Search Results (50)

This paper presents a further step in the development of scale invariant fully conformal cosmology (FCC), formulated in our previous study. Whereas the previous paper focused mainly on the global cosmological consequences of the fully conformal metric and their confrontation with selected astrophysical data, here we analyze its local gravitational and background consequences. On the background of the fully conformal metric we formulate an effective generalization of the weak Schwarzschild field in the corresponding FCC global coordinates and derive from it the associated modified intensity of the Newtonian central field. We further derive the cosmological state/constitutive equation p = − ε/3 as a direct consequence of the fully conformal metric rather than as an ad hoc additional postulate. Likewise, within the fully conformal metric, spatial flatness and the critical density ρ_crit are understood as direct consequences of this metric structure rather than as independently postulated inputs. From the condition of global equilibrium between negative cosmological pressure and the gravitational cohesive pressure of homogeneously distributed matter, the effective particulate fraction is obtained as β ≈ 0.45 of the total critical density ρ_crit. For the relatively well-confirmed baryonic matter fraction ${\overline{\mathrm{\Omega }}}^{bar} \approx 0.05$, this stable-equilibrium condition then leads to the corresponding particulate fraction of collisionless dark matter ${\overline{\mathrm{\Omega }}}_{FCC}^{dm} \approx 0.40$, which is in principle determined by the global cosmological equilibrium within this framework. Because direct identification of the entire dark fraction with standard collisionless cold dark matter would very probably be incompatible with the main structural observables, we discuss an effective phenomenological decomposition into a structuring cold dark matter component (cdm) and an almost homogeneous residual warm-dark-matter-like component (wdm). In this interpretation, the paper preserves the previously introduced global FCC framework while simultaneously providing a concrete background prediction for the matter content and a physically motivated basis for further testing of structure formation within scale invariant fully conformal cosmology. Full article

We first take a closer look at the original warp drive proposal by Alcubierre, examine its kinematics in the context of a covariant 3+1 setting, and explain some drawbacks of this construction. In this model, changes in the velocity profile are suppressed, apart from an externally given amplitude. We then discuss Einstein’s equations for currently employed spacetime restrictions, and provide the governing equations for the Natário class of metrics with one-component coordinate velocity in a subcase. Following Synge’s G-method we determine the constraints on realizations for two examples: assuming the form of the solution a priori as in Alcubierre’s model, and determining the solution through an assumption imposed along geodesics. We analyze in detail the role of coordinate acceleration and coordinate vorticity, providing illustrations for both example solutions. For the second we find an expected generic instability of the warp field. We then propose a framework that allows for spatial curvature and the description of warp field dynamics within a relativistic Lagrangian perturbation approach, also including exact solutions of the Szekeres class II. These generalizations allow us to link studies on warp fields to relativistic cosmology. A direct correspondence between solutions of Newtonian gravity and general relativity is exploited. We conclude by discussing possible future paths towards physical warp drives within tilted fluid flows. Full article

This entry surveys the role of extra dimensions in Newtonian quantum cosmology, with particular emphasis on large, compactified, and warped dimensional geometries and their impact on the Newtonian potential in the early universe. The discussion begins with a review of Kaluza–Klein type toy models, followed by models with large extra dimensions in which gravity propagates into a higher-dimensional bulk, producing Yukawa-like modifications to the inverse-square law at submillimeter scales. Compactification schemes on toroidal and spherical dimensions are then examined, yielding the spectrum of Kaluza–Klein modes and quantifying their corrections to the Newtonian potential. Warped extra dimensions of the Randall–Sundrum type are also considered, in which a warp factor dimension is introduced; the resulting modifications to the Newtonian interaction in quantum-corrected cosmological settings are discussed in detail. Full article

The two most severe cosmological tensions in the Hubble constant $H_0$ and the matter clustering amplitude $S_8$ have the same relative discrepancy of 8.3%, which suggests that they may have a common origin. Modifications of gravity and exotic dark fields with numerous free parameters introduced in the Einstein field equations often struggle to simultaneously alleviate both tensions; thus, we need to look for a common cause within the standard $\Lambda$CDM framework. At the same time, linear perturbation analyses of matter in the expanding $\Lambda$CDM universe have always neglected the impact of comoving peculiar velocities $\mathbf{v}$ (generally thought to be a second-order effect), the same velocities that, in physical space, cannot be fully accounted for in the observed late-time universe when the cosmic distance ladder is used to determine the local value of $H_0$. We have reworked the linear density perturbation equations in the conformal Newtonian gauge (sub-horizon limit) by introducing an additional drag force per unit mass $-\Gamma \left(t\right)\mathbf{v}$ in the Euler equation with $\Gamma \equiv \gamma \left(2H\right)$, where $\gamma \ll 1$ is a positive dimensionless constant and $2H\left(t\right)$ is the time-dependent Hubble friction. We find that a damping parameter of $\gamma =0.083$ is sufficient to resolve the $S_8$ tension by suppressing the growth of structure at low redshifts, starting at $z_{★}\simeq 3.5–6.5$ to achieve $S_8\simeq 0.78–0.76$, respectively. Furthermore, we argue that the physical source causing this additional friction (a tidal field generated by nonlinear structures in the late-time universe) is also responsible for a systematic error in the local determinations of $H_0$—the inability to subtract peculiar tidal velocities along the lines of sight when determining the Hubble flow via the cosmic distance ladder. Finally, the dual action of the tidal field on the expanding background—reducing both the matter and the dark energy sources of the squared Hubble rate $H^2$, thereby holding back the cosmic acceleration $\ddot{a}$—is of fundamental importance in resolving cosmological tensions and can also substantially alleviate the density coincidence problem. Full article

We envision a minimalist way to explain a number of astronomical facts associated with the unsolved missing mass problem by considering a new phenomenological paradigm. In this model, no new exotic particles need to be added, and the gravity is not modified; it is the perception that we have of a purely Newtonian (or purely Einsteinian) Universe, dubbed the Newton basis or Einstein basis (actually “viewed through a pinhole” which is “optically” distorted in some manner by a so-called magnifying effect). The $\kappa$ model is not a theory but rather an exploratory technique that assumes that the sizes of the astronomical objects (galaxies and galaxy clusters or fluctuations in the CMB) are not commensurable with respect to our usual standard measurement. To address this problem, we propose a rescaling of the lengths when these are larger than some critical values, say >100 pc - 1 kpc for the galaxies and ∼1 Mpc for the galaxy clusters. At the scale of the solar system or of a binary star system, the $\kappa$ effect is not suspected, and the undistorted Newtonian metric fully prevails. A key point of an ontological nature rising from the $\kappa$ model is the distinction which is made between the distances depending on how they are obtained: (1) distances deduced from luminosity measurements (i.e., the real distances as potentially measured in the Newton basis, which are currently used in the standard cosmological model) and (2) even though it is not technically possible to deduce them, the distances which would be deduced by trigonometry. Those “trigonometric” distances are, in our model, altered by the kappa effect, except in the solar environment where they are obviously accurate. In outer galaxies, the determination of distances (by parallax measurement) cannot be carried out, and it is difficult to validate or falsify the kappa model with this method. On the other hand, it is not the same within the Milky Way, for which we have valuable trigonometric data (from the Gaia satellite). Interestingly, it turns out that for this particular object, there is strong tension between the results of different works regarding the rotation curve of the galaxy. At the present time, when the dark matter concept seems to be more and more illusive, it is important to explore new ideas, even the seemingly incredibly odd ones, with an open mind. The approach taken here is, however, different from that adopted in previous papers. The analysis is first carried out in a space called the Newton basis with pure Newtonian gravity (the gravity is not modified) and in the absence of dark matter-type exotic particles. Then, the results (velocity fields) are transported into the leaves of a bundle (observer space) using a universal transformation associated with the average mass density expressed in the Newton basis. This approach will make it much easier to deal with situations where matter is not distributed centrosymmetrically around a center of maximum density. As examples, we can cite the interaction of two galaxies or the case of the collision between two galaxy clusters in the bullet cluster. These few examples are difficult to treat directly in the bundle, especially since we would include time-based monitoring (with an evolving $\kappa$ effect in the bundle). We will return to these questions later, as well as the concept of average mass density at a point. The relationship between this density and the coefficient $\kappa$ must also be precisely defined. Full article

The geometric foundations of General Relativity are revisited here, with particular attention to its gauge invariance, as a key to understanding the true nature of spacetime. Beyond the common image of spacetime as a deformable “fabric” filling the Universe, curvature is interpreted as the dynamic interplay between matter and interacting fields, a view already emphasized by Einstein and Weyl but sometimes overlooked in the literature. Building on these tools, a Newtonian framework is reconstructed that captures essential aspects of cosmology, showing how classical intuition can coexist with modern geometric insights. This perspective shifts the focus from substance to relationships, offering a fresh magnifying glass through which to reinterpret gravitational dynamics and the large-scale structure of the Universe. The similarities of this approach with other recent, more ambitious ones carried out at the quantum level are quite remarkable. Full article

We review a metric theory of gravitation that combines Newtonian gravity with Lorentz invariance. Beginning with a conformastatic metric justified by the Weak Equivalence Principle. We describe, within the Newtonian approximation, the spacetime geometry generated by a static distribution of dust matter. To extend this description to moving sources, we apply a Lorentz transformation to the static metric. This procedure yields, again within the Newtonian approximation, the metric associated with moving bodies. In doing so, we construct a gravitational framework that captures key relativistic features—such as covariance under Lorentz transformations—while remaining rooted in Newtonian dynamics. This approach offers an alternative route to describing weak-field gravitational interactions, without relying directly on Einstein’s field equations. Full article

We explore a modified, including some relativistic effects, Newtonian formalism in cosmology, using a system of constituent equations that includes a modified first Friedmann equation—incorporating its homogeneous counterpart—alongside the classical Poisson equation. Furthermore, we include the dynamical equations arising from stress-energy tensor conservation. Within this framework, we examine stellar equilibrium under spherical symmetry. By specifying the equation of state, we derive the corresponding equilibrium configurations. Finally, we investigate gravitational collapse in this context. Full article

We study the impact on the cosmic microwave background (CMB) landscape of peculiar rotational general relativistic effects. These effects, on galactic scales, do not possess a Newtonian analogue, and therefore could a priori impact CMB analysis. We find that the velocity inferred from the CMB dipole, under the kinematic interpretation, coincides with that measured by a stationary observer within the Milky Way and not with the one measured by the zero angular momentum observer. We show that the galaxy peculiar frame-dragging effects do not impact the standard CMB analysis, as these modify the multipole coefficients only at higher orders with respect to the dominant terms. Moreover, we prove that no general relativistic framework at the galactic scale patched within the standard cosmological model can account for the current tension on the CMB quadrupole amplitude. Full article

As an alternative gravitational theory to General Relativity (GR), Conformal Gravity (CG) can be verified through astronomical observations. Currently, Mannheim and Kazanas have provided vacuum solutions for cosmological and local gravitational systems, and these solutions may resolve the dark matter and dark energy issues encountered in GR, making them particularly valuable. For static, spherically symmetric systems, CG predicts an additional linear potential generated by luminous matter in addition to the conventional Newtonian potential. This extra potential is expected to account for the observations of galaxies and galaxy clusters without the need of dark matter. It is characterized by the parameter ${\gamma }^{*}$, which corresponds to the linear potential generated by the unit of the solar mass, and it is thus a universal constant. The value of ${\gamma }^{*}$ was determined by fitting the rotation curve data of spiral galaxies. These predictions of CG should also be verified by the observations of strong gravitational lensing. To date, in the existing literature, the observations of strong lensing employed to test CG have been limited to a few galaxy clusters. It has been found that the value of ${\gamma }^{*}$ estimated from strong lensing is several orders of magnitude greater than that obtained from fitting rotation curves. In this study, building upon the previous research, we tested CG via strong lensing statistics. We used a well-defined sample that consisted of both galaxies and galaxy clusters. This allowed us to test CG through statistical strong lensing in a way similar to the conventional approach in GR. As anticipated, our results were consistent with previous studies, namely that the fitted ${\gamma }^{*}$ is much larger than that from rotation curves. Intriguingly, we further discovered that, in order to fit the strong lensing data of another sample, the value of ${\gamma }^{*}$ cannot be a constant, as is required in CG. Instead, we derived a formula for ${\gamma }^{*}$ as a function of the stellar mass $M_{*}$ of the galaxies or galaxy clusters. It was found that ${\gamma }^{*}$ decreases as $M_{*}$ increases. Full article

The phenomenon of augmented gravity on the scale of galaxies, conventionally attributed to dark matter halos, is shown to possibly result from the incremental growth of galactic masses and radii over time. This approach elucidates the cosmological origins of the acceleration scale $a_0\approx c{H}_0/2\pi \approx {10}^{-10}$ ms⁻² at which galaxy rotation curves deviate from Keplerian behavior, with no need for new particles or modifications to the laws of gravity, i.e., it constitutes a new explanatory path beyond Cold Dark Matter (CDM) and Modified Newtonian Dynamics (MOND). Once one formally equates the energy density of the universe to the critical value ($\rho ={\rho }_c$) and the cosmic age to the reciprocal of the Hubble parameter ($t=H^{-1}$), independently of the epoch of observation, the result is the Zero-Energy condition for the cosmic fluid’s equation of state, with key repercussions for the study of dark energy since the observables can be explained in the absence of a cosmological constant. Furthermore, this mass-energy evolution framework is able to reconcile the success of CDM models in describing structure assembly at $z\lesssim 6$ with the unexpected discovery of massive objects at $z\gtrsim 10$. Models that feature a strong coupling between cosmic time and energy are favored by this analysis. Full article

Based on Newtonian mechanics, in this article, we present a heuristic derivation of the Friedmann equations, providing an intuitive foundation for these fundamental relations in cosmology. Additionally, using the first law of thermodynamics and Euler’s equation, we derive a set of equations that, at linear order, coincide with those obtained from the conservation of the stress-energy tensor in general relativity. This approach not only highlights the consistency between Newtonian and relativistic frameworks in certain limits, but also serves as a pedagogical bridge, offering insights into the physical principles underlying the dynamics of the universe. Full article

We first briefly review the adventure of scale invariance in physics, from Galileo Galilei, Weyl, Einstein, and Feynman to the revival by Dirac (1973) and Canuto et al. (1977). In the way that the geometry of space–time can be described by the coefficients $g_{\mu \nu }$, a gauging condition given by a scale factor $\lambda \left(x^{\mu }\right)$ is needed to express the scaling. In general relativity (GR), $\lambda =1$. The “Large Number Hypothesis” was taken by Dirac and by Canuto et al. to fix $\lambda$. The condition that the macroscopic empty space is scale-invariant was further preferred (Maeder 2017a), the resulting gauge is also supported by an action principle. Cosmological equations and a modified Newton equation were then derived. In short, except in extremely low density regions, the scale-invariant effects are largely dominated by Newtonian effects. However, their cumulative effects may still play a significant role in cosmic evolution. The theory contains no “adjustment parameter”. In this work, we gather concrete observational evidence that scale-invariant effects are present and measurable in astronomical objects spanning a vast range of masses (0.5 ${\mathrm{M}}_{\odot }<$ M $<{10}^{14}$${\mathrm{M}}_{\odot }$) and an equally impressive range of spatial scales (0.01 pc < r < 1 Gpc). Scale invariance accounts for the observed excess in velocity in galaxy clusters with respect to the visible mass, the relatively flat/small slope of rotation curves in local galaxies, the observed steep rotation curves of high-redshift galaxies, and the excess of velocity in wide binary stars with separations above 3000 kau found in Gaia DR3. Last but not least, we investigate the effect of scale invariance on gravitational lensing. We show that scale invariance does not affect the geodesics of light rays as they pass in the vicinity of a massive galaxy. However, scale-invariant effects do change the inferred mass-to-light ratio of lens galaxies as compared to GR. As a result, the discrepancies seen in GR between the total lensing mass of galaxies and their stellar mass from photometry may be accounted for. This holds true both for lenses at high redshift like JWST-ER1 and at low redshift like in the SLACS sample. Of note is that none of the above observational tests require dark matter or any adjustable parameter to tweak the theory at any given mass or spatial scale. Full article

In relativity, the Newtonian concepts of velocity and acceleration are observer-dependent quantities that vary with the chosen frame of reference. It is well established that in the comoving frame, cosmic expansion is currently accelerating; however, in the rest frame, this expansion is actually decelerating. In this paper, we explore the implications of this distinction. The traditional measure of cosmic acceleration, denoted by q, is derived from the comoving frame and describes the acceleration of the scale factor a for a 3D space-like homogeneous sphere. We introduce a new parameter $q_E$ representing the acceleration experienced between observers within the light cone. By comparing $q_E$ to the traditional q using observational data from Type Ia supernovae (SN) and the radial clustering of galaxies and quasars (BAO)—including the latest results from DESI2024—our analysis demonstrates that $q_E$ aligns more closely with these data. The core argument of the paper is that $\Lambda$—regardless of its origin—creates an event horizon that divides the manifold into two causally disconnected regions analogous to conditions inside a black hole’s interior, thereby allowing for a rest-frame perspective $q_E$ in which cosmic expansion appears to be decelerating and the horizon acts like a friction term. Such a horizon suggests that the universe cannot maintain homogeneity outside. The observed cosmological constant $\Lambda$ can then be interpreted not as a driver of new dark energy or a modification of gravity but as a boundary term exerting an attractive force, akin to a rubber band, resisting further expansion and preventing event horizon crossings. This interpretation calls for a reconsideration of current cosmological models and the assumptions underlying them. Full article

The last few decades have provided abundant evidence for physics beyond the two standard models of particle physics and cosmology. As is now known, the by far largest part of our universe’s matter/energy content lies in the ‘dark’, and consists of dark energy and dark matter. Despite intensive efforts on the experimental as well as the theoretical side, the origins of both are still completely unknown. Screened scalar fields have been hypothesized as potential candidates for dark energy or dark matter. Among these, some of the most prominent models are the chameleon, symmetron, and environment-dependent dilaton. In this article, we present a summary containing the most recent experimental constraints on the parameters of these three models. For this, experimental results have been employed from the qBounce collaboration, neutron interferometry, and Lunar Laser Ranging (LLR), among others. In addition, constraints are forecast for the Casimir and Non-Newtonian force Experiment (Cannex). Combining these results with previous ones, this article collects the most up-to-date constraints on the three considered screened scalar field models. Full article