We identify a large class of systems of semilinear wave equations, on fixed accelerated expanding FLRW spacetimes, with nearly at spatial slices, for which we prove small data future global well-posedness. The family of systems we consider is large in the sense that, among other examples, it includes general wave maps, as well as natural generalizations of some of Fritz John's "blow up" equations (whose future blow up disappears, in our setting, as a consequence of the spacetime expansion). We also establish decay upper bounds, which are sharp within the family of systems under analysis.
Future stability of expanding spatially homogeneous FLRW solutions of the spherically symmetric Einstein--massless Vlasov system with spatial topology $\mathbb{R}^3$
The decay of solutions to the Klein-Gordon equation is studied in two expanding cosmological spacetimes, namely the de Sitter universe in flat Friedmann-Lemaître-Robertson-Walker (FLRW) form, and the cosmological region of the Reissner-Nordström-de Sitter (RNdS) model. Using energy methods, for initial data with finite higher order energies, decay rates for the solution are obtained. Also, a previously established decay rate of the time derivative of the solution to the wave equation, in an expanding de Sitter universe in flat FLRW form, is improved, proving Rendall's conjecture. A similar imp…
In this report, we discuss the behavior of coordinate-time dependent lapse function of FLRW metric of an accelerated expanding universe in the de Rham-Gabadadze-Tolley massive gravity theory. We find for the conventional dRGT formalism the corresponding lapse function can exhibit unphysical behaviors in the associated parameter space with a negative cosmological-constant-like term that leads to the decelerated universe model. To solve this problem, we introduce the so-called cosmological background density parameter to the perfect fluid stress-energy tensor which induces negative pressure. It …
New spherical scalar modes on the expanding part of Sitter spacetime, eigenfunctions of a conserved Hamiltonian-like operator are found by solving the Klein-Gordon equation in the appropriate coordinate chart, with the help of a time evolution picture technique specially developed for spatially flat FLRW charts. Transition coefficients are computed between these modes and the rest of the scalar spherical and plane wave modes, either momentum or energy eigenfunctions on the spatially flat FLRW chart.
A Newtonian uniform ball expanding in empty space constitutes a common heuristic analogy for FLRW cosmology. We discuss possible implementations of the corresponding general-relativistic problem and a variety of new cosmological analogies arising from them. We highlight essential ingredients of the Newtonian analogy, including that the quasilocal energy is always `Newtonian' in the sense that the magnetic part of the Weyl tensor does not contribute to it. A symmetry of the Einstein-Friedmann equations produces another one in the original Newtonian system.
We present a (hopefully) novel calculation of the vacuum energy in expanding FLRW spacetimes based on the renormalization of quantum field theory in non-zero backgrounds. We compute the renormalized effective action up to the $2-$point function and then apply the formalism to the cosmological backgrounds of interest. As an example we calculate for quasi de Sitter spacetimes the leading correction to the vacuum energy given by the tadpole diagram and show that it behaves as $\sim H_0^2 Λ_{\rm pl}$ where $H_0$ is the Hubble constant and $Λ_{\rm pl}$ is the Planck constant. This is of the same or…
Modified Newtonian equations for gravitational orbits in the expanding universe indicate that local gravitationally bounded systems like galaxies and planetary systems are unaffected by the expansion of the Universe. This result is derived under the assumption of the space expansion described by the standard FLRW metric. In this paper, an alternative metric is applied and the modified Newtonian equations are derived for the space expansion described by the conformal FLRW metric. As shown by Vavryčuk (Frontiers in Physics, 2022), this metric is advantageous, because it properly predicts the cos…
We establish the future nonlinear stability of a large class of FLRW models as solutions to the Einstein-Dust system. We consider the case of a vanishing cosmological constant, which in particular implies that the expansion rate of the respective models is linear i.e. has zero acceleration. The resulting spacetimes are future globally regular. These solutions constitute the first generic class of future regular Einstein-Dust spacetimes not undergoing accelerated expansion and are thereby the slowest expanding generic family of future complete Einstein-Dust spacetimes currently known.
We consider an exponentially expanding, flat, Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe filled with a free Schroedinger field. The probability fluid of the latter is used to mimic the cosmological fluid (baryonic plus dark matter), thus providing the matter density and pressure terms in the corresponding Friedmann-Lemaitre equations. We first obtain the eigenfunctions of the Laplacian operator on flat FLRW space. A quantum operator qualifying as a cosmological constant is defined to act on the Schroedinger field. We then compute the matrix representing the cosmological constant in th…
We prove nonlinear Lyapunov stability of a family of `$n+1$'-dimensional cosmological models of general relativity locally isometric to the Friedman Lemaître Robertson Walker (FLRW) spacetimes including a positive cosmological constant. In particular, we show that the perturbed solutions to the Einstein-Euler field equations around a class of spatially compact FLRW metrics (for which the spatial slices are compact negative Einstein spaces in general and hyperbolic for the physically relevant $n=3$ case) arising from regular Cauchy data remain uniformly bounded and decay to a family of metrics …
The framework of the relativistic quantum mechanics on spatially flat FLRW space-times is considered for deriving the analytical solutions of the Dirac equation in different local charts of these manifolds. Systems of commuting conserved operators are used for determining the fundamental solutions as common eigenspinors giving thus physical meaning to the integration constants related to the eigenvalues of these operators. Since these systems, in general, are incomplete on the FLRW space-times there are integration constants that must be fixed by setting the vacuum either as the traditional ad…
The closed Friedmann--Lemaître--Robertson--Walker (FLRW) universe of Einstein gravity with positive cosmological constant in three dimensions is investigated by using the Collins--Williams formalism in Regge calculus. A spherical Cauchy surface is replaced with regular polyhedrons. The Regge equations are reduced to differential equations in the continuum time limit. Numerical solutions to the Regge equations approximate well the continuum FLRW universe during the era of small edge length. The deviation from the continuum solution becomes larger and larger with time. Unlike the continuum unive…
In the present paper we provide new examples of marginally trapped surfaces and tubes in FLRW spacetimes by using a basic relation between these objects and CMC surfaces in 3-manifolds. We also provide a new method to construct marginally trapped surfaces in closed FLRW spacetimes, which is based on the classical Hopf map. The utility of this method is illustrated by providing marginally trapped surfaces crossing expanding and collapsing regions of a closed FLRW spacetime. The approach introduced in this paper is also extended to twisted spaces.
We study the decay of solutions of the wave equation in some expanding cosmological spacetimes, namely flat Friedmann-Lemaître-Robertson-Walker (FLRW) models and the cosmological region of the Reissner-Nordström-de Sitter (RNdS) solution. By introducing a partial energy and using an iteration scheme, we find that, for initial data with finite higher order energies, the decay rate of the time derivative is faster than previously existing estimates. For models undergoing accelerated expansion, our decay rate appears to be (almost) sharp.
We propose a method of projecting the quantum states from a state space of a given geometry into another state space generated by a different geometry, taking care on the correct normalization which is crucial in interpreting the quantum theory. Thanks to this method we can define on any spatially flat FLRW spacetime states in which genuine Minkowskian parameters are measured. We use these Minkowskian states for separating the frequencies in the rest frames of the massive scalar particles defining thus the scalar rest frame vacuum. We show that this vacuum is stable on the de Sitter expanding …
We present a time-dependent and spatially inhomogeneous solution that interpolates the extremal Reissner-Nordström (RN) black hole and the Friedmann-Lemaître-Robertson-Walker (FLRW) universe with arbitrary power-law expansion. It is an exact solution of the $D$-dimensional Einstein-"Maxwell"-dilaton system, where two Abelian gauge fields couple to the dilaton with different coupling constants, and the dilaton field has a Liouville-type exponential potential. It is shown that the system satisfies the weak energy condition. The solution involves two harmonic functions on a $(D-1)$-dimensional Ri…
Perturbative aspects of analogue FLRW spacetime Jellium models
Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）；Universidade Federal de Ouro Preto（奥罗普雷托联邦大学）；CONICET-UNC（阿根廷国家科学研究委员会-科尔多瓦国立大学）；Universidade Estadual do Ceará（塞阿拉州立大学）
Quantum creation processes during the very rapid early expansion of the universe are believed to give rise to temperature anisotropies and polarization patterns in the CMB radiation. These have been observed by satellites such as COBE, WMAP, and PLANCK, and by bolometric instruments placed near the South Pole by the BICEP collaborations. The expected temperature anisotropies are well-confirmed. The B-mode polarization patterns in the CMB are currently under measurement jointly by the PLANCK and BICEP groups to determine the extent to which the B-modes can be attributed to gravitational waves f…
Quantum fluctuations of a nonminimally coupled scalar field in D-dimensional homogeneous and isotropic background are calculated within the operator formalism in curved models with time evolutions of the scale factor that allow smooth transitions between contracting and expanding and between decelerating and accelerating regimes. The coincident propagator is derived and used to compute the one-loop backreaction from the scalar field. The inflationary infrared divergences are absent in Bunch-Davies vacuum when taking into account a preceding cosmological era or spatial curvature which can be ei…
We obtain a non-relativistic diffeomorphism invariant string action as a special limit of the Nambu-Goto action in an FLRW background. We use this action to study non-relativistic string dynamics in an expanding universe and construct an analytic model describing the macroscopic properties of non-relativistic string networks. The non-relativistic constraint equations allow arbitrarily small string velocities and thus a `frustrated' equation of state for non-interacting strings can be obtained without the need of a velocity damping mechanism. Assuming that colliding string segments reconnect by…
We establish the future stability of nonlinear perturbations of a class of homogeneous solutions to the relativistic Euler equations with a linear equation of state $p=Kρ$ on exponentially expanding FLRW spacetimes for the equation of state parameter values $1/3 < K < 1/2$.
McVittie spacetimes embed the vacuum Schwarzschild(-(anti) de Sitter) spacetime in an isotropic FLRW background universe. We study the global structure of McVittie spacetimes with spatially non-flat FLRW backgrounds. This requires the extension of the definition of such spacetimes, previously given only for the flat and open cases, to the closed case. We revisit this definition and show how it gives rise to a unique spacetime (given the FLRW background, the mass parameter $M$ and the cosmological constant $Λ$) in the open and flat cases. In the closed case, an additional free function of the c…
Post-Newtonian theory was instrumental in conducting the critical experimental tests of general relativity and in building the astronomical ephemerides of celestial bodies in the solar system with an unparalleled precision. The cornerstone of the theory is the postulate that the solar system is gravitationally isolated from the rest of the universe and the background spacetime is asymptotically flat. The present article extends this theoretical concept and formulates the principles of celestial dynamics of particles and light moving in gravitational field of a localized astronomical system emb…
We discuss cosmological effects of the quantum loops of massless particles, which lead to temporal non-localities in the equations of motion governing the scale factor a(t). For the effects discussed here, loops cause the evolution of a(t) to depend on the memory of the curvature in the past with a weight that scales initially as 1/(t-t'). As one of our primary examples we discuss the situation with a large number of light particles, such that these effects occur in a region where gravity may still be treated classically. However, we also describe the effect of quantum graviton loops and the f…
The Collins-Williams Regge calculus models of FLRW space-times and Brewin's subdivided models are applied to closed vacuum $Λ$-FLRW universes. In each case, we embed the Regge Cauchy surfaces into 3-spheres in $\mathbf{E}^4$ and consider possible measures of Cauchy surface radius that can be derived from the embedding. Regge equations are obtained from both global variation, where entire sets of identical edges get varied simultaneously, and local variation, where each edge gets varied individually. We explore the relationship between the two sets of solutions, the conditions under which the R…
This paper analyzes the supersymmetric solutions to five and six-dimensional minimal (un)gauged supergravities for which the bilinear Killing vector constructed from the Killing spinor is null. We focus on the spacetimes which admit an additional ${\rm SO}(1,1)$ boost symmetry. Upon the toroidal dimensional reduction along the Killing vector corresponding to the boost, we show that the solution in the ungauged case describes a charged, nonextremal black hole in a Friedmann-Lemaître-Robertson-Walker (FLRW) universe with an expansion driven by a massless scalar field. For the gauged case, the so…
In the present work we present the full treatment of scalar and vector cosmological perturbations in a non-singular bouncing universe in the context of metric $f(R)$ cosmology. Scalar metric perturbations in $f(R)$ cosmology were previously calculated in the Jordan frame, in the present paper we successfully use the Einstein frame to calculate the scalar metric perturbations where the cosmological bounce takes place in the Jordan frame. The Einstein frame picture presented corrects and completes a previous calculation of scalar perturbations and adds new information. Behavior of fluid velocity…
We compute the circuit complexity of scalar curvature perturbations on FLRW cosmological backgrounds with fixed equation of state $w$ using the language of squeezed vacuum states. Backgrounds that are accelerating and expanding, or decelerating and contracting, exhibit features consistent with chaotic behavior, including linearly growing complexity. Remarkably, we uncover a bound on the growth of complexity for both expanding and contracting backgrounds $λ\leq \sqrt{2} \ |H|$, similar to other bounds proposed independently in the literature. The bound is saturated for expanding backgrounds wit…
We present a novel homogeneous and geometrically flat exact solution of Einstein's General Relativity equations for an ideal fluid. The solution, which describes an expanding/contracting hypercylinder, fits well with the observational pillars upon which rely the standard FLRW cosmology and, furthermore, it can naturally solve some of its most outstanding problems.
A numerical approach is considered for spherically symmetric spacetimes that generalize Lemaitre-Tolman-Bondi dust solutions to nonzero pressure ("LTB spacetimes"). We introduce quasi-local (QL) variables that are covariant LTB objects satisfying evolution equations of Friedman-Lemaitre-Robertson-Walker (FLRW) cosmologies. We prove rigorously that relative deviations of the local covariant scalars from the QL scalars are non-linear, gauge invariant and covariant perturbations on a FLRW formal "background" given by the QL scalars. The dynamics of LTB spacetimes is completely determined by the Q…
We establish global regularity and stability for the irrotational relativistic Euler equations with equation of state $\overline{p}=K\overlineρ$, where $0<K<1/3$, for small initial data in the expanding direction of FLRW spacetimes of the form $(\mathbb R\times\mathbb T^3,-d\tb^2+\tb^2δ_{ij} dx^i dx^j)$. This provides the first case of non-dust fluid stabilization by spacetime expansion where the expansion rate is of power law type but non-accelerated. In particular, the time integral of the inverse scale factor diverges as $t\rightarrow\infty$.
The discretized closed Friedmann-Lemaître-Robertson-Walker (FLRW) universe with positive cosmological constant is investigated by Regge calculus. According to the Collins-Williams formalism, a hyperspherical Cauchy surface is replaced with regular 4-polytopes. Numerical solutions to the Regge equations approximate well to the continuum solution during the era of small edge length. Unlike the expanding polyhedral universe in three dimensions, the 4-polytopal universes repeat expansions and contractions. To go beyond the approximation using regular 4-polytopes we introduce pseudo-regular 4-polyt…
We study physical properties and global structures of a time-dependent, spherically symmetric solution obtained via the dimensional reduction of intersecting M-branes. We find that the spacetime describes a maximally charged black hole which asymptotically tends to the Friedmann-Lemaître-Robertson-Walker (FLRW) universe filled by a stiff matter. The metric solves the field equations of Einstein-Maxwell-dilaton system, in which four Abelian gauge fields couple to the dilation with different coupling constants. The spacetime satisfies the dominant energy condition and is characterized by two par…
We investigate a flat FLRW-model in $f(R,T)$-gravity, which includes the quadratic variation in scalar curvature $R$ and the linear term of the trace of the stress-energy tensor $T$. In turn, we establish the model has the behaviour of the late time Universe, which is accelerated expanding and ends up in a big rip. Using the parametrization of scale factor $a(t)$, we propose a model, which begins with point-type singularity, i.e., the model starts with a point of zero volume, infinite energy density and infinite temperature. The model's behaviour is accelerated expanding at present and $Λ$CDM …
The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe is studied. The mathematical problem of solving the full nonlinear relativistic Boltzmann equation is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. Momentum-space resolution is determined by the number of non-hydrodynamic modes included in the moment hierarchy, i.e., by the truncation order. We show that in the FLRW spacetime the non-hydrodynamic modes decou…
We study a previously largely unexplored branch of homogeneous and isotropic background solutions in ghost-free massive bigravity with consistent double matter coupling. For a certain family of parameters we find `self-inflated' FLRW cosmologies, i.e. solutions with an accelerated early-time period during the radiation-dominated era. In addition, these solutions also display an accelerated late-time period closely mimicking GR with a cosmological constant. Interestingly, within this family, the particular case of $β_1=β_3=0$ gives bouncing cosmologies, where there is an infinite contracting pa…
We carry out a thorough analysis on a class of cosmological spacetimes which admit three space-like Killing vectors of Bianchi class B and contain electromagnetic fields. Using dynamical system analysis, we show that a family of vacuum plane-wave solutions of the Einstein-Maxwell equations is the stable attractor for expanding universes. Phase dynamics are investigated in detail for particular symmetric models. We integrate the system exactly for some special cases to confirm the qualitative features. Some of the obtained solutions have not been presented previously to the best of our knowledg…
In this paper we consider a massless scalar field, with a possible coupling $ξ$ to the Ricci scalar in a $D$ dimensional FLRW spacetime with a constant deceleration parameter $q=ε-1$, $ε=-{\dot{H}}/{H^2}$. Correlation functions for the Bunch-Davies vacuum of such a theory have long been known to be infrared divergent for a wide range of values of $ε$. We resolve these divergences by explicitly matching the spacetime under consideration to a spacetime without infrared divergencies. Such a procedure ensures that all correlation functions with respect to the vacuum in the spacetime of interest ar…
In the context of Lorentz-Finsler spacetime theories the relativity principle holds at a spacetime point if the indicatrix (observer space) is homogeneous. We point out that in four spacetime dimensions there are just three kinematical models which respect an exact form of the relativity principle and for which all observers agree on the spacetime volume. They have necessarily affine sphere indicatrices. For them every observer which looks at a flash of light emitted by a point would observe, respectively, an expanding (a) sphere, (b) tetrahedron, or (c) cone, with barycenter at the point. The…
