Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 2019"

Hamilton’s approach in cosmological inflation with an exponential potential and its observational constraints

Abstract: The Friedmann-Robertson-Walker (FRW) cosmology is analyzed with a general potential $V(\phi)$ in the scalar field inflation scenario. The Bohmian approach (a WKB-like formalism) was employed in order to constraint a generic form of potential to the most suited to drive inflation, from here a family of potentials emerges; in particular we select an exponential potential as the first non trivial case and remains the object of interest of this work. The solution to the Wheeler-DeWitt (WDW) equation is also obtained for the selected potential in this scheme. Using Hamilton’s approach and equations of motion for a scalar field $\phi$ with standard kinetic energy, we find the exact solutions to the complete set of Einstein-Klein-Gordon (EKG) equations without the need of the slow-roll approximation (SR). In order to contrast this model with observational data (Akrami et al. 2018, arXiv:1807.06211 , (Planck Collaboration) results), the inflationary observables: the tensor-to-scalar ratio and the scalar spectral index are derived in our proper time, and then evaluated under the proper condition such as the number of e-folding corresponds exactly at 50–60 before inflation ends. The employed method exhibits a remarkable simplicity with rather interesting applications in the near future.

Direct test of the FLRW metric from strongly lensed gravitational wave observations.

Abstract: The assumptions of large-scale homogeneity and isotropy underly the familiar Friedmann-Lemaitre-Robertson-Walker (FLRW) metric that appears to be an accurate description of our Universe. In this paper, we propose a new strategy of testing the validity of the FLRW metric, based on the galactic-scale lensing systems where strongly lensed gravitational waves and their electromagnetic counterparts can be simultaneously detected. Each strong lensing system creates opportunity to infer the curvature parameter of the Universe. Consequently, combined analysis of many such systems will provide a model-independent tool to test the validity of the FLRW metric. Our study demonstrates that the third-generation ground based GW detectors, like the Einstein Telescope (ET) and space-based detectors, like the Big Bang Observer (BBO), are promising concerning determination of the curvature parameter or possible detection of deviation from the FLRW metric. Such accurate measurements of the FLRW metric can become a milestone in precision GW cosmology.

Quasi-topological Electromagnetism: Dark Energy, Dyonic Black Holes, Stable Photon Spheres and Hidden Electromagnetic Duality

Abstract: We introduce the quasi-topological electromagnetism which is defined to be the squared norm of the topological 4-form $F\wedge F$. A salient property is that its energy-momentum tensor is of the isotropic perfect fluid with the pressure being precisely the opposite to its energy density. It can thus provide a model for dark energy. We study its application in both black hole physics and cosmology. The quasi-topological term has no effect on the purely electric or magnetic Reissner-Nordstrom black holes, the dyonic solution is however completely modified. We find that the dyonic black holes can have four real horizons. For suitable parameters, the black hole can admit as many as three photon spheres, with one being stable. Another intriguing property is that although the quasi-topological term breaks the electromagnetic duality, the symmetry emerges in the on-shell action in the Wheeler-DeWitt patch. In cosmology, we demonstrate that the quasi-topological term alone is equivalent to a cosmological constant, but the model provides a mechanism for the dark energy to couple with other types of matter. We present a concrete example of the quasi-topological electromagnetism coupled to a scalar field that admits the standard FLRW cosmological solutions.

Constant-roll inflation in scalar-tensor gravity

Abstract: We generalize the notion of constant-roll inflation earlier introduced in General Relativity (GR) and $f(R)$ gravity to inflationary models in more general scalar-tensor gravity. A number of novel exact analytic solutions for a FLRW spatially flat cosmological background is found for this case. All forms of the scalar field potential and its coupling to gravity producing the exact de Sitter solution, while the scalar field is varying, are presented. In the particular cases of induced gravity and GR with a non-minimally coupled scalar field, all constant-roll inflationary solutions are found. In the former case they represent power-law inflation, while in the latter case the solution is novel and more complicated. Comparison of scalar perturbations generated during such inflation in induced gravity with observational data shows that the constant-roll parameter should be small, similar to constant-roll inflation in GR and $f(R)$ gravity. Then the solution reduces to the standard slow-roll one with small corrections.

Cosmological Polytopes and the Wavefuncton of the Universe for Light States

Abstract: We extend the investigation of the structure of the late-time wavefunction of the universe to a class of toy models of scalars with time-dependent masses and polynomial couplings, which contains general massive scalars in FRW cosmologies. We associate a universal integrand to each Feynman diagram contributing to the wavefunction of the universe. For certain (light) masses, such an integrand satisfies recursion relations involving differential operators, connecting states with different masses and having, as a seed, the massless scalar (which describes a conformally coupled scalar as a special case). We show that it is a degenerate limit of the canonical form of a generalisation of the cosmological polytopes describing the wavefunction for massless scalars. Intriguingly, the flat-space scattering amplitude appears as a higher codimension face: it is encoding the leading term in the Laurent expansion as the total energy is taken to zero, with the codimension of the face providing the order of the total energy pole. The same connection between the other faces and the Laurent expansion coefficients holds for the other singularities of the wavefunction of the universe, all of them connectable to flat-space processes. As the degenerate limit is taken, some of the singularities of the canonical form of the polytope collapse onto each other generating higher order poles. Finally, we consider the mass as a perturbative coupling, showing that the contribution to the wavefunction coming from graphs with mass two-point couplings can be identified with a degenerate limit of the canonical form of the cosmological polytope, if the perturbative expansion is done around the conformally coupled state; or as double degenerate limit of the canonical form of the extension of the cosmological polytopes introduced in the present paper, if the perturbative expansion is done around minimally coupled states.

Parity violating Friedmann Universes

Abstract: We revisit extensions of the Einstein-Cartan theory where the cosmological constant $\mathrm{\ensuremath{\Lambda}}$ is promoted to a variable, at the cost of allowing for torsion even in the absence of spinors. We remark that some standard notions about Friedmann-Robertson-Walker (FRW) universes collapse in these theories, most notably that spatial homogeneity and isotropy may now coexist with violations of parity invariance. The parity-violating solutions have nonvanishing Weyl curvature even within FRW models. The presence of parity-violating torsion opens up the space of possible such theories with relevant FRW modifications; in particular the Pontryagin term can play an important role even in the absence of spinorial matter. We present a number of parity-violating solutions with and without matter. The former are the non-self-dual vacuum solutions long suspected to exist. The latter lead to tracking and nontracking solutions with a number of observational problems, unless we invoke the Pontryagin term. An examination of the Hamiltonian structure of the theory reveals that the parity-even and the parity-violating solutions belong to two distinct branches of the theory, with different gauge symmetries (constraints) and different numbers of degrees of freedom (d.o.f.). The parity-even branch is nothing but standard relativity with a cosmological constant which has become pure gauge under conformal invariance if matter is absent, or a slave of matter (and so not an independent d.o.f.) if nonconformally invariant matter is present. In contrast, the parity-violating branch contains a genuinely new d.o.f.

Cosmological Implications of the Generalized Entropy Based Holographic Dark Energy Models in Dynamical Chern-Simons Modified Gravity

Abstract: Recently, Tsallis, Renyi, and Sharma-Mittal entropies have widely been used to study the gravitational and cosmological setups. We consider a flat FRW universe with linear interaction between dark energy and dark matter. We discuss the dark energy models using Tsallis, Renyi, and Sharma-Mittal entropies in the framework of Chern-Simons modified gravity. We explore various cosmological parameters (equation of state parameter, squared sound of speed ) and cosmological plane ( , where is the evolutionary equation of state parameter). It is observed that the equation of state parameter gives quintessence-like nature of the universe in most of the cases. Also, the squared speed of sound shows stability of Tsallis and Renyi dark energy model but unstable behavior for Sharma-Mittal dark energy model. The plane represents the thawing region for all dark energy models.

Constraining Cosmological Parameters in the FLRW Metric with Lensed GW+EM Signals

Abstract: We proposed a model-independent method to constrain cosmological parameters using the Distance Sum Rule of the Friedmann–Lemaitre–Robertson–Walker metric by combining the time delay distances and the comoving distances through a multi-messenger approach. The time delay distances are measured from lensed gravitational wave (GW) signals together with their corresponding electromagnetic wave (EM) counterparts, while the comoving distances are obtained from a parameterized fitting approach with independent supernova observations. With a series of simulations based on the Einstein Telescope, Large Synoptic Survey Telescope, and The Dark Energy Survey, we find that only 10 lensed GW+EM systems can achieve the constraining power comparable to and even stronger than 300 lensed quasar systems due to the more precise time delay from lensed GW signals. Specifically, the cosmological parameters can be constrained to and (1σ).5 Our results show that more precise time delay measurements could provide more stringent cosmological parameter values, and lensed GW+EM systems therefore can be applied as a powerful tool in the future precision cosmology.

Cosmology as a CFT$_1$

Abstract: We show that the simplest FLRW cosmological system consisting in the homo- geneous and isotropic massless Einstein-Scalar system enjoys a hidden conformal symmetry under the 1D conformal group SL(2, ℝ) acting as Mobius transformations in proper time. This invariance is made explicit through the mapping of FLRW cosmology onto conformal mechanics. On the one hand, we identify the corresponding conformal Noether charges, as combinations of the Hamiltonian scalar constraint, the extrinsic curvature and the 3D volume, which form a closed 𝔰𝔩 (2, ℝ) Lie algebra. On the other hand, this approach allows to write FLRW cosmology in terms of a AdS2 phase space and a Schwarzian action. Preserving this conformal structure at the quantum level fixes the ordering ambiguities in the Wheeler-de Witt quantization and allows to formulate FLRW quantum cosmology as a CFT1. We show that the CFT two-points correlator is realized as the overlap of the evolution in proper time of cosmological coherent wave-packets. In particular, the two-points function is built from a vacuum state which, although not conformally invariant, coincides with the cosmological vacuum annihilated by the scalar constraint. These results suggest new perspectives in classical and quantum cosmology, among which the possibility to apply the conformal bootstrap program to quantize cosmological backgrounds.

Propagation of polar gravitational waves in f(R, T) scenario

Abstract: This paper investigates the propagation of polar gravitational waves in the spatially flat FRW universe consisting of a perfect fluid in the scenario of $$R+2\lambda T$$ model of f(R, T) gravity ( $$\lambda $$ being the model parameter). The spatially flat universe model is perturbed via Regge–Wheeler perturbations inducing polar gravitational waves and the field equations are formulated for both unperturbed as well as perturbed spacetimes. We solve these field equations simultaneously for the perturbation parameters introduced in the metric, matter, and velocity in the radiation, as well as dark energy, dominated phases. It is found that the polar gravitational waves can produce changes in the background matter distribution as well as velocity components in the radiation era similar to general relativity case. Moreover, we have discussed the impact of model parameter on the amplitude of gravitational waves.

de Sitter, α′-corrections & duality invariant cosmology

Abstract: Demanding O(d,d)-duality covariance, Hohm and Zwiebach have written down the action for the most general cosmology involving the metric, b-field and dilaton, to all orders in α' in the string frame. Remarkably, for an FRW metric-dilaton ansatz the equations of motion turn out to be quite simple, except for the presence of an unknown function of a single variable. If this unknown function satisfies some simple properties, it allows de Sitter solutions in the string frame. In this note, we write down the Einstein frame analogues of these equations, and make some observations that make the system tractable. Perhaps surprisingly, we find that a necessary condition for de Sitter solutions to exist is that the unknown function must satisfy a certain second order non-linear ODE. The solutions of the ODE do not have a simple power series expansion compatible with the leading supergravity expectation. We discuss possible interpretations of this fact. After emphasizing that all (potential) string and Einstein frame de Sitter solutions have a running dilaton, we write down the most general cosmologies with a constant dilaton in string/Einstein frame: these have power law scale factors.

Fakeons and the classicization of quantum gravity: the FLRW metric

Abstract: Under certain assumptions, it is possible to make sense of higher derivative theories by quantizing the unwanted degrees of freedom as fakeons, which are later projected away. Then the true classical limit is obtained by classicizing the quantum theory. Since quantum field theory is formulated perturbatively, the classicization is also perturbative. After deriving a number of properties in a general setting, we consider the theory of quantum gravity that emerges from the fakeon idea and study its classicization, focusing on the FLRW metric. We point out cases where the fakeon projection can be handled exactly, which include radiation, the vacuum energy density and the combination of the two, and cases where it cannot, which include dust. Generically, the classical limit shares many features with the quantum theory it comes from, including the impossibility to write down complete, “exact” field equations, to the extent that asymptotic series and nonperturbative effects come into play.

Gravity in mimetic scalar-tensor theories after GW170817

Abstract: We derive the most general mimetic scalar-tensor theory assuming a healthy "seed" action and accounting for the constraints on the speed of gravitational-wave propagation arising from the GW170817 event. By analysing linear perturbations around a flat FLRW background in this model, we obtain a suitable form of the Poisson equation, which allows us to calculate the effective gravitational constant felt by "ordinary" matter. By restricting to a minimally coupled model, such an effective gravitational constant is equivalent to that obtained within General Relativity, with cold dark matter plus a perfect fluid dark energy component, with vanishing sound speed. Assuming, further, a $\Lambda$CDM background, the effective gravitational constant cannot be distinguished from that of the standard $\Lambda$CDM model, at linear order. For the full non-minimally coupled mimetic gravity model we obtain a non-vanishing gravitational slip and an effective gravitational constant which always differs from that of standard $\Lambda$CDM.

de Sitter, $\alpha'$-Corrections & Duality Invariant Cosmology

Abstract: Demanding $O(d,d)$-duality covariance, Hohm and Zwiebach have written down the action for the most general cosmology involving the metric, $b$-field and dilaton, to all orders in $\alpha'$ in the string frame. Remarkably, for an FRW metric-dilaton ansatz the equations of motion turn out to be quite simple, except for the presence of an unknown function of a single variable. If this unknown function satisfies some simple properties, it allows de Sitter solutions in the string frame. In this note, we write down the Einstein frame analogues of these equations, and make some observations that make the system tractable. Perhaps surprisingly, we find that a necessary condition for de Sitter solutions to exist is that the unknown function must satisfy a certain second order non-linear ODE. The solutions of the ODE do not have a simple power series expansion compatible with the leading supergravity expectation. We discuss possible interpretations of this fact. After emphasizing that all (potential) string and Einstein frame de Sitter solutions have a running dilaton, we write down the most general cosmologies with a constant dilaton in string/Einstein frame: these have power law scale factors.

Constant-roll inflation in scalar-tensor gravity

Abstract: We generalize the notion of constant-roll inflation earlier introduced in General Relativity (GR) and $f(R)$ gravity to inflationary models in more general scalar-tensor gravity. A number of novel exact analytic solutions for a FLRW spatially flat cosmological background is found for this case. All forms of the scalar field potential and its coupling to gravity producing the exact de Sitter solution, while the scalar field is varying, are presented. In the particular cases of induced gravity and GR with a non-minimally coupled scalar field, all constant-roll inflationary solutions are found. In the former case they represent power-law inflation, while in the latter case the solution is novel and more complicated. Comparison of scalar perturbations generated during such inflation in induced gravity with observational data shows that the constant-roll parameter should be small, similar to constant-roll inflation in GR and $f(R)$ gravity. Then the solution reduces to the standard slow-roll one with small corrections.

Late-time cosmic acceleration from compactification

Abstract: We investigate the implications of energy conditions on cosmological compactification solutions of the higher-dimensional Einstein field equations. It is known that the strong energy condition forbids time-independent compactifications to de Sitter space but allows time-dependent compactifications to other (homogeneous and isotropic) expanding universes that undergo a transient period of acceleration. Here we show that the same assumptions allow compactification to FLRW universes undergoing late-time accelerated expansion; the late-time stress tensor is a perfect fluid but with a lower bound on the pressure/energy-density ratio that excludes de Sitter but allows accelerated power-law expansion. The compact space undergoes a decelerating expansion that leads to decompactification, but on an arbitrarily long timescale.

Cosmology in mimetic SU(2) gauge theory

Abstract: It is well known that the standard scalar field mimetic cosmology provides a dark matter-like energy density component. Considering SU(2) gauge symmetry, we study the gauge field extension of the mimetic scenario in spatially flat and curved FLRW spacetimes. Because of the mimetic constraint, the standard Yang-Mills term plays the role of the cosmological constant while the mimetic term provides two different contributions: one is the standard radiation scaling like a−4 while the other contribution in energy density scales as ∝ a−2. Consequently, in the Friedmann equation we have two different energy densities which scale as ∝ a−2: one is the mimetic spatial curvature-like and the other is the standard spatial curvature which can compete with each other. The degeneracy between these two contributions are disentangled in this scenario since the mimetic spatial curvature-like term shows up only at the dynamical level while the standard spatial curvature term shows up at both dynamical and kinematical levels.

Propagation of Polar Gravitational Waves in f(R,T) Scenario

Abstract: This paper investigates the propagation of polar gravitational waves in the spatially flat FRW universe consisting of a perfect fluid in the scenario of $R+2\lambda T$ model of $f(R,T)$ gravity ($\lambda$ being the model parameter). The spatially flat universe model is perturbed via Regge-Wheeler perturbations inducing polar gravitational waves and the field equations are formulated for both unperturbed as well as perturbed spacetimes. We solve these field equations simultaneously for the perturbation parameters introduced in the metric, matter, and velocity in the radiation, as well as dark energy, dominated phases. It is found that the polar gravitational waves can produce changes in the background matter distribution as well as velocity components in the radiation era similar to general relativity case. Moreover, we have discussed the impact of model parameter on the amplitude of gravitational waves.

Reduced Lagrangians and analytic solutions in Einstein-æther cosmology

Abstract: We present the solution space of the field equations in the Einstein-aether theory for the case of a FLRW and a locally rotationally symmetric (LRS) Bianchi type III space-time. We also find that there are portions of the initial parameters space for which no solution is admitted by the reduced equations. The reduced Lagrangians deduced from the full action are, in general, correctly describing the dynamics whenever solutions do exist. Finally in the FLRW case a curvature singularity exists, while in the type III there are choices of the range of parametres for which there is no curvature singularity.

Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model

Abstract: We discuss a $(3{+}1)$-dimensional covariant quantum space-time describing a FLRW cosmology with Big Bounce, obtained by a projection of the fuzzy hyperboloid $H^4_n$. This provides a background solution of the IKKT matrix model with mass term. We characterize the bosonic fluctuation spectrum, which consists of a tower of higher-spin modes, truncated at $n$. The modes are organized in terms of an underlying $SO(4,2)$ structure group, which is broken to the $SO(3,1)$ isometry of the background. The resulting higher-spin gauge theory includes all degrees of freedom required for gravity, and should be well suited for quantization. All modes propagate with the same speed of light, even though local boost invariance is not manifest. The propagating metric perturbation modes comprise those of a massless graviton, as well as a scalar mode. Gauge invariance allows to obtain the analog of the linearized Einstein-Hilbert action, which is expected to be induced upon quantization.

Bouncing unitary cosmology I. Mini-superspace general solution

Abstract: We offer a new proposal for cosmic singularity resolution based upon a quantum cosmology with a unitary bounce. This proposal is illustrated via a novel quantization of a mini-superspace model in which there can be superpositions of the cosmological constant. This possibility leads to a finite, bouncing unitary cosmology. Whereas the usual Wheeler–DeWitt cosmology generically displays pathological behaviour in terms of non-finite expectation values and non-unitary dynamics, the finiteness and unitarity of our model are formally guaranteed. For classically singular models with a massless scalar field and cosmological constant, we show that well-behaved quantum observables can be constructed and generic solutions to the universal Schrodinger equation are singularity-free. Key features of the solutions of our model include a cosmic bounce due to quantum gravitational effects, a well-defined FLRW limit far from the bounce, and a super-inflationary epoch in the intermediate region. Furthermore, our model displays novel features including: i) superpositions of values of the cosmological constant; ii) a non-zero scattering length around the big bounce; and iii) bound ‘Efimov universe’ states for negative cosmological constant. The last feature provides a new platform for quantum simulation of the early universe. A companion paper provides detailed interpretation and analysis of particular cosmological solutions.

Cosmological aspects of sound speed parameterizations in fractal universe

Abstract: In the framework of fractal universe, the unified models of dark energy and dark matter are being presented with the background of homogenous and isotropic FLRW geometry. The aspects of fractal cosmology helps in better understanding of the universe in different dimensions. Relationship between the squared speed of the sound and the equation of state parameter is the key feature of these models. We have used constant as well as variable forms of speed of sound and express it as a function of equation of state parameter. By utilizing the four different forms of speed of sound, we construct the energy densities and pressures for these models and then various cosmological parameters like hubble parameter, EoS parameter, deceleration parameter and Om- diagnostic are investigated. Graphical analysis of these parameters show that in most of the cases EoS parameters and trajectories of Om-diagnostic corresponds to the quintessence like nature of the universe and the deceleration parameters represent accelerated and decelerated phase. In the end, we remark that cosmological analysis of these models indicates that these models correspond to different well known dark energy models.

Charged vector inflation

Abstract: We present a model of inflation in which the inflaton field is charged under a triplet of $U(1)$ gauge fields. The model enjoys an internal $O(3)$ symmetry supporting the isotropic FRW solution. With an appropriate coupling between the gauge fields and the inflaton field, the system reaches an attractor regime in which the gauge fields furnish a small constant fraction of the total energy density. We decompose the scalar perturbations into the adiabatic and entropy modes and calculate the contributions of the gauge fields into the curvature perturbations power spectrum. We also calculate the entropy power spectrum and the adiabatic-entropy cross-correlation. In addition to the metric tensor perturbations, there are tensor perturbations associated with the gauge field perturbations that are coupled to metric tensor perturbations. We show that the correction in the primordial gravitational tensor power spectrum induced from the matter tensor perturbation is a sensitive function of the gauge coupling.

Quantum-gravity effects for excited states of inflationary perturbations

Abstract: We generalize former findings regarding quantum-gravitational corrections arising from a canonical quantization of a perturbed Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) universe during inflation by considering an initial state for the scalar and tensor perturbations that generalizes the adiabatic vacuum state and allows us to consider the scenario that the perturbation modes start their evolution in an excited state. Our result shows that the quantum-gravitationally corrected power spectra get modified by prefactors including the excitation numbers.

Constraining cosmological parameters in FLRW metric with lensed GW+EM signals

Abstract: We proposed a model-independent method to constrain the cosmological parameters using the Distance Sum Rule of the FLRW metric by combining the time delay distances and the comoving distances through a multi-messenger approach. The time delay distances are measured from lensed gravitational wave~(GW) signals together with their corresponding electromagnetic wave~(EM) counterpart, while the comoving distances are obtained from a parametrized fitting approach with independent supernova observations. With a series of simulations based on Einstein Telescope, Large Synoptic Survey Telescope and The Dark Energy Survey, we find that only 10 lensed GW+EM systems can achieve the constraining power comparable to and even stronger than 300 lensed quasar systems due to more precise time delay from lensed GW signals. Specifically, the cosmological parameters can be constrained to ~$k=0.01_{-0.05}^{+0.05}$ and ~$H_0=69.7_{-0.35}^{+0.35}$ (1$\sigma$). Our results show that more precise time delay measurements could provide more stringent cosmological parameter values, and lensed GW+EM systems therefore can be applied as a powerful tool in the future precision cosmology.