We propose a toy model for the origin of the universe, where the scale-invariant fluctuations are generated together with the quantum creation process of the universe. The fluctuations arise inside an instanton in the Euclidean domain of time. In the Lorentzian point of view, the universe emerges with passive, coherent and scale-invariant fluctuations present from the beginning, without the need of inflation or a bounce. For this mechanism to work, we need anisotropic scaling in space and time, which is realized in a toy model of Horava-Lifshitz gravity with a Lifshitz scalar field.
Inflation in an open universe produced by Coleman-De Luccia (CDL) tunneling induces a friction term that is strong enough to allow for successful small-field inflation in models that would otherwise suffer from a severe overshoot problem. In this paper, we present a polynomial scalar potential which allows for a full analysis. This provides a simple model of single-field open inflation on a small-field inflection point after tunneling. We present numerical results and compare them with analytic approximations.
The open inflation scenario based on the theory of bubble formation in the models of a single scalar field suffered from a fatal defect. In all the versions of this scenario known so far, the Coleman-De Luccia instantons describing the creation of an open universe did not exist. We propose a simple one-field model where the CDL instanton does exist and the open inflation scenario can be realized.
The creation of 4d de Sitter (inflationary) boundary gluing two d5 de Sitter bulks on the classical as well as on quantum level (with account of brane QFT via corresponding trace anomaly induced effective action) is discussed. Quantum effects decrease the classical de Sitter brane radius or create new de Sitter brane with even smaller radius. It is important that brane CFT may be chosen to be dual to one of 5d de Sitter bulks, making the explicit relation of de Sitter brane-world with dS/CFT correspondence. In this way, the localization of gravity on the brane is shown. Moving (time-dependent)…
General ideas of gauge/gravity duality allow for the possibility of time dependent solutions that interpolate between a perturbative gauge theory phase and a weakly curved string/gravity phase. Such a scenario applied to cosmology would exhibit a non-geometric phase before the big bang. We investigate a toy model for such a cosmology, whose endpoint is the classical limit of the two-dimensional non-critical string. We discuss the basic dynamics of this model, in particular how it evolves toward the double scaling limit required for stringy dynamics. We further comment on the physics that will …
Discontinuities in non linear field theories propagate through null geodesics in an effective metric that depends on its dynamics and on the background geometry. Once information of the geometry of the universe comes mostly from photons, one should carefully analyze the effects of possible nonlinearities on Electrodynamics in the cosmic geometry. Such phenomenon of induced metric is rather general and may occurs for any nonlinear theory independently of its spin properties. We limit our analysis here to the simplest case of non linear scalar field. We show that a class of theories that have be…
We discuss a two-step mechanism to create a new inflationary domain beyond a wormhole throat which is created by a phase transition around an evaporating black hole. The first step is creation of a false vacuum bubble with a thin-wall boundary by the thermal effects of Hawking radiation. Then this wall induces a quantum tunneling to create a wormhole-like configuration. As the space beyond the wormhole throat can expand exponentially, being filled with false vacuum energy, this may be interpreted as creation of another inflationary universe in the final stage of the black hole evaporation.
A specific scale factor in Robertson-Walker metric with the prospect of giving the overall cosmic history in a unified picture roughly is considered. The corresponding energy-momentum tensor is identified as that of two scalar fields where one plays the roles of both inflaton and dark matter while the other accounts for dark energy. A preliminary phenomenological analysis gives an order of magnitude agreement with observational data. The resulting picture may be considered as a first step towards a single model for all epochs of cosmic evolution.
We study the cosmological particle creation in the tachyon inflation based on the D-brane dynamics in the RSII model extended to include matter in the bulk. The presence of matter modifies the warp factor which results in two effects: a modification of the RSII cosmology and a modification of the tachyon potential. Besides, a string theory D-brane supports among other fields a U(1) gauge field reflecting open strings attached to the brane. We demonstrate how the interaction of the tachyon with the U(1) gauge field drives cosmological creation of massless particles and estimate the resulting re…
Dilatonic Charged Nariai instantons mediate the nucleation of black hole pairs during extended chaotic inflation. Depending on the dilaton and inflaton fields, the black holes are described by one of two approximations in the Lorentzian regime. For each case we find Euclidean solutions that satisfy the no boundary proposal. The complex initial values of the dilaton and inflaton are determined, and the pair creation rate is calculated from the Euclidean action. Similar to standard inflation, black holes are abundantly produced near the Planck boundary, but highly suppressed later on. An unusual…
We consider a model of DBI inflation where two stacks of mobile branes are moving ultra relativistically in a warped throat. The stack closer to the tip of the throat is annihilated with the background anti-branes while inflation proceeds by the second stack. The effects of branes annihilation and particles creation during DBI inflation on the curvature perturbations power spectrum and the scalar spectral index are studied. We show that for super-horizon scales, modes which are outside the sound horizon at the time of branes collision, the spectral index has a shift to blue spectrum compared t…
We summarise recent work on the quantum production of black holes in the inflationary era. We describe, in simple terms, the Euclidean approach used, and the results obtained both for the pair creation rate and for the evolution of the black holes.
The role of bulk matter quantum effects (via the corresponding effective potential discussed on the example of conformal scalar) and of boundary matter quantum effects (via the conformal anomaly induced effective action) is considered in brane-world cosmology. Scenario is used where brane tension is not free parameter, and the initial bulk-brane classical action is defined by some considerations. The effective bulk-brane equations of motion are analyzed. The quantum creation of 4d de Sitter or Anti-de Sitter(AdS) brane Universe living in 5d AdS space is possible when quantum bulk and (or) bran…
If inflation can occur only at the energy density V much smaller than the Planck density, which is the case for many inflationary models based on string theory, then the probability of quantum creation of a closed or an infinitely large open inflationary universe is exponentially suppressed for all known choices of the wave function of the universe. Meanwhile under certain conditions there is no exponential suppression for creation of topologically nontrivial compact flat or open inflationary universes. This suggests, contrary to the standard textbook lore, that compact flat or open universes …
The creation of ultra-light dark particles in the late-time FLRW spacetime provides a cosmological model in accordance with precise observational tests. The matter creation backreaction implies in this context a vacuum energy density scaling linearly with the Hubble parameter H, which is consistent with the vacuum expectation value of the QCD condensate in a low-energy expanding spacetime. Both the cosmological constant and coincidence problems are alleviated in this scenario. We also explore the opposite, high energy limit of the particle creation process. We show that it leads to a non-singu…
Inflation provides a natural mechanism to account for the origin of cosmic structures. The generation of primordial inhomogeneities during inflation can be understood via the spontaneous creation of quanta from the vacuum. We show that when the corresponding {\it stimulated} creation of quanta is considered, the characteristics of the state of the universe at the onset of inflation are not diluted by the inflationary expansion and can be imprinted in the spectrum of primordial inhomogeneities. The non-gaussianities (particularly in the so-called squeezed configuration) in the cosmic microwave …
Black holes came into existence together with the universe through the quantum process of pair creation in the inflationary era. We present the instantons responsible for this process and calculate the pair creation rate from the no boundary proposal for the wave function of the universe. We find that this proposal leads to physically sensible results, which fit in with other descriptions of pair creation, while the tunnelling proposal makes unphysical predictions. We then describe how the pair created black holes evolve during inflation. In the classical solution, they grow with the horizon s…
We use the Bogoliubov formalism to study both, particles and gravitons creation at the reheating epoch, after a phase transition from inflation to a radiation dominated universe. The modes of the inflaton field fluctuations and the scalar fluctuations of the metric at the end of inflation are obtained by using a recently introduced formalism related to the Induced Matter theory of gravity. The interesting result is that the number of created particles is bigger than $10^{90}$ on cosmological scales. Furthermore, the number of gravitons are nearly $10^{-17}$ times smaller than the number of cre…
Cosmological inflation generates a spectrum of density perturbations that can seed the cosmic structures we observe today. These perturbations are usually computed as the result of the gravitationally-induced spontaneous creation of perturbations from an initial vacuum state. In this paper, we compute the perturbations arising from gravitationally-induced stimulated creation when perturbations are already present in the initial state. The effect of these initial perturbations is not diluted by inflation and survives to its end, and beyond. We consider a generic statistical density operator $ρ$…
We relate the mechanism of matter creation in the universe after inflation to a simple and universal mathematical property of extended N > 1 supergravities and related compactifications of superstring theory. We show that in all such models, the inflaton field may decay into vector fields due to a nonminimal scalar-vector coupling. This coupling is compulsory for all scalars except N=2 hyperscalars. The proof is based on the fact that all extended supergravities described by symmetric coset spaces G/H have duality groups G of type E7, with exception of U(p,n) models. For N=2 we prove separatel…
I present a very simplistic toy model for the inflationary paradigm where the size of the universe undergoes a period of exponential growth. The basic assumption I make use of is that black holes might have a quantized area (mass) spectrum with a stable ground state and that the universe has started with a tightly packed collection of these objects alone.
We study some gravitational instanton solutions that offer a natural realization of the spontaneous creation of inflationary universes in the brane world context in string theory. Decoherence due to couplings of higher (perturbative) modes of the metric as well as matter fields modifies the Hartle-Hawking wavefunction for de Sitter space. Generalizing this new wavefunction to be used in string theory, we propose a principle in string theory that hopefully will lead us to the particular vacuum we live in, thus avoiding the anthropic principle. As an illustration of this idea, we give a phenomen…
During cosmological inflation, it has been suggested that fields coupled to the inflaton can be excited by the slow-rolling inflaton into a quasi-stable non-vacuum state. Within this scenario of ``warm inflation'', this could allow for a smooth transition to a radiation dominated Universe without a separate reheating stage and a modification of the slow roll evolution, as the heat-bath backreacts on the inflaton through friction. In order to study this from first principles, we investigate the dynamics of a scalar field coupled to the inflaton and N light scalar boson fields, using the 2PI-1/N…
We investigate the matter creation processes during the reheating period at the end of inflation in the early Universe, by using the irreversible thermodynamic of open systems. The matter content of the Universe is assumed to consist of the inflationary scalar field, which, through its decay, generates relativistic matter, and pressureless dark matter, respectively. At the early stages of reheating the inflationary scalar field transfers its energy to the newly created matter particles, with the field energy decreasing to near zero. The general equations governing the irreversible matter creat…
It has been pointed out that the null energy condition can be violated stably in some non-canonical scalar-field theories. This allows us to consider the Galilean Genesis scenario in which the universe starts expanding from Minkowski spacetime and hence is free from the initial singularity. We use this scenario to study the early-time completion of inflation, pushing forward the recent idea of Pirtskhalava et al. We present a generic form of the Lagrangian governing the background and perturbation dynamics in the Genesis phase, the subsequent inflationary phase, and the graceful exit from infl…
Under certain circumstances, the collision of magnetic monopoles, topologically locked-in regions of false vacuum, leads to topological inflation and the creation of baby universes. The future evolution of initial data represented by the two incoming monopoles may contain a timelike singularity but this need not be the case. We discuss the global structure of the spacetime associated with monopole collisions and also that of topological inflation. We suggest that topological inflation within magnetic monopoles leads to an eternally reproducing universe.
We discuss a dramatic difference between the description of the quantum creation of an open universe using the Hartle-Hawking wave function and the tunneling wave function. Recently Hawking and Turok have found that the Hartle-Hawking wave function leads to a universe with Omega = 0.01, which is much smaller that the observed value of Omega > 0.3. Galaxies in such a universe would be about $10^{10^8}$ light years away from each other, so the universe would be practically structureless. We will argue that the Hartle-Hawking wave function does not describe the probability of the universe creatio…
Unlike crushing singularities, the so-called Type IV finite-time singularity offers the possibility that the Universe passes smoothly through it, without any catastrophic effects. Then the question is if the effects of a Type IV singularity can be detected in the process of cosmic evolution. In this paper we address this question in the context of $F(R)$ gravity. As we demonstrate, the effects of a Type IV singularity appear in the Hubble flow parameters, which determine the dynamical evolution of the cosmological system. So we study various inflation models incorporating a Type IV singularity…
We consider the toy model of a rigid rotor as an example of the Hodge theory within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism and show that the internal symmetries of this theory lead to the derivation of canonical brackets amongst the creation and annihilation operators of the dynamical variables where the definition of the canonical conjugate momenta is not required. We invoke only the spin-statistics theorem, normal ordering and basic concepts of continuous symmetries (and their generators) to derive the canonical brackets for the model of a one (0 + 1)-dimensional (1D…
We discuss the gravitational creation of superheavy particles $χ$ in an inflationary scenario with a quartic potential and a non-minimal coupling between the inflaton $φ$ and the Ricci curvature: $ξφ^2 R/2$. We show that for large constants $ξ>> 1$, there can be abundant production of particles $χ$ with masses largely exceeding the inflationary Hubble rate $H_{infl}$, up to $(a~few) \times ξH_{infl}$, even if they are conformally coupled to gravity. We discuss two scenarios involving these gravitationally produced particles $χ$. In the first scenario, the inflaton has only gravitational intera…
We reconsider the toy-model of topological inflation, based on the R*4-modified gravity. By using its equivalence to the certain scalar-tensor gravity model in four space-time dimensions, we compute the inflaton scalar potential and investigate a possibility of inflation. We confirm the existence of the slow-roll inflation with an exit. However, the model suffers from the eta-problem that gives rise to the unacceptable value of the spectral index n_s of scalar perturbations.
We consider dynamics of the massive minimally coupled scalar field theory in an expanding Friedmann-Lemaitre-Robertson-Walker universe. We consider the standard toy model of the conformally flat space-time where the conformal factor becomes constant at the distant past and the distant future. Employing Schwinger-Keldysh diagrammatic technique, we compute infrared loop corrections to the occupation number and anomalous quantum average of the scalar field and show that these corrections are growing with time. Using these observations, we demonstrate that the regularized stress-energy tensor at t…
A new ''twice loose shoe'' method in the Wheeler-DeWitt equation of the universe wave function on the cosmic scale factor a and a scalar field $ϕ$ is suggested in this letter. We analysis the both affects come from the tunneling effect of a and the potential well effect of $ϕ$, and obtain the initial values $a_0$ and $ϕ_0$ about a primary closed universe which is born with the largest probability in the quantum manner. Our result is able to overcome the ''large field difficulty'' of the universe quantum creation probability with only tunneling effect. This new born universe has to suffer a sta…
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is straightforward, several conceptual issues arise in such a study. We present a general formalism to address some of the conceptual issues like the emergence of classicality, definition of particle content, back reaction etc. In particular, we parametrize the wave function in terms of a complex number (which we call excitation parameter) and express all physica…
Starting with the vacuum fluctuation, it is known that gravitinos will be created just after inflation, with number density $\sim 10^{-2}M^3$ where $M$ is the mass of the inflaton. Here, we argue that creation may be expected to continue, maintaining about the same number density, until a usually much later epoch. This epoch is either the `intermediate epoch' when Hubble parameter falls below the gravitino mass, or the reheat epoch if that is earlier. We verify that such late-time creation indeed occurs if only a single chiral superfield is relevant, using the description of the helicity 1/2 g…
A scheme for incorporating the creation of radiation and matter into the cosmological evolution is introduced so that it becomes possible to merge the times before and after the creation of radiation and matter in a single scale factor in Robertson-Walker metric. This scheme is illustrated through a toy model that has the prospect of constituting a basis for a realistic model.
We study primordial gravitational waves from inflation in Randall-Sundrum braneworld model. The effect of small change of the Hubble parameter during inflation is investigated using a toy model given by connecting two de Sitter branes. We analyze the power spectrum of final zero-mode gravitons, which is generated from the vacuum fluctuations of both initial Kaluza-Klein modes and zero-mode. The amplitude of fluctuations is confirmed to agree with the four-dimensional one at low energies, whereas it is enhanced due to the normalization factor of zero-mode at high energies. We show that the five…
We consider two toy models of open inflation and investigate their ability to give a suppression of scalar power on large scales whilst also satisfying observational constraints on the spatial curvature of the universe. Qualitatively we find that both models are indeed capable of fulfilling these two requirements, but we also see that effects of the quantum tunnelling must be carefully taken into account if we wish to make quantitative predictions.
Krein approach is used to study the particle creation during quasi-de Sitter inflation in different background space-times. In the conventional method for calculating the created particles spectrum, the background space-time is automatically considered flat. Selecting a flat background poses two fundamental problems: First, the method of calculating is not covariant relative to the curved space-time. Second, the number of created particles becomes negative. Krein approach can be considered as a covariant method to calculate two-point functions in curved space-time. So we extend this method for…
Creation of an inflationary epoch from an Emergent Universe through quantum tunneling
Ben Gurion University of the Negev（内盖夫本-古里安大学）；Frankfurt Institute for Advanced Studies（法兰克福高等研究所）；Bahamas Advanced Studies Institute and Conferences（巴哈马高级研究与会议研究所）
Over the years, de Sitter spacetime has been a central focus, in studies involving quantum fields, for its importance in the early and late expansion stages of the universe. While de Sitter spacetime closely mimics characteristics of the inflationary and dark energy dominated universe it does not help to understand the radiation and matter dominated expansions. In this review, we revisit some recent works, involving the author, which study gravitational particle creation beyond the de Sitter stage. Specifically, we present novel aspects of particle creation in the radiation dominated universe,…
Based on an earlier introduced new class of generalized gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold, we derive an effective "Einstein-frame" theory featuring the following remarkable properties: (i) We obtain effective potential for the cosmological scalar field possessing two infinitely large flat regions which allows for a unified description of both early universe inflation as well as of present dark energy epoch; (ii) For a specific parameter range the model …
We investigate the creation of dark matter particles as a result of the decay of the scalar field in the framework of warm inflationary models, by using the irreversible thermodynamics of open systems with matter creation/annihilation. We consider the scalar fields, radiation and dark matter as an interacting three component cosmological fluid in a homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe, in the presence of the curvature terms. The thermodynamics of open systems as applied together with the gravitational field equations to the three component cosmological …
Inspired by the Randall-Sundrum brane-world scenario, we investigate the possibility of brane-world inflation driven not by an inflaton field on the brane, but by a bulk, dilaton-like gravitational field. As a toy model for the dilaton-like gravitational field, we consider a minimally coupled massive scalar field in the bulk 5-dimensional spacetime, and look for a perturbative solution in the anti-de Sitter (AdS) background. For an adequate range of the scalar field mass, we find a unique solution that has non-trivial dependence on the 5th dimensional coordinate and that induces slow-roll infl…
In this paper we investigate the cosmological dynamics of geometric inflation by means of the tools of the dynamical systems theory. We focus in the study of two explicit models where it is possible to sum the infinite series of higher curvature corrections that arises in the formalism. These would be very interesting possibilities since, if regard gravity as a quantum effective theory, a key feature is that higher powers of the curvature invariants are involved at higher loops. Hence, naively, consideration of the whole infinite tower of curvature invariants amounts to consideration of all of…
On the occasion of a century from the proposal of General relativity by Einstein, I attempt to tackle some open issues in modern cosmology, via a toy but non-trivial model. Specifically, I would like to link together: (i) the smallness of the cosmological constant today, (ii) the evolution of the universe from an inflationary era after the big-bang till now, and (iii) local supersymmetry in the gravitational sector (supergravity) with a broken spectrum at early eras, by making use of the concept of the "running vacuum" in the context of a simple toy model of four-dimensional N=1 supergravity. …
In this Letter we discuss the issues of the graceful exit from inflation and of matter creation in the context of a recent scenario \cite{RHBrev} in which the back-reaction of long wavelength cosmological perturbations induces a negative contribution to the cosmological constant and leads to a dynamical relaxation of the bare cosmological constant. The initially large cosmological constant gives rise to primordial inflation, during which cosmological perturbations are stretched beyond the Hubble radius. The cumulative effect of the long wavelength fluctuations back-reacts on the background geo…
A harmonic oscillator is an indefinite-frequency one if the parameter $ω$ is replaced by an operator. An ensemble of $N$ such oscillators may be regarded as a toy model of a bosonic quantum field. All the possible frequencies associated with a given problem are present already in a single oscillator and $N$ can be finite. Due to the operator character of $ω$ the resulting algebra of creation-annihilation operators is non-canonical. In the limit of large $N$ one recovers perturbation theory formulas of the canonical quantum field theory but with form factors automatically built in. Vacuum energ…
Upon embedding the axion-inflation in the minimal left-right symmetric gauge extension of the SM with gauge group $SU(2)_L\times SU(2)_R \times U(1)_{B-L}$, [arXiv:2012.11516] proposed a new particle physics model for inflation. In this work, we present a more detailed analysis. As a compelling consequence, this setup provides a new mechanism for simultaneous baryogenesis and right-handed neutrino creation by the chiral anomaly of $W_R$ in inflation. The lightest right-handed neutrino is the dark matter candidate. This setup has two unknown fundamental scales, i.e., the scale of inflation and …
We propose the mechanism of quantum creation of the open Universe in the observable range of values of $Ω$. This mechanism is based on the no-boundary quantum state with the Hawking-Turok instanton in the model with nonminimally coupled inflaton field and does not use any anthropic considerations. Rather, the probability distribution peak with necessary parameters of the inflation stage is generated on this instanton due to quantum loop effects. In contrast with a similar mechanism for closed models, existing only for the tunneling quantum state of the Universe, open inflation originates from …
In this paper the effects of time-dependent Newton constant G during inflation are studied. We present the formalism of curvature perturbations in an inflationary system with a time-dependent Newton constant. As an example we consider a toy model in which G undergoes a sudden change during inflation. By imposing the appropriate matching conditions the imprints of this sharp change in G on curvature perturbation power spectrum are studied. We show that if G increases (decreases) during the transition the amplitude of curvature perturbations on large scales decreases (increases). In our model wi…
Models of open inflation with a variable density parameter $Ω$ provide the most natural way to reconcile an open universe with inflation. The use of anthropic principle is essential to derive observational predictions of such models. I discuss how this principle can be used in a quantitative way to determine the most probable value of $Ω$. I also comment on recent work by Hawking and Turok on quantum creation of open universes from nothing.
We propose two new classes of instantons which describe the tunneling and/or quantum creation of closed and open universes. The instantons leading to an open universe can be considered as generalizations of the Coleman-De-Luccia solution. They are non-singular, unlike the instantons recently studied by Hawking and Turok, whose prescription has the problem that the singularity is located on the hypersurface connecting to the Lorentzian region, which makes it difficult to remove. We argue that such singularities are harmless if they are located purely in the Euclidean region. We thus obtain new …
The Friedman-Robertson-Walker (FRW) space-time exhibits particle creation similar to Hawking radiation of a black hole. In this essay we show that this FRW Hawking radiation leads to an effective negative pressure fluid which can drive an inflationary period of exponential expansion in the early Universe. Since the Hawking temperature of the FRW space-time decreases as the Universe expands this mechanism naturally turns off and the inflationary stage transitions to a power law expansion associated with an ordinary radiation dominated Universe.
The four-form field recently considered by Hawking and Turok couples naturally to a charged membrane, across which the effective cosmological constant has a discontinuity. We present instantons for the creation of an open inflationary universe surrounded by a membrane. They can also be used to describe the nucleation of a membrane on a pre-existing inflationary background. This process typically decreases the value of the effective cosmological constant and may lead to a novel scenario of eternal inflation. Moreover, by coupling the inflaton field to the membrane, the troublesome singularities…
