FLRW Spacetime Research Articles

Interacting dark energy in curved FLRW spacetime from Weyl Integrable Spacetime

In the present article, we show that a simple modification to the Einstein-Hilbert action can explain the possibility of mutual interaction between the cosmic fluids. That is achieved considering the Weyl Integrable Spacetime in the background of a nonflat Friedmann-Lemaître-Robertson-Walker geometry for the universe. We perform the dynamical system analysis of the underlying cosmological scenario and explore many possibilities extracted from this gravitational theory. Finally, we investigate if the specific model solves the flatness problem.

On holonomy singularities in general relativity and the Cloc0,1-inextendibility of space-times

This paper investigates the structure of gravitational singularities at the level of the connection. We show in particular that for FLRW space-times with particle horizons a local holonomy, which is related to a gravitational energy, becomes unbounded near the big-bang singularity. This implies the Cloc0,1-inextendibility of such FLRW space-times. Again using an unbounded local holonomy, we also give a general theorem establishing the Cloc0,1-inextendibility of spherically symmetric weak null singularities which arise at the Cauchy horizon in the interior of black holes. Our theorem does not presuppose the mass-inflation scenario and in particular applies to the Reissner–Nordström-Vaidya space-times, as well as to space-times which arise from small and generic spherically symmetric perturbations of two-ended subextremal Reissner–Nordström initial data for the Einstein–Maxwell scalar field system. In previous work, Luk and Oh proved the C2-formulation of strong cosmic censorship for this latter class of space-times—and based on their work we improve this to a Cloc0,1-formulation of strong cosmic censorship.

Entanglement harvesting from conformal vacuums between two Unruh-DeWitt detectors moving along null paths

It is well-known that the (1 + 1) dimensional Schwarzschild and spatially flat FLRW spacetimes are conformally flat. This work examines entanglement harvesting from the conformal field vacuums in these spacetimes between two Unruh-DeWitt detectors, moving along outgoing null trajectories. In (1 + 1) dimensional Schwarzschild spacetime, we considered the Boulware and Unruh vacuums for our investigations. In this analysis, one observes that while entanglement harvesting is possible in (1+1) dimensional Schwarzschild and (1 + 3) dimensional de Sitter spacetimes, it is not possible in the (1 + 1) dimensional de Sitter background for the same set of parameters when the detectors move along the same outgoing null trajectory. The qualitative results from the Boulware and the Unruh vacuums are alike. Furthermore, we observed that the concurrence depends on the distance d between the two null paths of the detectors periodically, and depending on the parameter values, there could be entanglement harvesting shadow points or regions. We also observe that the mutual information does not depend on d in (1 + 1) dimensional Schwarzschild and de Sitter spacetimes but periodically depends on it in (1 + 3) dimensional de Sitter background. We also provide elucidation on the origin of the harvested entanglement.

Cosmology in Painlevé-Gullstrand coordinates

Cosmology is most typically analyzed using standard co-moving coordinates, in which the galaxies are (on average, up to presumably small peculiar velocities) “at rest”, while “space” is expanding. But this is merely a specific coordinate choice; and it is important to realise that for certain purposes other, (sometimes radically, different) coordinate choices might also prove useful and informative, but without changing the underlying physics. Specifically, herein we shall consider the k= 0 spatially flat FLRW cosmology but in Painlevé-Gullstrand coordinates — these coordinates are very explicitly not co-moving: “space” is now no longer expanding, although the distance between galaxies is still certainly increasing. Working in these Painlevé-Gullstrand coordinates provides an alternate viewpoint on standard cosmology, and the symmetries thereof, and also makes it somewhat easier to handle cosmological horizons. With a longer view, we hope that investigating these Painlevé-Gullstrand coordinates might eventually provide a better framework for understanding large deviations from idealized FLRW spacetimes. We illustrate these issues with a careful look at the Kottler and McVittie spacetimes.

New time-dependent solutions of viable Horndeski gravity

We generate new spherical and time-dependent solutions of viable Horndeski gravity by disforming a solution of the Einstein equations with scalar field source and positive cosmological constant. They describe dynamical objects embedded in asymptotically FLRW spacetimes and contain apparent horizons and a finite radius singularity that evolve in time in peculiar ways apparently not encountered before in Einstein and “old” scalar-tensor gravity.

Quantum cosmology for double scalar field cosmological model: Symmetry analysis

The present cosmological model consists of two scalar fields which are minimally coupled to gravity and having a mixed kinetic term. In the background of homogeneous and isotropic FLRW space–time the present model is characterized by the coupling function and the potential function which are functions of one of the scalar fields. Using symmetries of the 3D augmented space, homothetic and killing vectors are determined. Finally, quantum cosmology has been formulated for the present model and the wave function of the universe has been evaluated.

The self-interacting Dirac fields in FLRW spacetime

We prove the existence of global in time solution with the small initial data for the semilinear equation of the spin-\(\frac{1}{2}\) particles in the Friedmann–Lemaître–Robertson–Walker spacetime. Moreover, we also prove that if the initial function satisfies the Lochak–Majorana condition, then the global solution exists for arbitrary large initial value. The solution scatters to free solution for large time. The mass term is assumed to be complex-valued. The conditions on the imaginary part of mass are discussed by proving nonexistence of the global solutions if certain relation between scale function and the mass are fulfilled.

Cosmological memory effect in scalar-tensor theories

The cosmological memory effect is a permanent change in the relative separation of test particles located in a Friedmann-Lema\'{\i}tre-Robertson-Walker (FLRW) spacetime due to the passage of gravitational waves. In the case of a spatially flat FLRW spacetime filled with a perfect fluid in general relativity, it is known that only tensor perturbations contribute to the memory effect while scalar and vector perturbations do not. In this paper, we show that in the context of scalar-tensor theories, the scalar perturbations associated to the scalar graviton contribute to the memory effect as well. We find that, depending on the mass and coupling, the influence of cosmic expansion on the memory effect due to the scalar perturbations can be either stronger or weaker than the one induced by the tensor perturbations. As a byproduct, in an appendix, we develop a general framework which can be used to study coupled wave equations in any curved spacetime region which admits a foliation by time slices.

Remarks on the cosmological constant appearing as an initial condition for Milne-like spacetimes

Milne-like spacetimes are a class of k = -1 FLRW spacetimes which admit continuous spacetime extensions through the big bang. In a previous paper Ling (Found. of Phys. 50:385–428, 2020), it was shown that the cosmological constant appears as an initial condition for Milne-like spacetimes. In this paper, we generalize this statement to spacetimes which share similar geometrical properties with Milne-like spacetimes but without the strong spatially isotropic assumption associated with them. We show how our results yield a “quasi de Sitter” expansion for the early universe which could have applications to inflationary scenarios.

Unruh-DeWitt detectors in cosmological spacetimes

We analyze the response and thermal behavior of an Unruh-DeWitt detector as it travels through cosmological spacetimes, with special reference to the question of how to define surface gravity and temperature in dynamical spacetimes. Working within the quantum field theory on curved spacetime approximation, we consider a detector as it travels along geodesic and accelerated Kodama trajectories in de Sitter and asymptotically de Sitter FLRW spacetimes. By modelling the temperature of the detector using the detailed-balance form of the Kubo-Martin-Schwinger (KMS) conditions as it thermalizes, we can better understand the thermal behavior of the detector as it interacts with the quantum field, and use this to compare competing definitions of surface gravity and temperature that persist in the literature. These include the approaches of Kodama [Prog. Theor. Phys. 63, 1217 (1980).], Ashtekar and Krishnan [Living Rev. Relativity 7, 10 (2004).], Fodor et al. [Phys. Rev. D 54, 3882 (1996).], and Nielsen [Classical Quantum Gravity 23, 4637 (2006).]. While these are most often examined within the context of a dynamical black hole, here we shift focus to surface gravity on the evolving cosmological horizon.

Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem

The renormalization of the vacuum energy in quantum field theory (QFT) is usually plagued with theoretical conundrums related not only with the renormalization procedure itself, but also with the fact that the final result leads usually to very large (finite) contributions incompatible with the measured value of Lambda in cosmology. As a consequence, one is bound to extreme fine-tuning of the parameters and so to sheer unnaturalness of the result and of the entire approach. We may however get over this adversity using a different perspective. Herein, we compute the zero-point energy (ZPE) for a nonminimally coupled (massive) scalar field in FLRW spacetime using the off-shell adiabatic renormalization technique employed in previous work. The on-shell renormalized result first appears at sixth adiabatic order, so the calculation is rather cumbersome. The general off-shell result yields a smooth function rho _{mathrm{vac}}(H) made out of powers of the Hubble rate and/or of its time derivatives involving different (even) adiabatic orders sim H^N (N=0, 2,4,6,ldots ), i.e. it leads, remarkably enough, to the running vacuum model (RVM) structure. We have verified the same result from the effective action formalism and used it to find the beta -function of the running quantum vacuum. No undesired contributions sim m^4 from particle masses appear and hence no fine-tuning of the parameters is needed in rho _{mathrm{vac}}(H). Furthermore, we find that the higher power sim H^6 could naturally drive RVM-inflation in the early universe. Our calculation also elucidates in detail the equation of state of the quantum vacuum: it proves to be not exactly -1 and is moderately dynamical. The form of rho _{mathrm{vac}}(H) at low energies is also characteristic of the RVM and consists of an additive term (the so-called ‘cosmological constant’) together with a small dynamical component sim nu H^2 (|nu |ll 1). Finally, we predict a slow (sim ln H) running of Newton’s gravitational coupling G(H). The physical outcome of our semiclassical QFT calculation is revealing: today’s cosmic vacuum and the gravitational strength should be both mildly dynamical.

Special cosmological models derived from the semiclassical Einstein equation on flat FLRW space-times

This article presents numerical work on a special case of the cosmological semiclassical Einstein equation (SCE). The SCE describes the interaction of relativistic quantum matter by the expected value of the renormalized stress–energy tensor of a quantum field with classical gravity. Here, we consider a free, massless scalar field with general (not necessarily conformal) coupling to curvature. In a cosmological scenario with flat spatial sections for special choices of the initial conditions, we observe a separation of the dynamics of the quantum degrees of freedom from the dynamics of the scale factor, which extends a classical result by Starobinski (1980 Phys. Lett. B 91 99–102) to general coupling. For this new equation of fourth order governing the dynamics of the scale factor, we study numerical solutions. Typical solutions show a radiation-like Big Bang for the early Universe and de Sitter-like expansion for the late Universe. We discuss a specific solution to the cosmological horizon problem that can be produced by tuning parameters in the given equation. Although the model proposed here only contains massless matter, we give a preliminary comparison of the obtained cosmology with the ΛCDM standard model of cosmology and investigate parameter ranges in which the new models, to a certain extent, is capable of assimilating standard cosmology.

Blow-up of waves on singular spacetimes with generic spatial metrics

We study the asymptotic behaviour of solutions to the linear wave equation on cosmological spacetimes with Big Bang singularities and show that appropriately rescaled waves converge against a blow-up profile. Our class of spacetimes includes Friedman–Lemaître–Robertson–Walker (FLRW) spacetimes with negative sectional curvature that solve the Einstein equations in the presence of a perfect irrotational fluid with p=(gamma -1)rho . As such, these results are closely related to the still open problem of past nonlinear stability of such FLRW spacetimes within the Einstein scalar field equations. In contrast to earlier works, our results hold for spatial metrics of arbitrary geometry, hence indicating that the matter blow-up in the aforementioned problem is not dependent on spatial geometry. Additionally, we use the energy estimates derived in the proof in order to formulate open conditions on the initial data that ensure a non-trivial blow-up profile, for initial data sufficiently close to the Big Bang singularity and with less harsh assumptions for gamma <2.

Small solutions of the Einstein–Boltzmann-scalar field system in a spatially flat FLRW spacetime

The Cauchy problem for the Einstein–Boltzmann-scalar field system is studied. A spatially flat Friedmann-Lemaître-Robertson-Walker spacetime is considered with matter contents described by the relativistic Boltzmann equation for Israel particles and a nonlinear scalar field with an exponential potential. The initial data are assumed to be small in a suitable sense, and we obtain the global existence and asymptotic behavior of small solutions.

Influence of cosmological expansion in local experiments

Whether the cosmological expansion can influence the local dynamics, below the galaxy clusters scale, has been the subject of intense investigations in the past three decades. In this work, we consider McVittie and Kottler spacetimes, embedding a spherical object in a FLRW spacetime. We calculate the influence of the cosmological expansion on the frequency shift of a resonator and estimate its effect on the exchange of light signals between local observers. In passing, we also clarify some of the statements made in the literature.

Gravitational waves from bubble collisions in FLRW spacetime

Stochastic gravitational wave background (SGWB) is a promising tool to probe the very early universe where the standard model of particle physics and cosmology are connected closely. As a possible component of SGWB, gravitational waves (GW) from bubble collisions during the first order cosmological phase transitions deserve comprehensive analyses. In 2017, Ryusuke Jinno and Masahiro Takimoto proposed an elegant analysis approach to derive the analytical expressions of energy spectra of GW from bubble collisions in Minkowski spacetime avoiding large-scale numerical simulations for the first time [26]. However, they neglect the expansion of the universe and regard the duration of phase transitions as infinity in their derivation which could deviate their estimations from true values. For these two reasons, we give a new expression of GW spectra by adopting their method, switching spacetime background to FLRW spacetime, and considering a finite duration of phase transitions. By denoting σ as the fraction of the speed of phase transitions to the expansion speed of the universe, we find when σ is around mathcal{O} (10), the maxima of estimated GW energy spectra drop by around 1 order of magnitude than the results given by their previous work. Even when σ = 100, the maximum of GW energy spectrum is only 65% of their previous estimation. Such a significant decrease may bring about new challenges for the detectability of GW from bubble collisions. Luckily, by comparing new spectra with PLI (power-law integrated) sensitivity curves of GW detectors, we find that the detection prospect for GW from bubble collisions is still promising for DECIGO, BBO, LISA, and TianQin in the foreseeable future.

On Glassey\u2019s conjecture for semilinear wave equations in Friedmann\u2013Lema\xeetre\u2013Robertson\u2013Walker spacetime

Consider nonlinear wave equations in the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes. We show blow-up in finite time of solutions and upper bounds of the lifespan of blow-up solutions to give the FLRW spacetime version of Glassey’s conjecture for the time derivative nonlinearity. We also show blow-up results for the space derivative nonlinear term.

A dynamical system analysis of cosmic evolution with coupled phantom dark energy with dark matter

This work is an example of the application of the dynamical system analysis in the context of cosmology. Here cosmic evolution is considered in the background of homogeneous and isotropic flat FLRW spacetime with interacting dark energy and varying mass dark matter as the matter content. The DE is chosen as phantom scalar field with self-interacting potential while the DM is in the form of dust. The potential of the scalar field and the mass function of dark matter are chosen as exponential or power-law form or in their product form. Using suitable dimensionless variables, the Einstein field equations and the conservation equations constitute an autonomous system. The stability of the nonhyperbolic critical points is analyzed by using center manifold theory. Finally, cosmological phase transitions have been detected through bifurcation analysis which has been done by Poincaré index theory.

Kinemaitcs in spatially flat FLRW spacetimes

The kinematics on spatially flat FLRW spacetimes is presented for the first time in local charts with physical coordinates, i.e., the cosmic time and proper Cartesian space coordinates of Painlevé-type. It is shown that there exists a conserved momentum that determines the form of the covariant four-momentum on geodesics in terms of physical coordinates. Moreover, with the help of this conserved momentum, the peculiar momentum can be defined, thus separating the peculiar and recessional motions without ambiguity. It is shown that the energy and peculiar momentum satisfy the mass-shell condition of special relativity while the recessional momentum does not produce energy. In this framework, the measurements of the kinetic quantities along geodesics performed by different observers are analyzed, pointing out an energy loss of the massive particles similar to that producing the photon redshift. The examples of the kinematics on the de Sitter expanding universe and a new Milne-type spacetime are extensively analyzed.

Understanding the Dyer-Roeder approximation as a consequence of local cancellations of projected shear and expansion rate fluctuations

It is shown with several concrete examples that the Dyer-Roeder approximation is valid in spacetimes which fulfill the condition that fluctuations in the expansion rate along a light ray locally cancels with the shear contribution to the redshift. This is the case for standard cosmological scenarios including perturbed FLRW spacetimes, N-body simulations and Swiss-cheese models. With another concrete example it is then illustrated that it is possible to construct statistically homogeneous and effectively statistically isotropic cosmological models which do not fulfill the condition. In this case, the Dyer-Roeder approximation is invalid. Instead, the mean redshift-distance relation can be described using a relation based on the spatial averages of the transparent part of the spacetime.