Papers by Ivan de Martino
A&A 670, L4, 2023
Aims. It is well known that N-body simulations of ultralight bosons display the formation of a so... more Aims. It is well known that N-body simulations of ultralight bosons display the formation of a solitonic dark matter core in the innermost part of the halo. The scale-length of such a soliton depends on the inverse of the mass of the boson. On the other hand, the orbital motion of stars in the Galactic Center depends on the distribution of matter, no matter whether it is baryonic or dark, providing an excellent probe for the gravitational field of the region. In this Letter, we propose the S-stars in the Galactic Center as a new observational tool, complementary to other astrophysical systems, to narrow down the range of allowed values for an ultralight dark matter candidate boson mass. Methods. We built mock catalogs mirroring the forthcoming astrometric and spectroscopic observations of S2 and we used a MCMC analysis to predict the accuracy down to which the mass of an ultralight boson may be bounded. We show that once complementary constraints are considered, this analysis will help to restrict the allowed range of the boson mass. Results. Our analysis forecasts the boundary limit on the mass of an ultralight boson to be <10 −19 eV at a 95% confidence level.
Phys Rev D, 107, 044038, 2023
We investigate a nonsingular black hole spacetime representing a strong deformation of the Schwar... more We investigate a nonsingular black hole spacetime representing a strong deformation of the Schwarzschild solution with mass M by an additional hair l, which may be hierarchically larger than the Planck scale. The spacetime is an exact solution of Einstein's equations sourced by an anisotropic fluid. The model presents a de Sitter core and Oðl 2 =r 2 Þ slow-decaying corrections to the Schwarzschild solution. These solutions are thermodynamically preferred when 0.2 ≲ l=GM ≲ 0.3 and are characterized by strong deviations in the orbits of test particles from the Schwarzschild case. In particular, we find corrections to the perihelion precession angle scaling linearly with l. We test our model using the available data for the orbits of the S2 star around SgrA Ã. These data strongly constrain the value of the hair l, casting an upper bound on it of ∼0.47GM but do not rule out the possible existence of regular black holes with super-Planckian hair.
MNRAS 519, 4424-4433 , 2023
We use the kinematic data of the stars in eight dwarf spheroidal galaxies to assess whether f (R)... more We use the kinematic data of the stars in eight dwarf spheroidal galaxies to assess whether f (R) gravity can fit the observed profiles of the line-of-sight velocity dispersion of these systems without resorting to dark matter. Our model assumes that each galaxy is spherically symmetric and has a constant velocity anisotropy parameter β and constant mass-to-light ratio consistent with stellar population synthesis models. We solve the spherical Jeans equation that includes the Yukaw a-lik e gravitational potential appearing in the weak field limit of f (R) gravity, and a Plummer density profile for the stellar distribution. The f (R) velocity dispersion profiles depends on two parameters: the scale length ξ −1 , below which the Yukawa term is negligible, and the boost of the gravitational field δ > −1. δ and ξ are not universal parameters, but their variation within the same class of objects is expected to be limited. The f (R) velocity dispersion profiles fit the data with a value ξ −1 = 1. 2 + 18. 6 −0. 9 Mpc for the entire galaxy sample. On the contrary, the values of δ show a bimodal distribution that picks at δ = −0. 986 ± 0. 002 and δ = −0. 92 ± 0. 01. These two values disagree at 6 σ and suggest a severe tension for f (R) gravity. It remains to be seen whether an impro v ed model of the dwarf galaxies or additional constraints provided by the proper motions of stars measured by future astrometric space missions can return consistent δ's for the entire sample and remo v e this tension.
MNRAS 519, 1981–1988 , 2023
We have explored a completely new and alternative way to restrict the parameter space of Horndesk... more We have explored a completely new and alternative way to restrict the parameter space of Horndeski theory of gravity. Using its Newtonian limit, it is possible to test the theory at a regime where, given its complexity and the small magnitude of the expected effects, it is poorly probed. At Newtonian level, it gives rise to a generalized Yukaw a-lik e Newtonian potential which we have tested using S2 star orbit data. Our model adds five parameters to the General Relativity model, and the analysis constrains two of them with unprecedented precision to these energy scales, while it only gives an e xclusion re gion for the remaining parameters. We have shown the potential of weak-field tests to constrain Horndeski gravity opening, as a matter of fact, which is a new avenue that deserves to be further, and deeply, explored in the near future.
MNRAS 518, 3372–3385, 2023
We investigate the capability of Einstein Telescope to constrain the cosmological parameters of t... more We investigate the capability of Einstein Telescope to constrain the cosmological parameters of the non-flat CDM cosmological model. Two types of mock data sets are considered depending on whether or not a short gamma-ray burst is detected, and associated with the gravitational wave emitted by binary neutron stars merger, using the THESEUS satellite. Depending on the mock data set, two statistical estimators are applied: one assumes that the redshift is known, while the other marginalizes o v er it assuming a specific redshift prior distribution. We demonstrate that (i) using mock catalogues collecting gravitational wave signals emitted by binary neutron stars systems to which a short gamma-ray burst has been associated, Einstein Telescope may achieve an accuracy on the cosmological parameters of σ H 0 ≈ 0. 40 km s −1 Mpc −1 , σ k, 0 ≈ 0. 09, and σ , 0 ≈ 0. 07; while (ii) using mock catalogues collecting all gra vitational wa ve signals emitted by binary neutron stars systems for which an electromagnetic counterpart has not been detected, Einstein Telescope may achieve an accuracy on the cosmological parameters of σ H 0 ≈ 0. 04 km s −1 Mpc −1 , σ k, 0 ≈ 0. 01, and σ , 0 ≈ 0. 01, once the redshift probability distribution of GW events is known from from population synthesis simulations and/or the measure of the tidal deformability parameter. These results show an impro v ement of a factor 2-75 with respect to earlier results using complementary data sets.
MNRAS 516, 3556–3568 (2022) , 2022
We show that measuring the proper motion of ∼2000 stars within a dwarf galaxy, with an uncertaint... more We show that measuring the proper motion of ∼2000 stars within a dwarf galaxy, with an uncertainty of 1 km s −1 at most, can establish whether the dark matter (DM) density profile of the dwarf has a central core or cusp. We derive these limits by building mock star catalogues similar to those expected from future astrometric Theia-like missions and including celestial coordinates, radial velocity and proper motion of the stars. The density field of the DM halo of the dwarf is sampled from an extended Navarro-Frank-White (eNFW) spherical model, whereas the number density distribution of the stars is a Plummer sphere. The velocity field of the stars is set according to the Jeans equations. A Monte Carlo Markov chain algorithm applied to a sample of N 2000 stars returns unbiased estimates of the eNFW DM parameters within 10 per cent of the true values and with 1 σ relative uncertainties ࣠ 20 per cent. The proper motions of the stars lift the de generac y among the eNFW parameters which appears when the line-of-sight velocities alone are available. Our analysis demonstrates that, by estimating the log-slope of the mass density profile estimated at the half-light radius, a sample of N = 2000 stars can distinguish between a core and a cusp at more than 8 σ. Proper motions also return unbiased estimates of the dwarf mass profile with 1 σ uncertainties that decrease, on average, from 2.65 dex to 0.15 dex when the size of the star sample increases from N = 100 to N = 6000 stars. The measure of the proper motions can thus strongly constrain the distribution of DM in nearby dwarfs and provides fundamental contribution to understanding the nature and the properties of DM.
Monthly Notices of the Royal Astronomical Society, Volume 510, Issue 4, pp.4757-4766, 2022
We have obtained the first constraint of the parameter space of Scalar-Tensor-Vector-Gravity usin... more We have obtained the first constraint of the parameter space of Scalar-Tensor-Vector-Gravity using the motion of the S2-star around the supermassive black hole at the centre of the Milky Way, and we did not find any serious tension with General Relativity. We used the Schwarzschild-like metric of Scalar-Tensor-Vector-Gravity to predict the orbital motion of S2-star, and to compare it with the publicly available astrometric data, which include 145 measurements of the positions, 44 measurements of the radial velocities of S2-star along its orbit, and the recent measurement of the orbital precession. We employed a Monte Carlo Markov Chain algorithm to explore the parameter space, and constrained the only one additional parameter of Scalar-Tensor-Vector-Gravity to 0.410 at 99,7% confidence level, where = 0 reduces this modified theory of gravity to General Relativity.
Journal of Cosmology and Astroparticle Physics, Volume 2022, Issue 03, id.007, 27 pp., 2022
Despite the huge improvements guaranteed by future GRAVITY observations of the S0-2 star, these w... more Despite the huge improvements guaranteed by future GRAVITY observations of the S0-2 star, these will not be able to unveil the fundamental nature, whether black hole or wormhole, of the central supermassive object. Nevertheless, observing stars orbiting closer to the central gravitational source could allow to distinguish between the black hole and wormhole nature of this object at more than 5σ. Firstly, we have used publicly available astrometric and spectroscopic measurements of the S0-2 star to constrain the metric around the supermassive object without finding any evidence either favouring or ruling out the wormhole nature. Secondly, we have designed a mock catalogue of future observations of the S0-2 star mirroring the accuracy and precision of GRAVITY. Afterwards, we firstly tested our methodology showing that our procedure recovers the input model, and subsequently we demonstrated that the constraining power of such a dataset is not enough to distinguish between black hole and wormhole. Finally, we built some toy models representing stars orbiting much closer the central object than S0-2. We used these toy models to investigate which are the ideal orbital features and observational strategies to achieve our aim of unveiling the fundamental nature of the central supermassive object, demonstrating that a star with a period of the order of ~ 5 years and a pericentre distance of ~ 5 AU could identify the nature of the central object at almost 5σ accuracy.
Physical Review D, Volume 105, Issue 4, article id.044014, 2022
In this paper, we introduce the post-Minkowskian approximation of energy-momentum-squared gravity... more In this paper, we introduce the post-Minkowskian approximation of energy-momentum-squared gravity (EMSG). This approximation is used to study the gravitational energy flux in the context of EMSG. As an application of our results, we investigate the EMSG effect on the first time derivative of the orbital period of the binary pulsars. Utilizing this post-Keplerian parameter, the free parameter of the EMSG theory, f 0 , is estimated for six known binary pulsars. Taking the binaries that have the most accurate observations, it turns out that −6 × 10 −37 m s 2 kg −1 < f 0 < +10 −36 m s 2 kg −1. This bound is in agreement with the precedent studies.
Physical Review D, Volume 104, Issue 10, article id.L101502, 2021
The GRAVITY Collaboration achieved the remarkable detection of the orbital precession of the S2 s... more The GRAVITY Collaboration achieved the remarkable detection of the orbital precession of the S2 star around the Galactic centre supermassive black hole, providing yet another proof of the validity of the General Relativity. The departure from the Schwarzschild precession is encoded in the parameter fSP which multiplies the predicted general relativistic precession. Such a parameter results to be fSP = 1.10 ± 0.19, which is consistent with General Relativity (fSP = 1) at 1σ level. Nevertheless, this parameter may also hide an effect of modified theories of gravity. Thus, we consider the orbital precession due to the Yukawa-like gravitational potential arising in the weak field limit of f (R)-gravity, and we use the current bound on the fSP to constrain the strength and the scale length of the Yukawa-like potential. No deviation from GR are revealed at scale of λ < 6300 AU with the strength of the Yukawa potential restricted to δ = −0.01 +0.61 −0.14 .
Monthly Notices of the Royal Astronomical Society, Volume 504, Issue 2, pp.2868-2876, 2021
Dark matter as a Bose-Einstein condensate, such as the axionic scalar field particles of String T... more Dark matter as a Bose-Einstein condensate, such as the axionic scalar field particles of String Theory, can explain the coldness of dark matter on large scales. Pioneering simulations in this context predict a rich wave-like structure, with a ground state soliton core in every galaxy surrounded by a halo of excited states that interfere on the de Broglie scale. This de Broglie scale is largest for low mass galaxies as momentum is lower, providing a simple explanation for the wide cores of dwarf spheroidal galaxies. Here we extend these "wave dark matter" (ψDM) predictions to the newly discovered class of "Ultra Diffuse Galaxies" (UDG) that resemble dwarf spheroidal galaxies but with more extended stellar profiles. Currently the best studied example, DF44, has a uniform velocity dispersion of 33km/s, extending to at least 3 kpc, that we show is reproduced by our ψDM simulations with a soliton radius of 0.5 kpc. In the ψDM context, we show the relatively flat dispersion profile of DF44 lies between massive galaxies with compact dense solitons, as may be present in the Milky Way on a scale of 100pc and lower mass galaxies where the velocity dispersion declines centrally within a wide, low density soliton, like Antlia II, of radius 3 kpc.
In Cosmology and in Fundamental Physics there is a crucial question like: where the elusive subst... more In Cosmology and in Fundamental Physics there is a crucial question like: where the elusive substance that we call Dark Matter is hidden in the Universe and what is it made of? that, even after 40 years from the Vera Rubin seminal discovery [1] does not have a proper answer. Actually, the more we have investigated, the more this issue has become strongly entangled with aspects that go beyond the established Quantum Physics, the Standard Model of Elementary particles and the General Relativity and related to processes like the Inflation, the accelerated expansion of the Universe and High Energy Phenomena around compact objects. Even Quantum Gravity and very exotic Dark Matter particle candidates may play a role in framing the Dark Matter mystery that seems to be accomplice of new unknown Physics. Observations and experiments have clearly indicated that the above phenomenon cannot be considered as already theoretically framed, as hoped for decades. The Special Topic to which this review belongs wants to penetrate this newly realized mystery from different angles, including that of a contamination of different fields of Physics apparently unrelated. We show with the works of this ST that this contamination is able to guide us into the required new Physics. This review wants to provide a good number of these “paths or contamination” beyond/among the three worlds above; in most of the cases, the results presented here open a direct link with the multi-scale dark matter phenomenon, enlightening some of its important aspects. Also in the remaining cases, possible interesting contacts emerges. Finally, a very complete and accurate bibliography is provided to help the reader in navigating all these issues.
A wavelike solution for the non-relativistic universal dark matter (wave-DM) is rapidly gaining i... more A wavelike solution for the non-relativistic universal dark matter (wave-DM) is rapidly gaining interest, following pioneering simulations of cosmic structure as an interference pattern of coherently oscillating bosons. A prominent solitonic standing wave is predicted at the center of every galaxy, representing the ground state solution of the coupled Schrödinger-Poisson equations, and it has been identified with the wide, kpc scale dark cores of common dwarf-spheroidal galaxies. A denser soliton is predicted for Milky Way sized galaxies where momentum is higher, so the de Broglie scale of the soliton is smaller, ≃ 100 pc, of mass ≃ 10 9 M ⊙. Here we show the central motion of bulge stars in the Milky Way implies the presence of such a dark core, where the velocity dispersion rises inversely with radius to a maximum of ≃ 130 km/s, corresponding to an excess central mass of ≃ 1.5 × 10 9 M ⊙ within ≃ 100 pc, favoring a boson mass of ≃ 10 −22 eV. This quantitative agreement with such a unique and distinctive prediction is therefore strong evidence for a light bosonic solution to the long standing Dark Matter puzzle.
The large dark cores of common dwarf galaxies are unexplained by the standard heavy particle inte... more The large dark cores of common dwarf galaxies are unexplained by the standard heavy particle interpretation of dark matter. This puzzle is exacerbated by the discovery of a very large but barely visible, dark matter dominated galaxy Antlia II orbiting the Milky Way, uncovered by tracking star motions with the Ĝaia satellite. Although Antlia II has a low mass, its visible radius is more than double any known dwarf galaxy, with an unprecedentedly low density core. We show that Antlia II favors dark matter as a Bose-Einstein condensate, for which the ground state is a stable soliton with a core radius given by the de Broglie wavelength. The lower the galaxy mass, the larger the de Broglie wavelength, so the least massive galaxies should have the widest soliton cores of lowest density. An ultralight boson of m ψ ∼ 1.1 × 10 −22 eV accounts well for the large size and slowly moving stars within Antlia II and agrees with boson mass estimates derived from the denser cores of more massive dwarf galaxies. For this very light boson, Antlia II is close to the lower limiting Jeans scale for galaxy formation permitted by the uncertainty principle, so other examples are expected but none significantly larger in size. This simple explanation for the puzzling dark cores of dwarf galaxies implies dark matter as an ultralight boson, such as an axion generic in string theory.
The cold dark-matter model successfully explains both the emergence and evolution of cosmic struc... more The cold dark-matter model successfully explains both the emergence and evolution of cosmic structures on large scales and, when we include a cosmological constant, the properties of the homogeneous and isotropic Universe. However, the cold dark-matter model faces persistent challenges on the scales of galaxies. Indeed, N-body simulations predict some galaxy properties that are at odds with the observations. These discrepancies are primarily related to the dark-matter distribution in the innermost regions of the halos of galaxies and to the dynamical properties of dwarf galaxies. They may have three different origins: (1) the baryonic physics affecting galaxy formation is still poorly understood and it is thus not properly included in the model; (2) the actual properties of dark matter differs from those of the conventional cold dark matter; (3) the theory of gravity departs from General Relativity. Solving these discrepancies is a rapidly evolving research field. We illustrate some of the solutions proposed within the cold dark-matter model, and solutions when including warm dark matter, self-interacting dark matter, axion-like particles, or fuzzy dark matter. We also illustrate some modifications of the theory of gravity: Modified Newtonian Dynamics (MOND), MOdified Gravity (MOG), and f (R) gravity.
Physical Review D, 2020
Cosmic history can be traced considering further curvature contributions inside the gravitational... more Cosmic history can be traced considering further curvature contributions inside the gravitational action. Assuming that standard General Relativity can be extended by other curvature invariants, we discuss the possibility that an action containing higher-order curvature terms can fit, in principle, the whole universe evolution. In particular , a theory like F (R, G), with R the Ricci scalar and G the Gauss-Bonnet topological term, contains all the curvature invariants that, depending on the energy regime, can address inflation, matter dominated and dark energy regimes. In this paper, we investigate this possibility considering how F (R, G) models can lead gravity from ultraviolet to infrared scales. Specifically, we will take into account a cosmographic approach for this purpose. PACS numbers: 98.80.-k, 95.35.+d, 95.36.+x
The European Physical Journal C, 2020
In this paper, we study the Jeans analysis in the context of energy-momentum-squared gravity (EMS... more In this paper, we study the Jeans analysis in the context of energy-momentum-squared gravity (EMSG). More specifically we find the new Jeans mass for non-rotating infinite mediums as the smallest mass scale for local perturbations that can be stable against its own gravity. Furthermore, for rotating mediums , specifically for rotating thin disks in the context of EMSG, we find a new Toomre-like criterion for the local gravitational stability. Finally, the results are applied to a hyper-massive neutron star, as an astrophysical system. Using a simplified toy model we have shown that, for a positive (negative) value of the EMSG parameter α, the system is stable (unstable) in a wide range of α. On the other hand, no observational evidence has been reported on the existence of local fragmentation in HMNS. Naturally, this means that EMSG with positive α is more acceptable from the physical point of view.
Monthly Notices of the Royal Astronomical Society, 2020
The lack of detection of supersymmetric particles is leading to look at alternative avenues for e... more The lack of detection of supersymmetric particles is leading to look at alternative avenues for explaining dark matter's effects. Among them, modified theories of gravity may play an important role accounting even for both dark components needed in the standard cosmological model. Scalar-Tensor-Vector Gravity theory has been proposed to resolve the dark matter puzzle. Such a modified gravity model introduces, in its weak field limit, a Yukawa-like correction to the Newtonian potential, and is capable to explain most of the phenomenology related to dark matter at scale of galaxies and galaxy clusters. Nevertheless, some inconsistencies appears when studying systems that are supposed to be dark matter dominated such as dwarf galaxies. In this sense Antlia II, an extremely diffuse galaxy which has been recently discovered in Gaia's second data release, may serve to probe the aforementioned theory against the need for invoking dark matter. Our analysis shows several inconsistencies and leads to argue that MOdified Gravity may not be able to shed light on the intriguing nature of dark matter.
Physics Letters B, 2019
We analyze axion--photon mixing in the framework of quantum field theory. The condensate structur... more We analyze axion--photon mixing in the framework of quantum field theory. The condensate structure of the vacuum for mixed fields
induces corrections to the oscillation formulae and leads to non-zero energy of the vacuum for the component of the photon mixed with the axion. This energy generates a new effect of the vacuum polarization and it has the state equation of the cosmological constant, $w = -1$. This result holds for any homogeneous and isotropic curved space-time, as well as for diagonal metrics.
Numerical estimates of the corrections to the oscillation formulae are presented by considering the intensity of the magnetic field available in the laboratory. Moreover, we estimate the vacuum energy density induced by axion--photon mixing in the Minkowski space-time.
A value compatible with that of the energy density of the universe can be obtained for axions with a mass of $(10^{-3}-10^{-2}) eV$ in the presence of the strong magnetic fields that characterize astrophysical objects such as pulsars or neutron stars.
In addition, a value of the energy density less than that of the Casimir effect is obtained for magnetic fields used in experiments such as PVLAS. The vacuum polarization induced by this energy could be detected in next experiments and it might provide an indirect proof of the existence of the axion--photon mixing.
The quantum field theory effects presented in this work may lead to new methods for studying axion-like particles.
The European Physics Journal C, 2018
The study of the dynamics of a two-body system in modified gravity constitutes a more complex pro... more The study of the dynamics of a two-body system in modified gravity constitutes a more complex problem than in Newtonian gravity. Numerical methods are typically needed to solve the equations of geodesics. Despite the complexity of the problem, the study of a two-body system in f (R) gravity leads to a new exciting perspective hinting the right strategy to adopt in order to probe modified gravity. Our results point out some differences between the semiclassical (Newtonian) approach, and the relativistic (geodesic) one thus suggesting that the latter represents the best strategy for future tests of modified theories of gravity. Finally, we have also highlighted the capability of forthcoming observations to serve as smoking gun of modified gravity revealing a departure from GR or further reducing the parameter space of f (R) gravity.
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Papers by Ivan de Martino
induces corrections to the oscillation formulae and leads to non-zero energy of the vacuum for the component of the photon mixed with the axion. This energy generates a new effect of the vacuum polarization and it has the state equation of the cosmological constant, $w = -1$. This result holds for any homogeneous and isotropic curved space-time, as well as for diagonal metrics.
Numerical estimates of the corrections to the oscillation formulae are presented by considering the intensity of the magnetic field available in the laboratory. Moreover, we estimate the vacuum energy density induced by axion--photon mixing in the Minkowski space-time.
A value compatible with that of the energy density of the universe can be obtained for axions with a mass of $(10^{-3}-10^{-2}) eV$ in the presence of the strong magnetic fields that characterize astrophysical objects such as pulsars or neutron stars.
In addition, a value of the energy density less than that of the Casimir effect is obtained for magnetic fields used in experiments such as PVLAS. The vacuum polarization induced by this energy could be detected in next experiments and it might provide an indirect proof of the existence of the axion--photon mixing.
The quantum field theory effects presented in this work may lead to new methods for studying axion-like particles.
induces corrections to the oscillation formulae and leads to non-zero energy of the vacuum for the component of the photon mixed with the axion. This energy generates a new effect of the vacuum polarization and it has the state equation of the cosmological constant, $w = -1$. This result holds for any homogeneous and isotropic curved space-time, as well as for diagonal metrics.
Numerical estimates of the corrections to the oscillation formulae are presented by considering the intensity of the magnetic field available in the laboratory. Moreover, we estimate the vacuum energy density induced by axion--photon mixing in the Minkowski space-time.
A value compatible with that of the energy density of the universe can be obtained for axions with a mass of $(10^{-3}-10^{-2}) eV$ in the presence of the strong magnetic fields that characterize astrophysical objects such as pulsars or neutron stars.
In addition, a value of the energy density less than that of the Casimir effect is obtained for magnetic fields used in experiments such as PVLAS. The vacuum polarization induced by this energy could be detected in next experiments and it might provide an indirect proof of the existence of the axion--photon mixing.
The quantum field theory effects presented in this work may lead to new methods for studying axion-like particles.
the data of 579 clusters in the Planck foreground clean map SMICA. Our results show that the resulting profiles of these systems fit the data without requiring a dominant dark matter component, with model parameters similar to those required to explain the dynamics of galaxies. Extended theories of gravity could provide explanation to the dynamics of self-gravitating systems and to the present period of accelerated expansion alternative to the concordance cosmological model.
galaxy clusters, in both $f(R)$ and MOG theories, agrees with the observed profile
when their Intra Cluster gas is in hydrostatic equilibrium within the modified Newtonian
potential. There is no need to introduce a dominant DM component. We particularize our
analysis for the Coma cluster since is located close to the galactic pole where the foreground
emission is comparatively low. We use Planck 2013 Nominal maps to measure its SZ profile and
constrain the parameters of the modified gravitational potential of both theories.
"Constraining spatial variations of the fine structure constant using clusters of galaxies and Planck data", 2016, arXiv:1605.03053
Specifically, we describe a system at equilibrium by a time-independent distribution function f0(x; v)
and two potentials Phi0(x) and Psi0(x) solutions of the modified Poisson and collisionless Boltzmann equations. Considering a small perturbation from the equilibrium and linearizing the field equations, it can be obtained a dispersion relation. A dispersion equation is achieved for neutral dust-particle systems
where a generalized Jeans wave number is obtained. This analysis gives rise to unstable modes not present in the standard Jeans analysis (derived assuming Newtonian gravity as weak filed limit of f(R). In this perspective, we discuss several self-gravitating astrophysical systems whose dynamics could be fully
addressed in the framework of f(R) gravity.
evolves linearly with redshift. This assumption nedds to be tested observationally.
There are currently two methods to determine the CMB temperature, T(z), at redshifts z>0:
(a) using the Quasar's absorption lines; (b) from the thermal Sunyaev-Zeldovich (SZ) anisotropies.
Recently, T(z) scaling relation was tested using the spectral measurements of the SZ effect and the results are
in agreement with adiabatic evolution. We analyze how PLANCK data can be used to test the standard scaling
relation of the CMB temperature with redshift. "
test the model, we have computed the pressure profile of 579 X-ray galaxy clusters assuming the gas is in hydrostatic equilibrium within the potential well of the modified gravitational potential. We have compared those profiles
with the ones measured in the foreground cleaned SMICA released by the Planck Collaboration. Our results show that Extended Theories of Gravity explain the dynamics of self-gravitating systems at cluster scales and represent an alternative to dark matter haloes.