We investigate cosmological solutions of f(R,T) modified theories of gravity for perfect fluid in spatially FLRW metric through phase space analysis, where R is Ricci scalar and T denotes the trace of energy-momentum tensor of matter content. We explore and analyze three general theories with Lagrangians of minimal $g(R)+h(T)$, pure non--minimal g(R)h(T) and non-minimal $g(R)(1+h(T))$ couplings through dynamical systems approach. We introduce a few variables and dimensionless parameters to simplify the equations in more concise forms. The conservation of energy-momentum tensor leads to a constraint equation that, in the minimal gravity, confines functionality of h(T) to a particular form, hence, relates the dynamical variables. In this case, acceptable cosmological solutions that contain a long enough matter dominated era followed by a late-time accelerated expansion are found. To support theoretical results, we also obtain numerical solutions for a few functions of g(R), and results of the corresponding models confirm the predictions. We classify solutions into six classes which demonstrate more acceptable solutions and there is more freedom to have the matter dominated era than in the f(R) gravity. In particular, there is a new fixed point which can represent late-time acceleration. We draw different diagrams of the matter densities (consistent with the present values), the related scale factors and effective equation of state. The corresponding diagrams of parameters illustrate that there is a saddle acceleration era which is a middle era before final stable acceleration de Sitter era for some models. All presented diagrams determine radiation, matter and late-time acceleration eras very well.
A global phase time is identified for homogeneous and isotropic cosmological models yielding from the low energy effective action of closed bosonic string theory. When the Hamiltonian constraint allows for the existence of an intrinsic time, the quantum transition amplitude is obtained by means of the usual path integral procedure for gauge systems.
We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space. We work in 2+1 dimensions, but these results may be relevant also for the physical 3+1 case.
Regarding axion electrodynamics in the background flat FRW universe, we show that cosmological birefringence arises from an adiabatic noncyclic geometric phase that appears in the quantum state of photons because of their interaction with the axion field. We also show that the axion electrodynamics is equivalent to standard electrodynamics in time-dependent bi-isotropic magnetoelectric Tellegen media, which serves as an analogue system that can simulate cosmological birefringence.
We review several cosmological backgrounds of gravitational waves accessible to direct-detection experiments, with a special emphasis on those backgrounds due to first-order phase transitions and networks of cosmic (super-)strings. For these two particular sources, we revisit in detail the computation of the gravitational wave background and improve the results of previous works in the literature. We apply our results to identify the scientific potential of the NGO/eLISA mission of ESA regarding the detectability of cosmological backgrounds.
Phase-plane stability analysis of a dynamical system describing the Universe as a two-fraction fluid containing baryonic dust and real virial gas quintessence is presented. Existence of a stable periodic solution experiencing inflationary periods is shown. A van der Waals quintessence model is revisited and cyclic Universe solution again found.
We show that the cosmological phase transition from the first accelerated expansion in the early universe to the second accelerated expansion over the intermediate decelerated expansion is possible in the HL gravity without the ``detailed balance'' condition if the dark scalar energy density is assumed to be negative. Moreover, we obtain various evolutions depending on the scale factor and the expansion rate. Finally, we discuss the existence of the minimum scale in connection with the singularity free condition.
In this paper we study the effects of noncommutative phase space deformations on the Schwarzschild black hole. This idea has been previously studied in {Friedmann-Robertson-Walker (FRW)} cosmology, where this "noncommutativity" provides a simple mechanism that can explain the origin of the cosmological constant. In this paper we obtain the same relationship between the cosmological constant and the deformation parameter that appears in deformed phase space cosmology, but in the context of the deformed phase space black holes. This was achieved by comparing the entropy of the deformed Schwarzsc…
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.
Examining the propagation of electromagnetic plane waves with the wavevector directed in opposition to the time-averaged Poynting vector in cosmological spacetime with piecewise uniform metric, we show that such negative-phase-velocity (NPV) propagation is possible in certain de Sitter spacetimes but not in anti-de Sitter spacetimes. This difference suggests the possibility of an optical/electromagnetic experiment to discern the cosmological constant of a four-dimensional universe stemming from a five-dimensional brane universe.
Fisher's arrow of `time' in a cosmological phase space defined as in quantum optics (i.e., whose points are coherent states) is introduced as follows. Assuming that the phase space evolution of the universe starts from an initial squeezed cosmological state towards a final thermal one, a Fokker-Planck equation for the time-dependent, cosmological Q phase space probability distribution can be written down. Next, using some recent results in the literature, we derive an information arrow of time for the Fisher phase space cosmological entropy based on the Q function. We also mention the applicat…
Double-layered vacuum bubbles and cosmological phase transitions
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（杭州高等研究院基础物理与数学学院，中国科学院大学）；School of Physical Sciences, University of Chinese Academy of Sciences（物理科学学院，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（理论物理研究所，中国科学院）；School of Physics and Astronomy, Sun Yat-sen University（物理与天文学院，中山大学）
We consider cosmological scalar field evolving under exponential potential of the Non-minimal Derivative Coupling (NMDC) gravity model in Palatini formalism. Slow-roll regime is assumed. GR and metric formalism NMDC cases are compared in this study. Phase portraits show that Palatini NMDC effect restricts acceleration phase into smaller region in the phase space. NMDC effect of the Palatini case suppresses expansion rate than that of the GR while the metric NMDC enhances rate of expansion of the GR case.
The path integral, which generates in-in correlation functions of a scalar field in a cosmological spacetime, is shown to admit nontrivial classical solutions as stationary phases. Although the solutions exist for Lorentzian signature, their contribution to the path integral is reminiscent that of the instantons in Euclidean field theories. When the scalar potential has more than one locally stable vacua, the correlation functions receive contributions from all of them via these instanton-like configurations, which is similar to tunneling. We present some explicit solutions for toy models and …
We study the generation of cosmological perturbations during the Hagedorn phase of string gas cosmology. Using tools of string thermodynamics we provide indications that it may be possible to obtain a nearly scale-invariant spectrum of cosmological fluctuations on scales which are of cosmological interest today. In our cosmological scenario, the early Hagedorn phase of string gas cosmology goes over smoothly into the radiation-dominated phase of standard cosmology, without having a period of cosmological inflation.
A special model of a massless vector-field is presented, which has an extra modified-gravity-type interaction term in the action. The cosmology of the model is studied with standard noninteracting relativistic matter added. It is found that this cosmology can have an early phase where the vector-field starts to compensate a (Planck-scale) cosmological constant and a late Friedmann-Robertson-Walker (FRW) phase where the relativistic-matter energy density dominates the dynamic vacuum energy density.
We investigate the potential for the eLISA space-based interferometer to detect the stochastic gravitational wave background produced by strong first-order cosmological phase transitions. We discuss the resulting contributions from bubble collisions, magnetohydrodynamic turbulence, and sound waves to the stochastic background, and estimate the total corresponding signal predicted in gravitational waves. The projected sensitivity of eLISA to cosmological phase transitions is computed in a model-independent way for various detector designs and configurations. By applying these results to several…
The free Dirac equation is solved in a Bianchi Type I space-time, which represents a homogeneous but anisotropic universe, to show the creation of fermionic particles. It is found that unlike in the isotropic case, massless fermion production is possible. An estimate of the energy density of massless particles created during an early anisotropic phase of cosmological expansion is shown to cause substantial back-reaction on the gravitational field. The potential relevance to dark matter particle production, primordial magnetogenesis, and early universe cosmology is discussed briefly.
The one-loop renormalized effective potentials for the massive $ϕ^4$ theory on the spatially homogeneous models of Bianchi type I and Kantowski-Sachs type are evaluated. It is used to see how the quantum field affects the cosmological phase transition in the anisotropic spacetimes. For reasons of the mathematical technique it is assumed that the spacetimes are slowly varying or have specially metric forms. We obtain the analytic results and present detailed discussions about the quantum field corrections to the symmetry breaking or symmetry restoration in the model spacetimes.
Cosmological phase transitions are thought to have taken place at the early Universe imprinting their properties on the observable Universe. There is strong evidence that, through the dynamics of a scalar field that lead a second order phase transition, inflation shaped the Universe accounting for the most conspicuous features of the observed Universe. It is argued that inflation has also striking implications for the vacuum energy. Considerations for subsequent second order phase transitions are also discussed.
The physical history of the Universe is completed by including the quantum planckian and trans-planckian phase before Inflation in the Standard Model of the Universe in agreement with observations. A new quantum precursor phase appears beyond the Planck scale. We extend de Sitter universe to the quantum domain: classical-quantum de Sitter duality. As a result: The classical and quantum dual de Sitter Temperatures and Entropies are naturally included, and the different (classical, semiclassical, quantum planckian and super-planckian) de Sitter regimes characterized in a precise and unifying way…
In this paper, using the concept of Lewis Riesenfeld invariant quantum operator method for finding continuous eigenvalues of quantum mechanical wave functions we derive the analytical expressions for the cosmological geometric phase, which is commonly identified to be the Pancharatnam Berry phase from primordial cosmological perturbation scenario. We compute this cosmological geometric phase from two possible physical situations,(1) In the absence of Bell's inequality violation and (2) In the presence of Bell's inequality violation having the contributions in the sub Hubble region ($-kτ\gg 1$)…
A particular compensation-type solution of the main cosmological constant problem has been proposed recently, with two massless vector fields dynamically canceling an arbitrary cosmological constant Λ. The naive expectation is that such a compensation mechanism does not allow for the existence of an inflationary phase in the very early Universe. However, it is shown that certain initial boundary conditions on the vector fields can in fact give rise to an inflationary phase.
The flows of phase trajectories of cosmological models based on the vacuum classical Higgs field and their behavior on the Einstein-Higgs surface near singular points of a dynamical system are investigated by numerical simulation. The influence of the singular points on the process of phase flow splitting is shown and the efficiency of the Einstein-Higgs hypersurface application is demonstrated.
The evolution of the cosmological perturbation during the oscillatory stage of the scalar field is investigated. For the power law potential of the inflaton field, the evolution equation of the Mukhanov's gauge invariant variable is reduced to the Mathieu equation and the density perturbation grows by the parametric resonance.
A two-component formulation of the Klein-Gordon equation is used to investigate the cyclic and noncyclic adiabatic geometric phases due to spatially homogeneous (Bianchi) cosmological models. It is shown that no adiabatic geometric phases arise for Bianchi type I models. For general Bianchi type IX models the problem of the adiabatic geometric phase is shown to be equivalent to the one for nuclear quadrupole interactions of a spin. For these models nontrivial non-Abelian adiabatic geometrical phases may occur in general.
In brane world scenarios the Friedmann equation is modified, resulting in an increased expansion at early times. This has important effects on cosmological phase transitions which we investigate, elucidating significant differences to the standard case. First order phase transitions require a higher nucleation rate to complete; baryogenesis and particle abundances could be suppressed. Topological defect evolution is also affected, though the current defect densities are largely unchanged. In particular, the increased expansion does not solve the usual monopole and domain wall problems.
Quantum fluctuation of unstable modes about gravitational instantons causes the instability of flat space at finite temperature, leading to the spontaneous process of nucleating quantum black holes. The energy-density of quantum black holes, depending on the initial temperature, gives the cosmological term, which naturally accounts for the inflationary phase of Early Universe. The reheating phase is attributed to the Hawking radiation and annihilation of these quantum black holes. Then, the radiation energy-density dominates over the energy-density of quantum black holes, the Universe started …
The phase-integral approximation devised by Fröman and Fröman, is used for computing cosmological perturbations in the quadratic chaotic inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to fifth order of the phase-integral approximation. We show that, the phase integral gives a very good approximation for the shape of the power spectra associated with scalar and tensor perturbations as well as the spectral indices. We find that the accuracy of the phase-integral approximation compares favorably with the numerical results and tho…
A brief outline is given of the description of phase transition kinetics in condensed matter systems with a continuous symmetry, emphasising the roles of dissipation, coarse-graining and scaling. The possible relevance of these ideas to the early universe is explored in the contexts of the GUT string transition and the electroweak transition.
We study the phase transition from quark-gluon plasma to hadrons in the early universe in the context of non-equilibrium thermodynamics. According to the standard model of cosmology, a phase transition associated with chiral symmetry breaking after the electro-weak transition has occurred when the universe was about $1-10μs$ old. We focus attention on such a phase transition in the presence of a viscous relativistic cosmological background fluid in the framework of non-detailed balance Hořava-Lifshitz cosmology within an effective model of QCD. We consider a flat Friedmann-Robertson-Walker Uni…
The phase-integral approximation devised by Fröman and Fröman, is used for computing cosmological perturbations in the power-law inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to ninth-order of the phase-integral approximation. We show that, the phase-integral approximation exactly reproduces the shape of the power spectra for scalar and tensor perturbations as well as the spectral indices. We compare the accuracy of the phase-integral approximation with the results for the power spectrum obtained with the slow-roll and unifor…
At a very rapid superfluid transition in $^3$He, follows after a reaction with single neutron, the creation of topological defects (vortices) has recently been demonstrated in accordance with the Kibble-Zurek scenario for the cosmological analogue. We discuss here the extension of the Kibble-Zurek scenario to the case when alternative symmetries may be broken and different states nucleated independently. We have calculated the nucleation probability of the various states of superfluid $^3$He during a superfluid transition. Our results can explain the transition from supercooled $A$ phase to th…
Vacuum energy changes during cosmological phase transitions and becomes relatively important at epochs just before phase transitions. For a viable cosmology the vacuum energy just after a phase transition must be set by the critical temperature of the next phase transition, which exposes the cosmological constant problem from a different angle. Here we propose to experimentally test the properties of vacuum energy under circumstances different from our current vacuum. One promising avenue is to consider the effect of high density phases of QCD in neutron stars. Such phases have different vacuu…
The current acceleration of the universe can be modeled in terms of a cosmological constant. We show that the extremely small value of ΛL_P^2 ~ 3.4 x 10^{-122}, the holy grail of theoretical physics, can be understood in terms of a new, dimensionless, conserved number CosMIn (N), which counts the number of modes crossing the Hubble radius during the three phases of evolution of the universe. Theoretical considerations suggest that N ~ 4π. This single postulate leads us to the correct, observed numerical value of the cosmological constant! This approach also provides a unified picture of cosmic…
We study cosmological phase transitions from modified equations of motion by introducing two non-commutative parameters in the Poisson brackets, which describes the initial- and future-singularity-free phase transition in the soluble semi-classical dilaton gravity with a non-vanishing cosmological constant. Accelerated expansion and decelerated expansion corresponding to the FRW phase appear alternatively, and then it ends up with the second accelerated expansion. The final stage of the universe approaches the flat spacetime independent of the initial state of the curvature scalar as long as t…
Using the qualitative theory of differential equations, the global dynamics of a cosmological model based on Horava-Lifshitz gravity is studied in the space with zero curvature in the presence of the non-zero cosmological constant.
We investigate thoroughly the temporal evolution of the universe temperature as a function of the Hubble parameter associated with the Stochastic Gravitational Wave (SGW), that formed at the cosmological QCD phase transition epoch to the current epoch, within the Generalized Uncertainty Principle (GUP) framework. Here we use GUP version which provide constraints on the minimum measurable length and the maximum observable momentum, that characterized by a free parameter $α$. We study the effect of this parameter on the SGW background. We show that the effect can slightly enhance the SGW frequen…
We propose a mechanism to have a smooth transition from a pre-Big Bang phase to a standard cosmological phase. Such transition is driven by gravitational production of heavy massive string states that backreact on the geometry to stop the growth of the curvature. Close to the string scale, particle creation can become effective because the string phase space compensate the exponential suppression of the particle production. Numerical solutions for the evolution of the Universe with this source are presented.
The evolution of the luminosity distance in a contracting universe is studied. It is shown that for quite a lot of natural dynamical evolutions, its behavior is far from trivial and its value can even decrease with an increasing time interval between events. The consequences are investigated and it is underlined that this could both put stringent consistency conditions on bouncing models and open a new observational window on "pre Big Bang" physics using standard gravitational waves.
We study the gravitational waves produced by the collision of the bubbles as a probe for the cosmological first order QCD phase transition, considering heavy static quarks. Using AdS/QCD and the correspondence between a first order Hawking-Page phase transition and confinement-deconfinement phase transition, we find the spectrum and the strain amplitude of the gravitational wave within the hard and soft wall models. We postulate the duration of the phase transition corresponds to the evaporation time of the black hole in the five dimensional dual gravity space, and thereby obtain a bound on th…
We study the hydrodynamics of bubble expansion in cosmological first-order phase transition in the Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) background with probe limit. Different from previous studies for fast first-order phase transition in flat background, we find that, for slow first-order phase transition in FLRW background with a given peculiar velocity of the bubble wall, the efficiency factor of energy transfer into bulk motion of thermal fluid is significantly reduced, thus decreasing the previously-thought dominated contribution from sound wave to the stochastic gravitational-wave…
With the help of our own software package DifEqTools, numerical modeling of the cosmological evolution of a system consisting of an asymmetric scalar doublet of nonlinear, minimally interacting scalar fields, a classical field and a phantom field, has been performed. Peculiarities of the behavior of the model near zeroenergy hypersurfaces have been revealed.
Tensor type perturbations in the expanding brane world of the Randall Sundrum type are investigated. We consider a model composed of slow-roll inflation phase and the succeeding radiation phase. The effect of the presence of an extra dimension through the transition to the radiation phase is studied, giving an analytic formula for leading order corrections.
We revisit the perturbative expansion at high temperature and investigate its convergence by inspecting the renormalisation scale dependence of the effective potential. Although at zero temperature the renormalisation group improved effective potential is scale independent at one-loop, we show how this breaks down at high temperature, due to the misalignment of loop and coupling expansions. Following this, we show how one can recover renormalisation scale independence at high temperature, and that it requires computations at two-loop order. We demonstrate how this resolves some of the huge the…
In this letter we study the effects of a noncommutative in the phase space of an empty (4+1) Kaluza-Klein universe with cosmological constant. We analyze the effects of the noncommutative deformations on the cosmological constant. Finally we comment on the possibility that the origin of the cosmological constant in this model, is related to the noncommutativity between the 4 dimensional scale factor and the compact extra dimension.
It has been shown by Remmen and Carroll that, for a model universe which contains only a kinetically canonical scalar field minimally coupled to gravity it is possible to choose 'special coordinates' to describe a two-dimensional effective phase space. The special, non-canonical, coordinates are $ϕ$,$\dotϕ$ and the ability to describe an effective phase space with these coordinates empowers the common usage of $ϕ-\dotϕ$ as the space to define inflationary initial conditions. This paper extends the result to the full Horndeski action. The existence of a two-dimensional effective phase space is …
The finite-temperature effective potential customarily employed to describe the physics of cosmological phase transitions often relies on specific gauge choices, and is manifestly not gauge-invariant at finite order in its perturbative expansion. As a result, quantities relevant for the calculation of the spectrum of stochastic gravity waves resulting from bubble collisions in first-order phase transitions are also not gauge-invariant. We assess the quantitative impact of this gauge-dependence on key quantities entering predictions for gravity waves from first order cosmological phase transiti…
It has recently been suggested that collapse of neutron stars induced by a phase transition to quark matter can be a considerable source of gravitational waves with kHz frequencies. We demonstrate that if about one percent of all neutron stars undergo this process, the resulting cosmological gravitational wave background would reach about 10^-10 times the critical density. The background would peak at kHz frequencies and could have an observationally significant tail down to Hz frequencies. It would be comparable or higher than other astrophysical backgrounds, for example, from ordinary core c…
We present here the canonical treatment of spherically symmetric (quantum) gravity coupled to spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is coordinatized by the mass and the electric charge as well as their canonically conjugate momenta, whose geometrical interpretation is explored. The dimension of the reduced phase space depends on the topology chosen, quite similar to the case of pure (2+1) gravity. We also compare the reduced phase space quantization to the algebraic quantization. Altogether, we o…
We critically examine the magnitude of theoretical uncertainties in perturbative calculations of first-order phase transitions, using the Standard Model effective field theory as our guide. In the usual daisy-resummed approach, we find large uncertainties due to renormalisation scale dependence, which amount to two to three orders-of-magnitude uncertainty in the peak gravitational wave amplitude, relevant to experiments such as LISA. Alternatively, utilising dimensional reduction in a more sophisticated perturbative approach drastically reduces this scale dependence, pushing it to higher order…
The separate-universe approach provides an effective description of cosmological perturbations at large scales, where the universe can be described by an ensemble of independent, locally homogeneous and isotropic patches. By reducing the phase space to homogeneous and isotropic degrees of freedom, it greatly simplifies the analysis of large-scale fluctuations. It is also a prerequisite for the stochastic-inflation formalism. In this work, we formulate the separate-universe approach in the Hamiltonian formalism, which allows us to analyse the full phase-space structure of the perturbations. Suc…
We extend here the canonical treatment of spherically symmetric (quantum) gravity to the most simple matter coupling, namely spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is coordinatized by the mass and the electric charge as well as their canonically conjugate momenta, whose geometrical interpretation is explored. The dimension of the reduced phase space depends on the topology chosen, quite similar to the case of pure (2+1) gravity. We investigate several conceptual and technical details that might be…
We show how to determine the typical phase space volume $Γ$ for primordial gravitational waves produced during an inflationary stage, which is invariant under squeezing. An expression for $Γ$ is found in the long wavelength regime. The quasi-classical entropy of a pure vacuum initial state defined as the logarithm of $Γ$ modulo a constant remains zero in spite of the generation of fluctuations (creation of real gravitons).
We study a recently proposed new cosmological phase where a scalar field moves periodically in an expanding spatially-flat Friedmann universe. This phase corresponds to a limiting cycle of the equations of motion and can be considered as a cosmological realization of a "time-crystal". We show that this phase is only possible, provided the Null Energy Condition is violated and the so-called Phantom divide is crossed. We prove that in general k-essence models: i) this crossing causes infinite growth of quantum perturbations on short scales, and ii) exactly periodic solutions are only possible, p…
We analyze the dynamical system defined by a universe filled with a barotropic fluid plus a scalar field with modified kinetic term of the form L = F (X) - V (phi). After a suitable choice of variables that allows us to study the phase space of the system we obtain the critical points and their stability. We find that they reduce to the ones defined for the canonical case when F (X) = X. We also study the field energy conditions to have a nonsingular bounce.
A detailed analysis of the phase trajectories of cosmological models based on classical and scalar fields near surfaces of zero effective energy has been carried out. A study of the differential parameters of the convergence of phase trajectories to a zero-energy surface boundary shows that the phase trajectories merge within a finite time with the phase trajectories of free oscillations corresponding to zero effective energy. This confirms the assumption formulated in a number of previous works by one of the authors about the existence of Euclidean limit cycles in cosmological models based on…
