Amplitude Of Density Fluctuations Research Articles

Arguments against using h−1 Mpc units in observational cosmology

It is common to express cosmological measurements in units of $h^{-1}{\rm Mpc}$. Here, we review some of the complications that originate from this practice. A crucial problem caused by these units is related to the normalization of the matter power spectrum, which is commonly characterized in terms of the linear-theory rms mass fluctuation in spheres of radius $8\,h^{-1}{\rm Mpc}$, $\sigma_8$. This parameter does not correctly capture the impact of $h$ on the amplitude of density fluctuations. We show that the use of $\sigma_8$ has caused critical misconceptions for both the so-called $\sigma_8$ tension regarding the consistency between low-redshift probes and cosmic microwave background data, and the way in which growth-rate estimates inferred from redshift-space distortions are commonly expressed. We propose to abandon the use of $h^{-1}{\rm Mpc}$ units in cosmology and to characterize the amplitude of the matter power spectrum in terms of $\sigma_{12}$, defined as the mass fluctuation in spheres of radius $12\,{\rm Mpc}$, whose value is similar to the standard $\sigma_8$ for $h\sim 0.67$.

Bimodal Behavior and Convergence Requirement in Macroscopic Properties of the Multiphase Interstellar Medium Formed by Atomic Converging Flows

Abstract We systematically perform hydrodynamics simulations of 20 converging flows of the warm neutral medium (WNM) to calculate the formation of the cold neutral medium (CNM), focusing especially on the mean properties of the multiphase interstellar medium (ISM), such as the mean density on a 10 pc scale. Our results show that convergence in those mean properties requires a 0.02 pc spatial resolution that resolves the cooling length of the thermally unstable neutral medium (UNM) to follow the dynamical condensation from the WNM to the CNM. We also find that two distinct postshock states appear in the mean properties depending on the amplitude of the upstream WNM density fluctuation ( ). When , the interaction between shocks and density inhomogeneity leads to a strong driving of the postshock turbulence of >3 km s−1, which dominates the energy budget in the shock-compressed layer. The turbulence prevents dynamical condensation by cooling, and the CNM mass fraction remains at ∼45%. In contrast, when , the CNM formation proceeds efficiently, resulting in the CNM mass fraction of ∼70%. The velocity dispersion is limited to the thermal-instability-mediated level of ∼2–3 km s−1, and the layer is supported by both turbulent and thermal energy equally. We also propose an effective equation of state that models the multiphase ISM formed by the WNM converging flow as a one-phase ISM in the form of P ∝ ργ eff , where γ eff varies from 0.9 (for a large pre-shock Δρ 0) to 0.7 (for a small pre-shock Δρ 0).

Impact of the temperature ratio on turbulent impurity transport in Wendelstein 7-X

First experimental observations in the Wendelstein 7-X stellarator indicate that the impurity confinement can be explained by turbulent processes. In particular, plasma discharges with increased ion to electron temperature ratio are accompanied by reduced electron density fluctuation amplitudes and anomalous impurity diffusion, suggesting a lower turbulent transport. Employing gyro-kinetic numerical simulations, we argue that the temperature ratio plays a key role for reducing the ion temperature gradient instability in Wendelstein 7-X, leading to an enhanced impurity confinement.

Early dark energy does not restore cosmological concordance

Current cosmological data exhibit a tension between inferences of the Hubble constant, $H_0$, derived from early and late-universe measurements. One proposed solution is to introduce a new component in the early universe, which initially acts as "early dark energy" (EDE), thus decreasing the physical size of the sound horizon imprinted in the cosmic microwave background (CMB) and increasing the inferred $H_0$. Previous EDE analyses have shown this model can relax the $H_0$ tension, but the CMB-preferred value of the density fluctuation amplitude, $\sigma_8$, increases in EDE as compared to $\Lambda$CDM, increasing tension with large-scale structure (LSS) data. We show that the EDE model fit to CMB and SH0ES data yields scale-dependent changes in the matter power spectrum compared to $\Lambda$CDM, including $10\%$ more power at $k = 1~h$/Mpc. Motivated by this observation, we reanalyze the EDE scenario, considering LSS data in detail. We also update previous analyses by including $Planck$ 2018 CMB likelihoods, and perform the first search for EDE in $Planck$ data alone, which yields no evidence for EDE. We consider several data set combinations involving the primary CMB, CMB lensing, SNIa, BAO, RSD, weak lensing, galaxy clustering, and local distance-ladder data (SH0ES). While the EDE component is weakly detected (3$\sigma$) when including the SH0ES data and excluding most LSS data, this drops below 2$\sigma$ when further LSS data are included. Further, this result is in tension with strong constraints imposed on EDE by CMB and LSS data without SH0ES, which show no evidence for this model. We also show that physical priors on the fundamental scalar field parameters further weaken evidence for EDE. We conclude that the EDE scenario is, at best, no more likely to be concordant with all current cosmological data sets than $\Lambda$CDM, and appears unlikely to resolve the $H_0$ tension.

Local Measurements of Radial Plasma Velocity Fluctuations in the FT-2 Tokamak Using Equatorial Enhanced Scattering

The possibility of local measurement of the fluctuation level of the radial plasma velocity using equatorial enhanced scattering of a narrow microwave beam in the upper hybrid resonance in internal regions of tokamak plasma is demonstrated. Restrictions of the proposed method at the plasma periphery where the density fluctuation amplitude increases and small-angle scattering of microwaves by the fluctuations along the path to the upper hybrid resonance and back becomes significant are clarified.

Thermodynamics-Structure-Dynamics Correlations and Nonuniversal Effects in the Elastically Collective Activated Hopping Theory of Glass-Forming Liquids.

We employ the microscopic Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated dynamics in combination with crystal-avoiding simulations to study four inter-related questions for metastable monodisperse hard sphere fluids. The first is how significantly improved integral equation theory structural input (Modified-Verlet (MV) closure) changes the dynamical predictions of ECNLE theory. The main consequence is a modest enhancement of the importance of the collective elastic barrier relative to its local cage contribution, which increases the alpha relaxation time and fragility relative to prior results based on the Percus-Yevick closure. Second, ECNLE-MV theory predictions for the alpha time and self-diffusion constant in the metastable regime are quantitatively compared to our new simulations. The small adjustment of a numerical prefactor that enters the collective elastic barrier leads to quantitative agreement over three decades. Third, using the more accurate MV structural input, ECNLE theory is shown to predict thermodynamics-structure-dynamics "correlations" based on various long and short wavelength scalar properties all related to static two-point collective density fluctuations. The logarithm of the alpha relaxation time scales as a power law with these scalar metrics with an exponent that is significantly lower in the less dense noncooperative activated regime compared to the very dense highly cooperative regime. However, the discovered correlation of activated relaxation with a thermodynamic property (dimensionless compressibility) is not causal in ECNLE theory, but rather reflects a strong connection between the local structural quantities that quantify kinetic constraints in the theory with the amplitude of long wavelength density fluctuations. Fourth, the consequences of chemically specific nonuniversalities associated with the onset condition and relative importance of collective elasticity are studied. The predicted thermodynamics-structure-dynamics correlations are found to be robust, albeit with nontrivial shifts of the onset condition.

Indentation-Induced Structural Changes in Vitreous Silica Probed by in-situ Small-Angle X-Ray Scattering

The transient (or permanent) structural modifications which occur during local deformation of oxide glasses are typically studied on the basis of short-range data, for example, obtained through vibrational spectroscopy. This is in contrast to macroscopic observations, where variations in material density can usually not be explained using next-neighbor correlations alone. Recent experiments employing low-frequency Raman spectroscopy have pointed-out this issue, emphasizing that the deformation behavior of glasses is mediated through structural heterogeneity and drawing an analogy to granular media. Here, we provide additional support to this understanding, using an alternative experimental method. Structural modification of vitreous silica in the stress field of a sharp diamond indenter tip was monitored by in-situ small-angle X-ray scattering. The influenced zone during loading and after unloading was compared, demonstrating that changes in the position of the first sharp diffraction peak (FSDP) directly in the center of the indent are of permanent character. On the other hand, variations in the amplitude of electron density fluctuations appear to fully recover after load release. The lateral extent of the modifications and their relaxation are related to the short- to intermediate-range structure and elastic heterogeneity pertinent to the glass network. With support from Finite Element Analysis, we suggest that different structural length scales govern shear and isotropic compaction in vitreous silica.

Gyrokinetic understanding of the edge pedestal transport driven by resonant magnetic perturbations in a realistic divertor geometry

Self-consistent simulations of neoclassical and electrostatic turbulent transport in a DIII-D H-mode edge plasma under resonant magnetic perturbations (RMPs) have been performed using the global total-f gyrokinetic particle-in-cell code x-point gyrokinetic code (XGC), in order to study density pump-out and electron heat confinement. The RMP field is imported from the extended magneto-hydrodynamics code M3D-C1, taking into account the linear two-fluid plasma response. With both neoclassical and turbulence physics considered together, the XGC simulation reproduces two key features of experimentally observed edge transport under RMPs: increased radial particle transport in the pedestal region that is sufficient to account for the experimental pump-out rate and suppression of the electron heat flux in the steepest part of the edge pedestal. In the simulation, the density fluctuation amplitude of modes moving in the electron diamagnetic direction increases due to interaction with RMPs in the pedestal shoulder and outward, while the electron temperature fluctuation amplitude decreases.

Integral equation theory of thermodynamics, pair structure, and growing static length scale in metastable hard sphere and Weeks-Chandler-Andersen fluids.

We employ the Ornstein-Zernike integral equation theory with the Percus-Yevick (PY) and modified-Verlet (MV) closures to study the equilibrium structural and thermodynamic properties of metastable monodisperse hard sphere and continuous repulsion Weeks-Chandler-Andersen (WCA) fluids under density and temperature conditions where the system is strongly overcompressed or supercooled, respectively. The theoretical results are compared to crystal-avoiding simulations of these dense monodisperse model one-component fluids. The equation of state (EOS) and dimensionless compressibility are computed using both the virial and compressibility routes. For hard spheres, the MV-based virial route EOS and dimensionless compressibility are in very good agreement with simulation for all packing fractions, much better than the PY analogs. The corresponding MV-based predictions for the static structure factor are also very good. The amplitude of density fluctuations on the local cage scale and in the long wavelength limit, and three technically different measures of the density correlation length, are studied with both closures. All five properties grow in a roughly exponential manner with density in the metastable regime up to packing fractions of 58% with no sign of saturation. The MV-based results are in good agreement with our crystal-avoiding simulations. Interestingly, the density dependences of long and short wavelength quantities are closely related. The MV-based theory is also quite accurate for the thermodynamics and structure of supercooled monodisperse WCA fluids. Overall our findings are also relevant as critical input to microscopic theories that relate the equilibrium pair correlation function or static structure factor to dynamical constraints, barriers, and activated relaxation in glass-forming liquids.

What magnetospheric and ionospheric researchers should know about the solar wind

Multiple properties of the solar wind that affect the earth are summarized in this overview. 13 specific solar-wind parameters that influence geomagnetic activity, the plasma sheet, the ionosphere, and the electron radiation belt are catalogued: these include the wind speed, number density, magnetic-field strength, field orientation, Mach number, Alfven speed, electron-strahl intensity, and magnetic-field fluctuation amplitude. The solar wind at Earth is categorized into four types of plasma emanating from different morphological features on the solar surface and the systematic differences between the four plasma types is assessed. The solar-cycle behavior of the solar wind is examined in terms of the changing occurrence rates of the four plasma types emanating from the changing Sun. A 27-day periodicity in the properties of the solar wind and in the reaction of the Earth are investigated: the periodicity is owed to features on the rotating Sun. The strong intercorrelations between solar-wind variables are considered and the origins of the intercorrelations are explained. Large-scale structures in the solar wind are reviewed and the different types of geomagnetic storms that they drive are summarized. The mesoscale magnetic structure of the solar wind is examined, the impact on Earth of its current sheets and cellular structure is explored, and a non-randomness in variations of the magnetic-field direction changes at Earth is demonstrated. Sudden strong velocity shears in the solar wind are discussed and their impact on the magnetosphere is shown via a global MHD simulation. The magnetic structure moving outward from the Sun faster than the plasma outflow is discussed, and it is pointed out that the velocity of the magnetic structure should be used when calculating the motional electric field of the Sun. Finally, drawbacks to monitoring the solar wind from L1 are identified.

Construction of a Universal Gel Model with Volume Phase Transition

The physical principle underlying the familiar condensation transition from vapor to liquid is the competition between the energetic tendency to condense owing to attractive forces among molecules of the fluid and the entropic tendency to disperse toward the maximum volume available as limited only by the walls of the container. Van der Waals incorporated this principle into his equation of state and was thus able to explain the discontinuous nature of condensation as the result of instability of intermediate states. The volume phase transition of gels, also discontinuous in its sharpest manifestation, can be understood similarly, as a competition between net free energy attraction of polymer segments and purely entropic dissolution into a maximum allowed volume. Viewed in this way, the gel phase transition would require nothing more to describe it than van der Waals’ original equation of state (with osmotic pressure replacing pressure P). But the polymer segments in a gel are networked by cross-links, and a consequent restoring force prevents complete dissolution. Like a solid material, and unlike a van der Waals fluid, a fully swollen gel possesses an intrinsic volume of its own. Although all thermodynamic descriptions of gel behavior contain an elastic component, frequently in the form of Flory-style rubber theory, the resulting isotherms usually have the same general appearance as van der Waals isotherms for fluids, so it is not clear whether the solid-like aspect of gels, that is, their intrinsic volume and shape, adds any fundamental physics to the volume phase transition of gels beyond what van der Waals already knew. To address this question, we have constructed a universal chemical potential for gels that captures the volume transition while containing no quantities specific to any particular gel. In this sense, it is analogous to the van der Waals theory of fluids in its universal form, but although it incorporates the van der Waals universal equation of state, it also contains a network elasticity component, not based on Flory theory but instead on a nonlinear Langevin model, that restricts the radius of a fully swollen spherical gel to a solid-like finite universal value of unity, transitioning to a value less than unity when the gel collapses. A new family of isotherms arises, not present in a preponderately van der Waals analysis, namely, profiles of gel density as a function of location in the gel. There is an abrupt onset of large amplitude density fluctuations in the gel at a critical temperature. Then, at a second critical temperature, the entire swollen gel collapses to a high-density phase.

New constraints on the mass bias of galaxy clusters from the power spectra of the thermal Sunyaev–Zeldovich effect and cosmic shear

Abstract The thermal Sunyaev–Zeldovich (tSZ) power spectrum is a powerful probe of the present-day amplitude of matter density fluctuations, and has been measured up to $\ell \approx 10^3$ from the Planck data. The largest systematic uncertainty in the interpretation of this data is the so-called “mass bias” parameter B, which relates the true halo mass to the mass proxy used by the Planck team as $M\,_{\rm 500c}^{\rm Planck}=M\,_{\rm 500c}^{\rm true}/B$. Since the power spectrum of the cosmic weak lensing shear is also sensitive to the amplitude of matter density fluctuations via $S_8\equiv \sigma _8 \Omega _{\rm m}^{\alpha }$ with $\alpha \sim 0.5$, we can break the degeneracy between the mass bias and the cosmological parameters by combining the tSZ and cosmic shear power spectra. In this paper, we perform a joint likelihood analysis of the tSZ power spectrum from Planck and the cosmic shear power spectrum from Subaru Hyper Suprime-Cam. Our analysis does not use the primordial cosmic microwave background (CMB) information. We obtain a new constraint on the mass bias as $B = 1.37 ^{+0.15}_{-0.23}$ or $(1-b) = B^{-1}=0.73^{+0.08}_{-0.13}$ ($68\%$ confidence limit), for $\sigma _8 < 0.9$. This value of B is lower than that needed to reconcile the tSZ data with the primordial CMB and CMB lensing data, i.e., $B = 1.64 \pm 0.19$, but is consistent with the mass bias expected from hydrodynamical simulations, $B = 1.28 \pm 0.20$. Thus our results indicate that the mass bias is consistent with the non-thermal pressure support from mass accretion of galaxy clusters via the cosmic structure formation, and that the cosmologies inferred from the tSZ and the cosmic shear are consistent with each other.

Локальные измерения флуктуаций радиальной скорости плазмы в токамаке ФТ-2 с помощью экваториального усиленного рассеяния

The possibility of local measurements of the level of the radial plasma velocity fluctuations by the equatorial enhanced scattering of a narrow microwave beam in the upper hybrid resonance in the core plasma of a tokamak is demonstrated. The limitations of the proposed method are clarified at the periphery of the plasma, where the amplitude of density fluctuations grows and small-angle scattering of microwaves on them along the path to the upper hybrid resonance and back becomes significant.

From a reflectrometry code to a ‘standard’ EC code to investigate the impact of the edge density fluctuations on the EC waves propagation

In this work we employ and extend a 2D/3D code (FWR2D/FWR3D), originally developed for reflectrometer simulations, to study the impact of the edge density fluctuations on the electron cyclotron (EC) wave beam propagation. 2D and 3D simulations for DIII-D-like plasma are discussed with and without the presence of the edge density fluctuations in order to evaluate the impact on the EC wave beam broadening at the location of the EC resonance. Moreover, a comparison between the paraxial and the full-wave solution (which are both implemented in the code, making it very flexible) of the EC beam with and without edge density fluctuations is shown. The paraxial solution is numerically convenient and in very good agreement with the full-wave solution. A scan in the amplitude of edge density fluctuations is performed together with an average with 1000 different fluctuations realizations. For the case shown in this work, an ensemble larger than 100 independent edge density fluctuations shows to reasonably represent the impact of the fluctuations on the EC beam. Our simulations shown here demonstrate the importance of the edge density fluctuations to the EC propagation in agreement with previous work.

Molecular dynamics study on drag reduction mechanism of nonwetting surfaces

In order to study the mechanism responsible for the flow drag reduction on nonwetting surfaces, molecular dynamics models of fluid flow past a smooth surface with different wettability were established in this paper. The effects of surface wettability on flow characteristics in main flow region and boundary region are simulated and analyzed. Results show that compared with the model containing the wetting surfaces, the fluid density fluctuation amplitude of the model containing nonwetting surface decreases greatly and the velocity slip length increases greatly. Skin friction coefficient is calculated to evaluate the drag reduction of surfaces, which indicates that skin friction coefficient of nonwetting decreases significantly compared with wetting surface. The boundary region fluid simulation shows that there is a low-density layer near the nonwetting surfaces. Compared with the “crystallized layer” in the wetting cases, the distribution of low-density layer atoms is sparse and disorganized. Based on the simulation results, the physical mechanism of drag reduction of nonwetting surfaces is proposed: Lower solid-liquid interaction leads to the reduction of energy dissipation on nonwetting surfaces, the energy dissipation consists of dissipation due to solid-liquid contact and energy dissipation within the boundary region.

Breaking cosmic degeneracies: Disentangling neutrinos and modified gravity with kinematic information

Searches for modified gravity in the large-scale structure try to detect the enhanced amplitude of density fluctuations caused by the fifth force present in many of these theories. Neutrinos, on the other hand, suppress structure growth below their free-streaming length. Both effects take place on comparable scales, and uncertainty in the neutrino mass leads to a degeneracy with modified gravity parameters for probes that are measuring the amplitude of the matter power spectrum. We explore the possibility to break the degeneracy between modified gravity and neutrino effects in the growth of structures by considering kinematic information related to either the growth rate on large scales or the virial velocities inside of collapsed structures. In order to study the degeneracy up to fully non-linear scales, we employ a suite of N-body simulations including bothf(R) modified gravity and massive neutrinos. Our results indicate that velocity information provides an excellent tool to distinguish massive neutrinos from modified gravity. Models with different values of neutrino masses and modified gravity parameters possessing a comparable matter power spectrum at a given time have different growth rates. This leaves imprints in the velocity divergence, which is therefore better suited than the amplitude of density fluctuations to tell the models apart. In such models with a power spectrum comparable to ΛCDM today, the growth rate is strictly enhanced. We also find the velocity dispersion of virialised clusters to be well suited to constrain deviations from general relativity without being affected by the uncertainty in the sum of neutrino masses.

Poloidally localized edge density fluctuation with applied and spontaneous 3-D fields in experimental advanced superconducting tokamak (EAST)

Poloidally localized density fluctuation with applied and spontaneous 3-D fields in high-confinement mode (H-mode) plasma is observed by using poloidally distributed multichannel interferometer diagnostics in the experimental advanced superconducting tokamak. With the application of an n = 1 rotating nonaxisymmetric magnetic perturbation (NAMP) field, a density fluctuation appears on different interferometer channels sequentially. Evidence shows that this fluctuation is located at the plasma edge. When an n = 1 static NAMP field is applied, the density fluctuation amplitude increases in parts of channels but decreases in other channels, implying a poloidal localization. This localization is enhanced with the increase in the NAMP field. In addition, when a spontaneous n = 1 external kink mode with a frequency of ∼3.5 kHz appears in the plasma edge, the amplitude of density fluctuation is modulated by the n = 1 kink. This modulation could be attributed to the localization effect on fluctuation by the 3-D fields of the spontaneous kink mode.

3D structure of density fluctuations in the T-10 tokamak and new approach for current profile estimation

The paper is focused on the new systematic measurements of the 3D spatial distributions of the amplitudes, the radial correlation lengths and the long-range correlations along the magnetic field lines for the different turbulence types. The density fluctuations were measured by the heterodyne correlation reflectometry (CR) using the plasma probing with ordinary mode. CR data was supported by recent experiments with the measurements of the perturbation properties using an heavy ion beam probe (HIBP). The new reflectometer antenna array in T-10 tokamak consists of sets of horns distributed at four places toroidally and poloidally over the torus. The experiments confirmed previously found strong poloidal asymmetry of the amplitude for the broadband (BB) and quasi-coherent (QC) fluctuations. It was found that amplitude of density fluctuations is uniform poloidally for the stochastic low frequency (SLF) fluctuations. The radial correlation were measured at four poloidal angles to reveal the poloidal dependence of the radial correlation length for the different fluctuation types. The significant decrease of the radial correlation lengths towards the high magnetic field side was observed for the QC and the SLF fluctuations. The long-range correlations along the field lines were measured by the reflectometers in two cross-sections separated by 1/4 of the torus. The reflectometers had the same probing frequency thus provide reflection from the same magnetic surface. The measurements were carried out at the low and the high field sides with two currents and two magnetic configurations with simultaneous reversal of the toroidal field and plasma current. The positions of the resonance radius were calculated also using 3D tracing of the magnetic field line and demonstrated good agreement with experiment ones. These results allow to propose the new approach for the current profile measurements in tokamaks.

Some Properties of the Solar Wind Turbulence at 1 AU Statistically Examined in the Different Types of Solar Wind Plasma

AbstractA four‐plasma classification scheme is used to categorize the ACE solar wind data set into four types of plasma: (1) coronal‐hole‐origin plasma, (2) streamer‐belt‐origin plasma, (3) sector‐reversal‐region plasma, and (4) ejecta. The statistical properties of the solar wind fluctuations at 1 AU are analyzed for each of the four types of plasma in the years 1998–2008 using ACE magnetic field and plasma measurements. Between the four types of solar wind plasma there are subtle statistical differences in the spectral indices of (a) trace‐B, (b) trace‐v, (c) total energy, (d) magnetic intensity, and (e) plasma number density. Between the four types of plasma there are significant statistical differences (a) in the Elsässer inward and outward spectral indices, (b) in the outward imbalance, (c) in the Alfvénicity, (d) in the normalized vector‐B, vector‐v, magnetic intensity, and number density fluctuation amplitudes, (e) in the population of strong current sheets, (f) in the population of sudden velocity shears, (g) in the anisotropies of magnetic field and velocity fluctuations, and (h) in the parallel‐to‐B magnetic field fluctuation spectral index. It is argued that the four‐plasma categorization scheme is superior to a slow‐versus‐fast categorization for the study of turbulence and fluctuations in the solar wind.

Cosmological inference from Bayesian forward modelling of deep galaxy redshift surveys

We present a large-scale Bayesian inference framework to constrain cosmological parameters using galaxy redshift surveys, via an application of the Alcock-Paczyński (AP) test. Our physical model of the non-linearly evolved density field, as probed by galaxy surveys, employs Lagrangian perturbation theory (LPT) to connect Gaussian initial conditions to the final density field, followed by a coordinate transformation to obtain the redshift space representation for comparison with data. We have implemented a Hamiltonian Monte Carlo sampler to generate realisations of three-dimensional (3D) primordial and present-day matter fluctuations from a non-Gaussian LPT-Poissonian density posterior given a set of observations. This hierarchical approach encodes a novel AP test, extracting several orders of magnitude more information from the cosmic expansion compared to classical approaches, to infer cosmological parameters and jointly reconstruct the underlying 3D dark matter density field. The novelty of this AP test lies in constraining the comoving-redshift transformation to infer the appropriate cosmology which yields isotropic correlations of the galaxy density field, with the underlying assumption relying purely on the geometrical symmetries of the cosmological principle. Such an AP test does not rely explicitly on modelling the full statistics of the field. We verified in depth via simulations that this renders our test robust to model misspecification. This leads to another crucial advantage, namely that the cosmological parameters exhibit extremely weak dependence on the currently unresolved phenomenon of galaxy bias, thereby circumventing a potentially key limitation. This is consequently among the first methods to extract a large fraction of information from statistics other than that of direct density contrast correlations, without being sensitive to the amplitude of density fluctuations. We perform several statistical efficiency and consistency tests on a mock galaxy catalogue, using the SDSS-III survey as template, taking into account the survey geometry and selection effects, to validate the Bayesian inference machinery implemented.