Search Results (85)

The discrepancy between observed galaxy rotation curves and predictions based on visible baryonic matter remains a central challenge in astrophysics. Within the standard ΛCDM framework, these observations are explained through extended halos of non-baryonic dark matter, while alternative approaches such as Modified Newtonian Dynamics reproduce many galactic scaling relations through empirical modifications of low-acceleration dynamics. Recent advances in symbolic machine learning provide a complementary route for investigating whether stable empirical relations can be discovered directly from observational data without imposing strong theoretical priors. In this work, we present the Phenomenological Dark Matter Nonlinear Pipeline, an AI-assisted symbolic discovery framework designed to identify mathematical relationships linking baryonic and observed gravitational accelerations. The analysis was performed using 3175 radial measurements from 175 galaxies derived from SPARC-based rotation-curve catalogs. Symbolic regression was conducted across 173 independent leave-one-galaxy-out validation folds, followed by bootstrap analysis, residual diagnostics, and regime-specific testing. The symbolic search repeatedly converged toward a stable family of non-linear logarithmic acceleration relations exhibiting strong recurrence across independent discovery folds. The resulting empirical relation successfully reproduces the observed Radial Acceleration Relation, naturally generates Baryonic Tully–Fisher Relation like scaling without explicit enforcement during training, and consistently outperforms classical Newtonian gravity while remaining competitive with a MOND-like reference model. Global validation yielded a coefficient of determination of R² = 0.9026 compared with R² = 0.8934 for the MOND-like model and R² = −0.0485 for the Newtonian baseline. Additional analyses demonstrate stable performance across low-acceleration systems, low-surface-brightness galaxies, and other galactic environments. The recovered relation should be interpreted as an empirically discovered scaling law rather than a replacement for General Relativity, ΛCDM, or existing modified-gravity theories. Nevertheless, the repeated emergence of a common symbolic structure across independent validation folds highlights the potential of AI-assisted symbolic discovery as a tool for uncovering interpretable empirical regularities in complex astrophysical datasets. Full article

We present a novel method for deriving radially resolved dynamical chronometers from galaxy rotation curves, allowing galaxy assembly histories to be reconstructed directly from kinematic data. In the Nexus Paradigm, the baryonic Tully–Fisher relation is used to estimate the dynamical mass profile. We compare this profile with independently derived intrinsic baryonic mass distributions obtained from stellar Sérsic fits and gas surface-density measurement yields. This yields a radial ratio that maps to formation redshift with radial resolution. Inverting this ratio within a standard cosmological framework produces a radial lookback-time profile, representing the time since each radial shell last experienced dynamical reconfiguration. Applying the method to a pilot sample of seven SPARC galaxies, including both high- and low-surface-brightness systems as well as the Milky Way, reveals diverse age structures: stratified profiles associated with inside-out growth and flatter profiles consistent with coherent disk assembly. The method requires no dark-matter halo fitting and offers a kinematic chronometer that complements stellar population and chemical evolution approaches. The NP rotation-curve parameters were determined by minimizing the chi-squared statistic between the observed and predicted velocities using a two-stage optimization consisting of a global differential-evolution search followed by nonlinear least-squares refinement. Observational uncertainties were taken from the published rotation-curve data, supplemented by a 5 km s⁻¹ systematic error floor added in quadrature to account for non-circular motions and other unresolved systematics. We also show that the governing dynamical equation admits a gravitoelectromagnetic interpretation, in which a velocity-dependent term generates disk-wide torques that regulate angular momentum transport. This leads to a unified stability framework in which galaxy morphology emerges from a single parameter regime: balanced conditions favor a coherent spiral structure, whereas dynamically hot regimes naturally produce diffuse and ultra-faint systems. The cosmological scaling of the effective gravitomagnetic field further suggests that the spiral structure is partly regulated by cosmic time. Although the inferred ages depend on the accuracy of the baryonic mass reconstruction and on the local validity of the evolving baryonic Tully–Fisher relation, our results show that rotation curves encode time-resolved dynamical information. This establishes the radial dynamical chronometer as a new observable for studying galaxy evolution and testing gravitational frameworks. Full article

We investigatewhether a finite local information capacity of spacetime can account for the gravitational phenomena commonly attributed to cold dark matter. Starting from a covariant effective-field-theory description, we modelcoarse-grained entropy deposition as a dynamical scalar field $S\left(x\right)$ whose stress–energy tensor contributes to structure formation. The macroscopic action contains a single dimensionless coupling λ multiplying the canonical kinetic term, ensuring ghost-free dynamics and conservation of the associated stress–energy tensor. In a slow-roll regime, defined by a covariant source term $\Gamma \equiv \ddot{S}+3H\dot{S}=0$, where H is the Hubble parameter and overdot denotes derivative with respect to cosmic time, and $|\ddot{S}|\ll H|\dot{S}|$, the entropy sector behaves as pressureless dust at background and in linear order. Implemented in a modified Cosmic Linear Anisotropy Solving System (CLASS) Boltzmann solver, the entropy component fits Planck satellite 2018 cosmic microwave background (CMB) data, baryon acoustic oscillation (BAO) measurements, and the Pantheon + Type Ia supernova sample for $0.5\lesssim \lambda \lesssim 2$, while preserving the linear growth factor to within 0.2% over Euclid space telescope scales. To regulate ultraviolet contributions, we introduce a holographically motivated prescription in which gravitationally active entropy deposition is confined to causal two-surfaces, yielding a $\rho \propto r^{-2}$ halo envelope with a finite-density core determined by local entropy saturation. Fixing the flux scale $\mathcal{A}$ from astrophysical entropy budgets reproduces Milky-Way-mass halos without introducing fine-tuned length scales. Pilot N-body simulations that evolve the entropy field on a staggered grid reproduce the halo mass function down to ${10}^{10.5}{M}_{\odot }$, mitigate the cusp–core and missing-satellite tensions, and remain consistent with cluster lensing constraints. On linear scales, the model predicts percent-level, scale-dependent deviations in the lensing convergence and matter power spectra, testable by Euclid space telescope, the Roman Space Telescope High Latitude Survey, and the CMB-S4 experiment. Full article

The weak-field, quasi-static regime of gravity is commonly described by the Newton–Poisson equation as an effective response law. We construct this response within a cost-first discrete variational framework. The Recognition Composition Law (RCL) uniquely selects a reciprocal closure cost within the restricted quadratic symmetric composition class; together with the discrete ledger axioms AX1–AX5 (including conservation) and standard DEC refinement, the Newton–Poisson baseline is then recovered in the instantaneous-closure limit. Conditional on Assumption AS1 (scale-free latency) and Assumption AS2 (causal frequency–wavenumber ansatz), allowing finite equilibration introduces fractional memory into the response, yielding a scale-free modification of the source–potential relation characterized by a power-law kernel $w_{\ker }\left(k\right)=1+C{(k_0/k)}^{\alpha }$ in Fourier space. The kernel exponent $\alpha =\frac{1}{2}(1-{\phi }^{-1})\approx 0.191$, where $\phi =(1+\sqrt{5})/2$, is derived from self-similarity of the discrete ledger closure; the amplitude $C={\phi }^{-2}\approx 0.382$ is identified as a hypothesis from a three-channel factorization argument. We evaluate this quasi-static kernel-motivated response against SPARC galaxy rotation curves under a strict global-only protocol (fixed $M/L=1$, no per-galaxy tuning, conservative ${\sigma }_{\mathrm{tot}}$), using a controlled multiplicative surrogate for the full nonlocal disk operator implied by the kernel. In this deliberately over-constrained setting, the surrogate interface achieves $\mathrm{median}({\chi }^2/N)=3.06$ over 147 galaxies (2933 points), outperforming a strict global-only NFW benchmark and remaining less efficient than MOND under identical constraints. The analysis is restricted to the non-relativistic, quasi-static sector and should be read as a falsifier-oriented galactic-regime consistency check of the scaling window, not as a relativistic completion or a claim of Solar System viability without additional UV regularization/screening. Full article

Recently, the experimental realization of a Kapitza potential in a Bose–Einstein condensate (BEC) was reported for the first time in the literature, motivating further theoretical investigations of such a system. At the same time, in the astrophysical context, BEC dark matter models have been widely studied as a possible phenomenological explanation for the dark matter phenomena. We model the galactic structure with an inner cored profile obtained from the ground state equilibrium solution of the Schrödinger–Poisson together with a Kapitza–BEC-like interaction for the tail region. We find reasonable agreement of the model with representative galaxy rotation curves available in the SPARC catalogue. Full article

One key piece of evidence for dark matter is the rotation-curve problem: the disagreement between measured galactic rotation curves and their luminous mass. A novel solution to this problem is presented here, in a model that predicts observed Doppler-shifted spectra based only on the luminous matter estimates and one free model parameter $\alpha$. This model is applied to fit the rotation curves of the SPARC sample of 175 galaxies, yielding mass-to-light ratios, goodness of fit measurements, and $\alpha$. The measured average ${\chi }_r^2=2.24$ compares favorably with the Navarro-Frenk-White dark matter model’s average of ${\chi }_r^2=4.19$ for the same data, and more galaxies are successfully fit by this model. The model provides a useful formulation linking luminous matter to the observed rotation curves, with the dark matter contribution to galaxies encoded in two transformation terms of the luminous mass. It also offers a lower-parameter characterization of the rotation curve problem, and a power law relationship between $\alpha$ and galactic photometric quantities is observed, potentially removing the need for the free parameter. Full article

We show that the FLRW metric, modified to include interrelated variation in the speed of light and gravitational constants, leads to Friedmann equations containing terms that behave like dark matter and dark energy without the cosmological constant. When we permit tired light (TL) to contribute to the redshift due to the expanding universe, thus defined by covarying coupling constants (CCCs), the resulting CCC+TL model has a critical density that is just enough to account for the baryon matter in the universe. The CCC+TL cosmology model is consistent with all of the observations that we had the time and the resources to study, including BAOs (baryon acoustic oscillations), the CMB (cosmic microwave background) sound horizon angular size, the time dilation effect, galaxy formation time scales at cosmic dawn, galaxy rotation curves, gravitational lensing, galaxy cluster and ultra-faint dwarf galaxy dynamics, and the mass, size, density, and luminosity evolution of galaxies. We briefly review them in this paper. Additionally, the new model does not suffer from the coincidence problem of the ΛCDM model and complies with the recent DESI findings of an increasing dark energy density with redshift. We present the fundamentals of the CCC+TL model and discuss its applications to some decisive observations. We have considered temporal variation in the constant for cosmological studies and their spherically symmetric variation in astrophysical situations. We conclude that the illusion of dark matter and dark energy in cosmological and astrophysical observations originates from CCC. 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

Objective: We examine whether a finite-range scalar–tensor modification of gravity can be simultaneously compatible with cosmological background data, galaxy rotation curves, and local/astrophysical consistency tests, while satisfying the luminal gravitational-wave propagation constraint ($c_T=1$) implied by GW170817 at low redshifts. Methods: We formulate the model at the level of an explicit covariant action and derive the corresponding field equations; for cosmological inferences, we adopt an effective background closure in which the late-time dark-energy density is modulated by a smooth activation function characterized by a length scale $\lambda$ and amplitude $ϵ$. We constrain this background model using Pantheon+, DESI Gaussian Baryon Acoustic Oscillations (BAOs), and a Planck acoustic-scale prior, including an explicit $\Lambda$CDM comparison. We then propagate the inferred characteristic length by fixing $\lambda$ in the weak-field Yukawa kernel used to model 175 SPARC galaxy rotation curves with standard baryonic components and a controlled spherical approximation for the scalar response. Results: The joint background fit yields ${\Omega }_m=0.293\pm 0.007$, $\lambda =7.{69}_{-1.71}^{+1.85}$$\mathrm{Mpc}$, and $H_0=72.33\pm 0.50$$\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. With $\lambda$ fixed, the baryons + scalar model describes the SPARC sample with a median reduced chi-square of ${\chi }_{\nu }^2=1.07$; for a 14-galaxy subset, this model is moderately preferred over the standard baryons + NFW halo description in the finite-sample information criteria, with a mean $\Delta$AICc outcome in favor of the baryons + scalar model (≈2.8). A Vainshtein-type screening completion with $\Lambda =1.3\times {10}^{-8}$ eV satisfies Cassini, Lunar Laser Ranging, and binary pulsar bounds while keeping the kpc scales effectively unscreened. For linear growth observables, we adopt a conservative General Relativity-like baseline (${\mu }_0=0$) and show that current $f{\sigma }_8$ data are consistent with ${\mu }_0\simeq 0$ for our best-fit background; the model predicts $S_8=0.791$, consistent with representative cosmic-shear constraints. Conclusions: Within the present scope (action-level weak-field dynamics for galaxy modeling plus an explicitly stated effective closure for background inference), the results support a mutually compatible characteristic length at the Mpc scale; however, a full perturbation-level implementation of the covariant theory remains an issue for future work, and the role of cold dark matter beyond galaxy scales is not ruled out. Full article

We resume our analysis of Newtonian Fractional-Dimension Gravity (NFDG), an alternative gravitational model that does not require the dark matter (DM) paradigm. We add three more galaxies (NGC 6946, NGC 3198, NGC 2841) to the catalog of those studied with NFDG methods. Once again, NFDG can successfully reproduce the observed rotation curves by using a variable fractional dimension $D\left(R\right)$, as with the nine other galaxies previously studied with these methods. In addition, we introduce a mass-dimension field equation for our model, which is capable of deriving the fractional mass dimension $D_m\left(R\right)$ from a single equation, as opposed to the previous $D\left(R\right)$, which was obtained simply by matching the experimental rotational velocity data for each galaxy. While the NFDG predictions computed with this new $D_m\left(R\right)$ dimension are not as accurate as those based on the original $D\left(R\right)$, they nevertheless confirm the validity of our fractional-dimension approach. Three previously studied galaxies (NGC 7814, NGC 6503, NGC 3741) were analyzed again with these new methods, and their structure was confirmed to be free from any dark matter components. Full article

The formation and evolution of galaxies and other astrophysical objects have become of great interest, especially since the launch of the James Webb Space Telescope in 2021. The mass, size, and density of objects in the early universe appear to be drastically different from those predicted by the standard cosmology—the $\mathsf{\Lambda }$CDM model. This work shows that the mass–size–density evolution is not surprising when we use the CCC+TL cosmology, which is based on the concepts of covarying coupling constants in an expanding universe and the tired light effect contributing to the observed redshift. This model is consistent with supernovae Pantheon+ data, the angular size of the cosmic dawn galaxies, BAO, CMB sound horizon, galaxy formation time scales, time dilation, galaxy rotation curves, etc., and does not have the coincidence problem. The effective radii $r_e$ of the objects are larger in the new model by $r_e\propto {\left(1+z\right)}^{0.93}$. Thus, the object size evolution in different studies, estimated as $r_e\propto {\left(1+z\right)}^s$ with $s=-1.0$ ± $0.3$, is modified to $r_e\propto {\left(1+z\right)}^{s+0.93}$, the dynamical mass by ${\left(1+z\right)}^{0.93},$ and number density by ${\left(1+z\right)}^{-2.80}$. The luminosity modification increases slowly with $z$ to 1.8 at $z=20$. Thus, the stellar mass increase is modest, and the luminosity and stellar density decrease are mainly due to the larger object size in the new model. Since the aging of the universe is stretched in the new model, its temporal evolution is much slower (e.g., at $z=10$, the age is about a dex longer); stars, black holes, and galaxies do not have to form at unrealistic rates. Full article

This paper aims to explore whether astrophysical observations, primarily galaxy rotation curves, result from covarying coupling constants (CCC) rather than from dark matter. We have shown in earlier papers that cosmological observations, such as supernovae type 1a (Pantheon+), the small size of galaxies at cosmic dawn, baryon acoustic oscillations (BAO), the sound horizon in the cosmic microwave background (CMB), and time dilation effect, can be easily accounted for without requiring dark energy and dark matter when coupling constants are permitted to evolve in an expanding Universe, as predicted by Dirac, and the redshift is considered jointly due to the Universe’s expansion and Zwicky’s tired light (TL) effect. Here, we show that the CCC parameter α is responsible for generating the illusion of dark matter and dark energy, which we call α-matter and α-energy, and is influenced by the baryonic matter density distribution. While cosmologically α is a constant determined for the homogenous and isotropic Universe, e.g., by fitting Pantheon+ data, it can vary locally due to the extreme anisotropy of the matter distribution. Thus, in high baryonic density regions, one expects α-matter and α-energy densities to be relatively low and vice versa. We present its application to a few galaxy rotation curves from the SPARC database and find the results promising. Full article

We investigate the behaviour of photons in Riemann spacetime, focusing on how their velocity and energy are affected by cosmic expansion. Specifically, we examine the differences in energy conservation depending on the cosmological model. Our findings indicate that photons exhibit fundamentally different behaviour based on the chosen metric. In the standard $\Lambda$CDM model, which relies on the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the energy conservation law for redshifted photons is violated. However, in a cosmological model based on the conformal cosmology (CC) metric, this law remains valid. The CC metric offers additional advantages, as it accurately reproduces the cosmological redshift, cosmic time dilation observed in Type Ia supernova light curves, and flat galaxy rotation curves without requiring the introduction of dark matter. These findings underscore the potential significance of the CC metric in cosmological applications. 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