theory; ii) this quantity admits a %convergent vertex expansion a la SFMs in which the $M$-th term refers just to $M$ volume transitions, without any reference to the time at which the transition takes place; iii) the exact physical inner product is obtained by summing over just the discrete geometries; no `continuum limit' is involved; and, iv) the vertex expansion can be interpreted as a perturbative expansion in the spirit of group field theory. This sum over histories reformulation of LQC also addresses certain other issues which are briefly summarized., 11 pages, no figures

We provide further evidence that the canonical quantization of cosmological models eliminates the classical Big Bang singularity, using the {\it DeBroglie-Bohm} interpretation of quantum mechanics. The usual criterion for absence of the Big Bang singularity in Friedmann-Robertson-Walker quantum cosmological models is the non-vanishing of the expectation value of the scale factor. We compute the `local expectation value' of the Ricci and Kretschmann scalars, for some quantum FRW models. We show that they are finite for all time. Since these scalars are elements of general scalar polynomials in the metric and the Riemann tensor, this result indicates that, for the quantum models treated here, the `local expectation value' of these general scalar polynomials should be finite everywhere. Therefore, we have further evidence that the quantization of the models treated here eliminates the classical Big Bang singularity. PACS: 04.40.Nr, 04.60.Ds, 98.80.Qc., Comment: 9 pages, 6 figures

Topical phenomena in high-energy physics related to collision experiments of heavy nuclei ("Little Bang") and early universe cosmology ("Big Bang") involve far-from-equilibrium dynamics described by quantum field theory. One example concerns the role of plasma instabilities for the process of thermalization in heavy-ion collisions. The reheating of the early universe after inflation may exhibit rather similar phenomena following a tachyonic or parametric resonance instability. Certain universal aspects associated to nonthermal fixed points even quantitatively agree, and considering these phenomena from a common perspective can be fruitful., Comment: Plenary talk at SEWM08, 9 pages, 6 figures

Unless our universe is decaying at an astronomical rate (i.e., on the present cosmological timescale of Gigayears, rather than on the quantum recurrence timescale of googolplexes), it would apparently produce an infinite number of observers per comoving volume by thermal or vacuum fluctuations (Boltzmann brains). If the number of ordinary observers per comoving volume is finite, this scenario seems to imply zero likelihood for us to be ordinary observers and minuscule likelihoods for our actual observations. Hence, our observations suggest that this scenario is incorrect and that perhaps our universe is decaying at an astronomical rate., 4 pages, RevTeX4

We quantize a flat FRW cosmology in the context of the f ( R ) gravity by Noether symmetry approach. We explicitly calculate the form of f ( R ) for which such symmetries exist. It is shown that the existence of a Noether symmetry yields a general solution of the Wheeler–DeWitt equation where can be expressed as a superposition of states of the form e i S . In terms of Hartle criterion, this type of wave function exhibits classical correlations, i.e. the emergent of classical universe is expected due to the oscillating behavior of the solutions of Wheeler–DeWitt equation. According to this interpretation we also provide the Noether symmetric classical solutions of our f ( R ) cosmological model.

The brick wall method in calculations of the entropy of black holes can be applied to the FRW cosmology in order to study the statistical entropy. An appropriate cutoff satisfying the covariant entropy bound can be chosen so that the entropy has a definite bound. Among the entropy for each of cosmological eras, the vacuum energy-dominated era turns out to give the maximal entropy which is in fact compatible with assumptions from the brick wall method., Comment: 10 pages, 2 figures

Quantum relativity as a generalized, or rather deformed, version of Einstein relativity may offer a new framework to think about the structure of space–time at the true microscopic/quantum level. The approach typically gives some picture of a noncommutative (quantum) space–time. We propose a formulation with two deformations implemented on the Poincare symmetry, using the independent Planck mass and Planck length as the invariant constraints. Together, they give the quantum ℏ. The scheme leads to SO ( 2 , 4 ) as the relativity symmetry. We present a linear realization on a classical six-geometry beyond the familiar setting of space–time. Two extra coordinates to be considered as neither space nor time are needed. The last deformation step implementing the Planck length invariant constraines the six-geometry, as an extension of 4D space–time, giving it the structure of a AdS hypersurface. The resulted quantum world hence does not admit coordinate translation symmetries, which terminates further extension to an unstable symmetry. The quantum world is shown to be parallel to the “conformal universe”, but not scale invariant.

We show that ( 1 + 2 ) nonlinear Klein–Gordon equation with negative coupling admits an exact solution which appears to be the linear superposition of the plane wave and the nonsingular rational soliton. We show that the same approach allows to construct the solution of similar properties for the Euclidean ϕ 4 model with broken symmetry. Interestingly, this regular solution will be of instanton type only in the D ⩽ 5 Euclidean space. Thus one can use the generalized Fubini instantons (in quantum cosmology for example) only for the case of the single infinite extra dimension.

We present a Friedmann-Robertson-Walker quantum cosmological model in the presence of Chaplygin gas and perfect fluid for early and late time epoches. In this work, we consider perfect fluid as an effective potential and apply Schutz's variational formalism to the Chaplygin gas which recovers the notion of time. These give rise to Schr\"odinger-Wheeler-DeWitt equation for the scale factor. We use the eigenfunctions in order to construct wave packets and study the time dependent behavior of the expectation value of the scale factor using the many-worlds interpretation of quantum mechanics. We show that contrary to the classical case, the expectation value of the scale factor avoids singularity at quantum level. Moreover, this model predicts that the expansion of Universe is accelerating for the late times., Comment: 18 pages, 2 figures, to appear in PLB

A new dark energy model, named as “agegraphic dark energy”, has been proposed by one of us (R.G. Cai) in [R.G. Cai, arXiv: 0707.4049 ], based on the Karolyhazy uncertainty relation, which arises from the quantum mechanics together with general relativity. Then, in [H. Wei, R.G. Cai, arXiv: 0707.4052 ], it has been extended by including the interaction between the agegraphic dark energy and the pressureless (dark) matter. In this note, we investigate the agegraphic dark energy models without and with interaction by means of statefinder diagnostic and w– w ′ analysis.

We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler-DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed., 8 pages, 3 figures, to appear in PLB

The K = 0 Friedmann–Robertson–Walker metric, which satisfies the Killing spinor equation and approximates a solution to the field equations of the quadratic gravity theory derived from the heterotic string effective action, generates a discontinuity in the derivative of the scale factor. The resulting change in the Hamiltonian is conjectured to be the origin of energy in the very early Universe.

Primordial black hole remnants (PBHRs) can be considered as a primary source of cold dark matter. Hybrid inflation provides a possible framework for production of primordial black holes (PBHs) and these PBHs evaporate subsequently to produce PBHRs. In this paper we provide another framework for production of these PBHs. Using signature changing cosmological model and the generalized uncertainty principle as our primary inputs, first we find a geometric cosmological constant for early stage of universe evolution. This geometric cosmological constant can lead to heavy vacuum density which may be interpreted as a source of PBHs production during the inflationary phase. In the next step, since it is possible in general to have non-vanishing energy-momentum tensor for signature changing hypersurface, this non-vanishing energy-momentum tensor can be considered as a source of PBHs production. These PBHs then evaporate via the Hawking process to produce PBHRs. Finally, possible observational schemes for detecting relics of these PBHRs are discussed.

We develop the harmonic space method for conifold and use it to study local complex deformations of T * S 3 preserving manifestly SL ( 2 , C ) isometry. We derive the perturbative manifestly SL ( 2 , C ) invariant partition function Z top of topological string B model on locally deformed conifold. Generic n momentum and winding modes of 2D c = 1 noncritical theory are described by highest υ ( n , 0 ) and lowest components υ ( 0 , n ) of SL ( 2 , C ) spin s = n 2 multiplets ( υ ( n − k , k ) ) , 0 ⩽ k ⩽ n and are shown to be naturally captured by harmonic monomials. Isodoublets ( n = 1 ) describe uncoupled units of momentum and winding modes and are exactly realized as the SL ( 2 , C ) harmonic variables U α + and V α − . We also derive a dictionary giving the passage from Laurent (Fourier) analysis on T * S 1 ( S 1 ) to the harmonic method on T * S 3 ( S 3 ). The manifestly SU ( 2 , C ) covariant correlation functions of the S 3 quantum cosmology model of Gukov–Saraikin–Vafa are also studied.

The causal interpretation of quantum mechanics is applied to a homogeneous and isotropic quantum universe, whose matter content is composed by non interacting dust and radiation. For wave functions which are eigenstates of the total dust mass operator, we find some bouncing quantum universes which reachs the classical limit for scale factors much larger than its minimum size. However these wave functions do not have unitary evolution. For wave functions which are not eigenstates of the dust total mass operator but do have unitary evolution, we show that, for flat spatial sections, matter can be created as a quantum effect in such a way that the universe can undergo a transition from an exotic matter dominated era to a matter dominated one., Comment: 27 pages, 6 figures

We study the quantum cosmology of an empty (4+1)-dimensional Kaluza-Klein cosmology with a negative cosmological constant and a FRW type metric with two scale factors, one for 4-D universe and the other for one compact extra dimension. By assuming the noncommutativity in the corresponding mini-superspace we suggest a solution for the Hierarchy problem, at the level of Wheeler-DeWitt equation., Comment: 7 pages; Title, abstract and text changed; references added; to appear in PLB

Since the conception of quantum cosmology was introduced by Lemaitre in 1931, many authors have discussed the quantum nature of the Universe. Yet the most significant new feature of quantum physics, the notion of quantum nonlocality and its verification using Earth-based experiments, is never addressed by cosmologists because they basically do not know how to deal with it. In the spirit of making the transition “from quarks to cosmos” we will demonstrate how this is done. We show how to estimate the temperature of the flat Friedmann–Lemaitre–Robertson–Walker spacetime using a spherically symmetric approximation of the metric in conjunction with Lee’s theorem for scalar quantum fields on curved backgrounds. This temperature dependence is not the same as the classical Gamow temperature which follows from general relativity for the radiation-dominated era of the Big Bang model, and we relate this result to the question of decoherence in the very early Universe.

In the n-dimensional Freund–Rubin model with an antisymmetric tensor field of rank s−1, the dimension of the external spacetime we live in must be min(s,n−s). This result is a generalization of the previous result in the d=11 supergravity case, where s=4.

We study the quantized Friedmann-Lema\^��tre-Robertson-Walker (FLRW) model minimally coupled to a free massless scalar field. In a previous paper, \cite{fab2}, solutions of this model were constructed as gaussian superpositions of negative and positive modes solutions of the Wheeler-DeWitt equation, and quantum bohmian trajectories were obtained in the framework of the Bohm-de Broglie (BdB) interpretation of quantum cosmology. In the present work, we analyze the quantum bohmian trajectories of a different class of gaussian packets. We are able to show that this new class generates bohmian trajectories which begin classical (with decelerated expansion), undergo an accelerated expansion in the middle of its evolution due to the presence of quantum cosmological effects in this period, and return to its classical decelerated expansion in the far future. We also show that the relation between luminosity distance and redshift in the quantum cosmological model can be made close to the corresponding relation coming from the classical model suplemented by a cosmological constant, for $z

The Callan–Symanzik type of equations have been utilized to study the cosmological constant Λ which is found to possess a fractal character. We have also derived the wavefunction of the universe as well as the inflationary potential.

This paper reviews the ups and downs of the cosmological constant since its introduction into general relativity theory by Einstein in 1917. Although it has never really been loved, and is a major headache to particle physicists, it keeps on coming back in various guises or with minor modifications. At present it plays a manor role in cosmology both in terms of the ‘false vacuum’ of inflationary theory in the very early universe, and as a large-scale repulsive force in the late universe, as evidenced by observations of distant supernovae. Its origin in terms of fundamental physics remains as obscure as ever.

Some applications of topological geometrodynamics (TGD) are reviewed. The new view about space-time implies new physics in all length scales and the p -adic length scale hypothesis makes it possible to make quantitative predictions. Two representative examples are microscopic mechanism of particle massivation allowing the prediction of elementary particle masses with surprising accuracy and fractal cosmology resolving the difficulties of the inflationary cosmology. Perhaps the most fascinating applications can be found biology, where the many-sheeted space-time concept allows one to understand how biosystems manage to be macroscopic quantum systems and explains also phenomena like chiral selection. TGD-inspired quantum measurement theory can be regarded also as quantum theory of consciousness and leads to visions about consciousness as a universal phenomenon as well as a concrete model for brain consciousness. The interpretation of the p -adic space-time regions as cognitive representations leads to a general theory of cognition. TGD encourages one to view physics as a number theory in a very general sense, and a sharpening of the Riemann hypothesis and detailed strategies for its proof emerge as an outcome of this philosophy.

Equilibrium reduced-density operators for subsystems of the Universe are derived from the generalised Schrodinger variational principle, additionally assuming that the values of von Neumann entropy for the subsystems are fixed and higher than zero. The obtained reduced-density operator may be useful for description of the thermodynamical properties of a nanoscopic system, ultrathin films and similar systems.

For the first time the present paper shows that the spacetime system must be considered as subject to the Kubo–Martin–Schwinger (KMS) condition at the Planck scale. Consequently in the interior of the KMS strip, i.e., from the scale s=0 to the scale s= l Planck, the fourth coordinate g44 must be considered as complex, the two real poles being s=0 and s= l Planck. This means that within the limits of the KMS strip the Lorentzian and the Euclidean metric are in a “quantum superposition state” (or coupled), thus entailing a “unification” (or coupling) between the topological (Euclidean) and the physical (Lorentzian) states of spacetime.

p -Adic quantum cosmology is one of the considerable applications of p -adic quantum theory, which takes into account possible nonarchimedean (ultrametric) aspects of space-time. For this reason, we consider minisuperspace cosmological models in the framework of p -adic and adelic quantum mechanics. In particular, we investigate the de Sitter model and obtain p -adic and adelic wave functions, which are briefly discussed.

The uses of the effective action are discussed in quantum and braneworld cosmology. The braneworld effective action is built in the two-brane Randall-Sundrum model. The radion mode is shown to be a field localizing the essentially nonlocal part of this action. Its non-minimal curvature coupling reflects the violation of AdS/CFT-correspondence for finite values of brane separation. Under small detuning of the brane tension from the Randall-Sundrum value, the radion mode can play the role of inflaton. Inflationary dynamics corresponds to branes moving apart in the field of repelling interbrane radion potential and implies the existence of acceleration stage caused by remnant cosmological constant at late (large brane separation) stages of cosmological evolution. We discuss the possibility of fixing initial conditions in this model within the context of braneworld creation from the tunneling or no-boundary cosmological states, which replaces the conventional moduli stabilization mechanism.

p-Adic and adelic generalization of ordinary quantum cosmology is considered. In [1], we have calculated p-adic wave functions for some minisuperspace cosmological models according to the "no-boundary" Hartle-Hawking proposal. In this article, applying p-adic and adelic quantum mechanics, we show existence of the corresponding vacuum eigenstates. Adelic wave function contains some information on discrete structure of space-time at the Planck scale.

We develop a general framework for effective equations of expectation values in quantum cosmology and pose for them the quantum Cauchy problem with no-boundary and tunneling wavefunctions. Cosmological configuration space is decomposed into two sectors that give qualitatively different contributions to the radiation currents in effective equations. The field-theoretical sector of inhomogeneous modes is treated by the method of Euclidean effective action, while the quantum mechanical sector of the spatially homogeneous inflaton is handled by the technique of manifest quantum reduction to gauge invariant cosmological perturbations. We apply this framework in the model with a big negative non-minimal coupling, which incorporates a recently proposed low energy (GUT scale) mechanism of the quantum origin of the inflationary Universe and study the effects of the quantum inflaton mode., 33 pages, LaTeX2e

The development of the N = 4 supersymmetric approach to quantum cosmology based on the non-compact global O(d,d) symmetries of the effective action is given. The N = 4 supersymmetric action whose bosonic sector is invariant under O(d,d) is determined. A representation for supercharges is obtained and the form of the zero and one-fermion quantum states leading to the Wheeler-DeWitt equation is found.The development of the N = 4 supersymmetric approach to quantum cosmology based on the non-compact global O(d,d) symmetries of the effective action is given. The N = 4 supersymmetric action whose bosonic sector is invariant under O(d,d) is determined. A representation for supercharges is obtained and the form of the zero and one-fermion quantum states leading to the Wheeler-DeWitt equation is found., Comment: 19 pages

We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies. We present an ansatz for the initial conditions which leads to a unique determination of the expansion coefficients in the construction of the wave packets with probability distributions which, in an interesting contrast to some of the earlier works, agree well with all possible classical paths. The possible relationship between these initial conditions and signature transition in the context of classical cosmology is also discussed., Comment: 12 pages, 12 eps figures, to appear in Phys. Lett. A