Gravitational Coupling Research Articles

Preserving quantum information in f(Q) non-metric gravity cosmology

The effects of cosmological expansion on quantum bosonic states are investigated, using quantum information theory. In particular, a generic Bogoliubov transformation of bosonic field modes is considered and the state change on a single mode is regarded as the effect of a quantum channel. Properties and capacities of this channel are thus explored in the framework of f(Q) non-metric gravity. The reason is that non-metric gravity can be considered under the standard of gauge theories with all the advantages of such a formulation. As immediate result, we obtain that the information on a single-mode state appears better preserved, whenever the number of particles produced by the cosmological expansion is small. Specifically, we investigate a power law f(Q) model, leaving unaltered the effective gravitational coupling, and minimise the corresponding particle production. We thus show how to optimise the preservation of classical and quantum information, stored in bosonic mode states in the remote past. Finally, we compare our findings with those obtained in General Relativity.

Cooling-heating properties of the FRW universe in gravity with a generalized conformal scalar field

In this paper, within the framework of modified gravity involving a conformal scalar field, we investigate the Joule-Thomson expansion of the Friedmann-Robertson-Walker (FRW) universe to identify cooling and heating regions. We observe a divergence in the Joule-Thomson coefficient (μ), precisely at the apparent horizon (RA=−2α) of the FRW universe, under conditions of negative gravitational coupling (α<0), which aligns with a thermodynamic singularity. Furthermore, we determine the inversion temperature and pressure for the FRW universe, and elucidate the salient features of inversion and isenthalpic curves in the temperature-pressure (T-P) plane. We compare these findings with results obtained under Einstein gravity, discussing the influence of the modification term on the cooling and heating properties of the FRW universe. This work presents insights into the formation of cooling and heating regions within the FRW universe, contributing to a deeper understanding of the physical mechanisms behind cosmic expansion history.

Theory of interacting vector dark energy and fluid

In this work, we study interaction between dark energy and dark matter, where dark energy is described by a massive vector field, and dark matter is modelled as a fluid. We present a new interaction term, which affects only perturbations and can give interesting phenomenology. Then we present a general Lagrangian for the interacting vector dark energy with dark matter. For the dark energy, we choose Proca theory with G 3 term to study its phenomenological consequence. For this model, we explore both background and perturbation dynamics. We also present the no-ghost condition for tensor modes, vector modes and scalar modes. Subsequently, we also study the evolution of the overdensities of both baryon and cold dark matter in the high-k limit. We show that the effective gravitational coupling is modified for cold dark matter and baryon. We also choose a simple concrete model and numerically show a suppression of the effective gravitational coupling for cold dark matter. However, in this simple model, the suppression of the effective gravitational coupling does not result in a suppression of the matter overdensity compared to that in the ΛCDM model due to the modified background expansion.

A universe from a Lagrangian fixed point

In this paper, we investigate the theoretical possibility that a Lagrangian fixed point, when applied to cosmological models, can drive dynamical evolution towards a bouncing universe. We analyze the physics of a Lagrangian fixed point within the context of a gravitational average effective action featuring scale-dependent couplings. To explore this concept, we develop a toy model set in a four-dimensional, spatially flat spacetime, anchored by a Lagrangian fixed point. Solving the cosmological equations of this model analytically, we identify several non-trivial solution branches. These branches are characterized by a modified scale factor and dynamic gravitational couplings, offering new insights into the behavior of cosmological models under these conditions.

Circular motion and QPOs near black holes in Kalb–Ramond gravity

General relativity (GR) theory modifications include different scalar, vector, and tensor fields with non-minimal gravitational coupling. Kalb–Ramond (KR) gravity is a modified theory formulated based on the presence of the bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BHs) using observational data. In the present work, we aimed to test KR gravity through theoretical studies of epicyclic frequencies of particle oscillations using quasi-periodic oscillation (QPO) frequency data from microquasars. First, we derive equations of motion and analyze the effective potential for circular orbits. Also, we studied the energy and angular momentum of particles corresponding to circular orbits. In addition, we analyze the stability of circular orbits. It is shown that the radius of the innermost stable circular orbits is inversely proportional to the KR parameter. We are also interested in how the energy and angular momentum of test particles at ISCO behave around the KR BHs. We found that the Keplerian frequency for the test particles in KR gravity is the same as that in GR. Finally, we study the QPOs by applying epicyclic oscillations in the relativistic precession (RP), warped disc (WD), and epicyclic resonance (ER) models. We also analyze QPO orbits in the resonance cases of upper and lower frequencies 3:2, 4:3, and 5:4 in the QPO as mentioned above models. We obtain constraints on the KR gravity parameter and BH mass using a Monte Carlo Markov Chain simulation in the multidimensional parameter space for the microquasars GRO J1655-40 & XTE J1550-564, M82 X-1, and Sgr A*.

Model on picometer-level light gravitational delay in the GRACE Follow-On-Like missions

Abstract Laser interferometry plays a crucial role for laser ranging in high-precision space missions such as GRACE (Gravity Recovery and Climate Experimen) Follow-On-Like missions and gravitational wave detectors. For such accuracy of modern space missions, a precise relativistic model of light propagation is requires. With the post-Newtonian approximation, we utilize the Synge world function method to study the light propagation in the Earth’s gravitational field, deriving the gravitational delays up to order c -4. Then, we investigate the influences of gravitational delays in the three inter-satellite laser ranging techniques, including one-way ranging, dual one-way ranging, and transponder-based ranging. By combining the parameters of Kepler orbit, the gravitational delays are expanded up to the order of e 2 (e is the orbital eccentricity). Finally, considering the GRACE Follow-On-Like missions, we estimate the gravitational delays to the level of picometer. The results demonstrate some high-order gravitational and coupling effects, such as c -4-order gravitational delays and coupling of Shapiro and beat frequency, may be non-negligible for higher precision laser ranging in the future.

Molecular clouds as hubs in spiral galaxies: gas inflow and evolutionary sequence

ABSTRACT We decomposed the molecular gas in the spiral galaxy NGC 628 (M74) into multiscale hub-filament structures using the CO (2$-$1) line by the dendrogram algorithm. All leaf structures as potential hubs were classified into three categories, i.e. leaf-HFs-A, leaf-HFs-B and leaf-HFs-C. Leaf-HFs-A exhibit the best hub-filament morphology, which also have the highest density contrast, the largest mass and the lowest virial ratio. We employed the filfinder algorithm to identify and characterize filaments within 185 leaf-HFs-A structures, and fitted the velocity gradients around the intensity peaks. Measurements of velocity gradients provide evidence for gas inflow within these structures, which can serve as a kinematic evidence that these structures are hub-filament structures. The numbers of the associated 21 μm and H α structures and the peak intensities of 7.7 μm, 21 μm, and H α emissions decrease from leaf-HFs-A to leaf-HFs-C. The spatial separations between the intensity peaks of CO and 21 μm structures of leaf-HFs-A are larger than those of leaf-HFs-C. These evidence indicate that leaf-HFs-A are more evolved than leaf-HFs-C. There may be an evolutionary sequence from leaf-HFs-C to leaf-HFs-A. Currently, leaf-HFs-C lack a distinct gravitational collapse process that would result in a significant density contrast. The density contrast can effectively measure the extent of the gravitational collapse and the depth of the gravitational potential of the structure which, in turn, shapes the hub-filament morphology. Combined with the kinematic analysis presented in previous studies, a picture emerges that molecular gas in spiral galaxies is organized into network structures through the gravitational coupling of multiscale hub-filament structures. Molecular clouds, acting as knots within these networks, serve as hubs, which are local gravitational centres and the main sites of star formation.

Early stages of gap opening by planets in protoplanetary discs

ABSTRACT Annular substructures in protoplanetary discs, ubiquitous in sub-mm observations, can be caused by gravitational coupling between a disc and its embedded planets. Planetary density waves inject angular momentum into the disc leading to gap opening only after travelling some distance and steepening into shocks (in the absence of linear damping); no angular momentum is deposited in the planetary co-orbital region, where the wave has not shocked yet. Despite that, simulations show mass evacuation from the co-orbital region even in inviscid discs, leading to smooth double-trough gap profiles. Here, we consider the early time-dependent stages of planetary gap opening in inviscid discs. We find that an often-overlooked contribution to the angular momentum balance caused by the time-variability of the specific angular momentum of the disc fluid (caused, in turn, by the time-variability of the radial pressure support) plays a key role in gap opening. Focusing on the regime of shallow gaps with depths of $\lesssim 20~{{\ \rm per\ cent}}$, we demonstrate analytically that early gap opening is a self-similar process, with the amplitude of the planet-driven perturbation growing linearly in time and the radial gap profile that can be computed semi-analytically. We show that mass indeed gets evacuated from the co-orbital region even in inviscid discs. This evolution pattern holds even in viscous discs over a limited period of time. These results are found to be in excellent agreement with 2D numerical simulations. Our simple gap evolution solutions can be used in studies of dust dynamics near planets and for interpreting protoplanetary disc observations.

Discrete Z4 Symmetry in Quantum Gravity

We consider the discrete Z4 symmetry i^, which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter—the vacuum expectation value of the bilinear combination of fermionic operators. Under this symmetry operation, i^, the emerging tetrads are multiplied by the imaginary unit, i^eμa=−ieμa. The existence of such symmetry and the spontaneous breaking of this symmetry are also supported by the consideration of the symmetry breaking scheme in the topological superfluid 3He-B. The order parameter in 3He-B is also the bilinear combination of the fermionic operators. This order parameter is the analog of the tetrad field, but it has complex values. The i^-symmetry operation changes the phase of the complex order parameter by π/2, which corresponds to the Z4 discrete symmetry in quantum gravity. We also considered the alternative scenario of the breaking of this Z4 symmetry, in which the i^-operation changes sign of the scalar curvature, i^R=−R, and thus the Einstein–Hilbert action violates the i^-symmetry. In the alternative scenario of symmetry breaking, the gravitational coupling K=1/16πG plays the role of the order parameter, which changes sign under i^-transformation.

Analytical QNMs of fields of various spin in the Hayward spacetime

By employing an expansion in terms of the inverse multipole number, we derive analytic expressions for the quasinormal modes (QNMs) of scalar, Dirac and Maxwell perturbations in the Hayward black hole (BH) background. The metric has three interpretations: as a model for a radiating BH, as a quantum-corrected BH owing to the running gravitational coupling in the Asymptotically Safe Gravity, and as a BH solution in the Effective Field Theory. We show that the obtained compact analytical formulas approximate QNMs with remarkable accuracy for ℓ > 0.

Emergence of negative mass in general relativity

We investigate a symmetric traversable wormhole model, integrating Einstein’s gravitational coupling phantom field and a nonlinear electromagnetic field. This work indicates the emergence of negative ADM mass within a specific parameter range, coinciding with distinct alterations in the wormhole’s spacetime properties. Despite violating the Null Energy Condition (NEC) and other energy conditions, the solution exhibits unique characteristics in certain energy-momentum tensor components, potentially accounting for the manifestation of negative mass.

Perturbative quantum evolution of the gravitational state and dressing in general backgrounds

This paper sets up a perturbative treatment of the evolving quantum state of a gravitational system, in a Schrödinger-like picture, working about a general background. This connects gauge symmetry, the constraints, gravitational dressing, and evolution. Starting with a general time slicing, we give a simple derivation of the relation between the constraints, the Hamiltonian, and its well-known boundary term. Among different approaches to quantization with constraints, we focus on a “gauge-invariant canonical quantization,” which is developed perturbatively in the gravitational coupling. The leading-order solution of the constraints (including the Wheeler-DeWitt equation) for perturbations about the background is given in terms of an explicit construction of gravitational dressings built using certain generalized Green’s functions; different such dressings corresponding to adding propagating gravitational waves to a particular solution of the constraints. Dressed operators commute with the constraints, expressing their gauge invariance, and have an algebraic structure differing significantly from the undressed operators of the underlying field theory. These operators can act on the vacuum to create dressed states, and evolution of general such states is then generated by the boundary Hamiltonian, and alternately may be characterized using other relational observables. This provides a concrete approach to studying perturbative time evolution, including the leading gravitational backreaction, of quantum states of black holes with flat or anti–de-Sitter asymptotics, for example on horizon-crossing slices. This description of evolution in turn provides a starting point for investigating possibly important corrections to quantum evolution, that go beyond quantized general relativity. Published by the American Physical Society 2024

Thermodynamics and Decay of de Sitter Vacuum

We discuss the consequences of the unique symmetry of de Sitter spacetime. This symmetry leads to the specific thermodynamic properties of the de Sitter vacuum, which produces a thermal bath for matter. de Sitter spacetime is invariant under the modified translations, r→r−eHta, where H is the Hubble parameter. For H→0, this symmetry corresponds to the conventional invariance of Minkowski spacetime under translations r→r−a. Due to this symmetry, all the comoving observers at any point of the de Sitter space perceive the de Sitter environment as the thermal bath with temperature T=H/π, which is twice as large as the Gibbons–Hawking temperature of the cosmological horizon. This temperature does not violate de Sitter symmetry and, thus, does not require the preferred reference frame, as distinct from the thermal state of matter, which violates de Sitter symmetry. This leads to the heat exchange between gravity and matter and to the instability of the de Sitter state towards the creation of matter, its further heating, and finally the decay of the de Sitter state. The temperature T=H/π determines different processes in the de Sitter environment that are not possible in the Minkowski vacuum, such as the process of ionization of an atom in the de Sitter environment. This temperature also determines the local entropy of the de Sitter vacuum state, and this allows us to calculate the total entropy of the volume inside the cosmological horizon. The result reproduces the Gibbons–Hawking area law, which is attributed to the cosmological horizon, Shor=4πKA, where K=1/(16πG). This supports the holographic properties of the cosmological event horizon. We extend the consideration of the local thermodynamics of the de Sitter state using the f(R) gravity. In this thermodynamics, the Ricci scalar curvature R and the effective gravitational coupling K are thermodynamically conjugate variables. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon remains the same but with the gravitational coupling K=df/dR. Such a connection takes place only in the 3+1 spacetime, where there is a special symmetry due to which the variables K and R have the same dimensionality. We also consider the lessons from de Sitter symmetry for the thermodynamics of black and white holes.

Next-to-eikonal corrected double graviton dressing and gravitational wave observables at OG2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({G}^2\\right) $$\\end{document}

Following a recent proposal to describe inelastic eikonal scattering processes in terms of gravitationally dressed elastic eikonal amplitudes, we motivate a collinear double graviton dressing and investigate its properties. This is derived from a generalized Wilson line operator in the worldline formalism by integrating over fluctuations of the eikonal trajectories of external particles in gravitationally interacting theories. The dressing can be expressed as a product of exponential terms — a coherent piece with contributions to all odd orders in the gravitational coupling constant and a term quadratic in graviton modes, with the former providing classical gravitational wave observables. In particular, the coherent dressing involves Oκ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\kappa}^3\\right) $$\\end{document} subleading double graviton corrections to the Weinberg soft factor. We use this dressing to derive expressions for the waveform, radiative momentum spectrum and angular momentum. In a limiting case of the waveform, we derive the nonlinear memory effect resulting from the emission of nearly soft gravitons from a scattering process.

Hierarchical hub-filament structures and gas inflows on galaxy-cloud scales

Abstract We investigated the kinematics and dynamics of gas structures on galaxy-cloud scales in two spiral galaxies NGC5236 (M83) and NGC4321 (M100) using CO (2–1) line. We utilized the FILFINDER algorithm on integrated intensity maps for the identification of filaments in two galaxies. Clear fluctuations in velocity and density were observed along these filaments, enabling the fitting of velocity gradients around intensity peaks. The variations in velocity gradient across different scales suggest a gradual and consistent increase in velocity gradient from large to small scales, indicative of gravitational collapse, something also revealed by the correlation between velocity dispersion and column density of gas structures. Gas structures at different scales in the galaxy may be organized into hierarchical systems through gravitational coupling. All the features of gas kinematics on galaxy-cloud scale are very similar to that on cloud-clump and clump-core scales studied in previous works. Thus, the interstellar medium from galaxy to dense core scales presents multi-scale/hierarchical hub-filament structures. Like dense core as the hub in clump, clump as the hub in molecular cloud, now we verify that cloud or cloud complex can be the hub in spiral galaxies. Although the scaling relations and the measured velocity gradients support the gravitational collapse of gas structures on galaxy-cloud scales, the collapse is much slower than a pure free-fall gravitational collapse.

Asymptotically safe cosmology with non-canonical scalar field

We investigate the quantum modified cosmological dynamical equations in a Friedmann–Lemaître–Robertson–Walker universe filled with a barotropic fluid and a general non-canonical scalar field characterized by a Lagrangian similar to k-essence model but with a potential term. Quantum corrections are incorporated by considering the running of the gravitational and potential couplings, employing the functional renormalization group approach. Covariant conservation of the non-canonical scalar field and the background barotropic fluid is considered separately, imposing a constraint resulting from the Bianchi identity. This constraint determines the evolution of the cut-off scale with the scale factor and also reveals the cosmic fixed points, depending on whether the flow ceases or continues to evolve. We explore how the general non-canonical scalar field parameter affects the different types of cosmic fixed points and how it differs from the canonical case. Furthermore, we establish a bound on the ratio of the renormalization group parameters involving the non-canonical parameter for which the universe may exhibit accelerated expansion for mixed fixed points. This bound indicates the non-canonical scalar field includes larger sets of asymptotically safe renormalization group fixed point which may give rise to an accelerated universe.

Gravitational spin-orbit coupling through the third-subleading post-Newtonian order: Exploring spin-gauge flexibility

Gravitational spin-orbit coupling through the third-subleading post-Newtonian order: Exploring spin-gauge flexibility

De Sitter Local Thermodynamics in f(R) Gravity

We consider the local thermodynamics of the de Sitter state in the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\mathcal{R})$$\\end{document} gravity. The local temperature, which is the same for all points of the de Sitter space, is \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = H{\ ext{/}}\\pi $$\\end{document}, where H is the Hubble parameter. It is twice larger than the Gibbons–Hawking temperature of the cosmological horizon, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{T}_{{{\ ext{GH}}}}} = H{\ ext{/}}2\\pi $$\\end{document}. The local temperature is not related to the cosmological horizon. It determines the rate of the activation processes, which are possible in the de Sitter environment. The typical example is the process of the ionization of the atom in the de Sitter environment, which rate is determined by temperature \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = H{\ ext{/}}\\pi $$\\end{document}. The local temperature determines the local entropy of the de Sitter vacuum state, and this allows to calculate the total entropy inside the cosmological horizon. The result reproduces the Gibbons–Hawking area law, which corresponds to the Wald entropy, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{S}_{{{\ ext{hor}}}}} = 4\\pi KA$$\\end{document}. Here, K is the effective gravitational coupling, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K = df{\ ext{/}}d\\mathcal{R}$$\\end{document}. In the local thermodynamic approach, K is the thermodynamic variable, which is conjugate to the Ricci scalar curvature \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{R}$$\\end{document}. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon supports the suggestion that the de Sitter quantum vacuum is characterized by the local thermodynamics with the local temperature \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = H{\ ext{/}}\\pi $$\\end{document}. The local temperature \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = H{\ ext{/}}\\pi $$\\end{document} of the de Sitter vacuum suggests that the de Sitter vacuum is locally unstable towards the creation of matter and its further heating. The decay of the de Sitter vacuum due to such processes determines the quantum breaking time of the space-times with positive cosmological constant.

Probing Weyl-type [formula omitted] gravity: Cosmological implications and constraints

In this paper, we investigate the cosmological implications and constraints of Weyl-type f(Q,T) gravity. This theory introduces a coupling between the non-metricity Q and the trace T of the energy–momentum tensor, using the principles of proper Weyl geometry. In this geometry, the scalar non-metricity Q, which characterizes the deviations from Riemannian geometry, is expressed in its standard Weyl form ∇μgαβ=−wμgαβ and is determined by a vector field wμ. To study the implications of this theory, we propose a deceleration parameter with a single unknown parameter χ, which we constrain by using the latest cosmological data. By solving the field equations derived from Weyl-type f(Q,T) gravity, we aim to understand the behavior of the energy conditions within this framework. In the present work, we consider two well-motivated forms of the function f(Q,T): (i) the linear model represented by f(Q,T)=αQ+β6κ2T, and (ii) the coupling model represented by f(Q,T)=γ6H02κ2QT, where α, β, and γ are free parameters. Here, κ2=116πG represents the gravitational coupling constant. In both of the models considered, the strong energy condition is violated, indicating consistency with the present accelerated expansion. However, the null, weak, and dominant energy conditions are satisfied in these models.

C=Anything and the switchback effect in Schwarzschild-de Sitter space

We investigate observables within the framework of the codimension-one C=Anything (CAny) proposal for Schwarzschild-de Sitter (SdS) space under the influence of shockwave sources. Within the proposal, there is a set of time-reversal invariant observables that display the same rate of growth at early and late times for a background with or without shockwave sources. Once we introduce shockwaves in the weak gravitational coupling regime, there is a decrease in the late-time complexity growth due to cancellations with early-time perturbations, known as the switchback effect. The result shows that some CAny observables in SdS may reproduce the same type of behavior found in anti-de Sitter black holes. We comment on how our results might guide us to new explorations in the putative quantum mechanical theory.