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The observed red shift $z$ might be composed by the expansion red shift $z_{\rm C}$ and an additional frequency shift $z_{\rm S}$, towards the red or the blue, by considering Extended Theories of Electromagnetism (ETE). Indeed, massive photon theories - the photon has a real mass as in the de Broglie-Proca theory or an effective mass as in the Standard-Model Extension (SME), based on Lorentz-Poincar\'e Symmetry Violation (LSV) - or Non-Linear Electro-Magnetism (NLEM) theories may induce a cosmological expansion independent frequency shift in presence of background (inter-) galactic electromagnetic fields, and where of relevance LSV fields, even when both fields are constant. We have tested this prediction considering the Pantheon Catalogue, composed by 1048 SNe Ia, and 15 BAO data, for different cosmological models characterised by the absence of a cosmological constant. From the data, we compute which values of $z_{\rm S}$ match the observations, spanning cosmological parameters ($\Omega$ densities and Hubble-Lema\^itre constant) domains. We conclude that the frequency shift $z_{\rm S}$ can support an alternative to accelerated expansion, naturally accommodating each SN Ia position in the distance-modulus versus red shift diagram, due to the light-path dependency of $z_{\rm S}$. Finally, we briefly mention laboratory test approaches to investigate the additional shift from ETE predictions., Comment: Accepted by Eur. Phys. J. Plus (Special Issue on: Tensions in cosmology from early to late universe: the value of the Hubble constant and the question of dark energy)

A main issue in cosmology and astrophysics is whether the dark sector phenomenology originates from particle physics, then requiring the detection of new fundamental components, or it can be addressed by modifying General Relativity. Extended Theories of Gravity are possible candidates aimed in framing dark energy and dark matter in a comprehensive geometric view. Considering the concept of perfect scalars, we show that the field equations of such theories naturally contain perfect fluid terms. Specific examples are developed for the Friedman-Lema\^itre-Roberson-Walker metric., Comment: 7 pages, accepted for publication in Europhysics Letters

We discuss some main aspects of theories of gravity containing non-local terms in view of cosmological applications. In particular, we consider various extensions of General Relativity based on geometrical invariants as $f(R, \Box^{-1} R)$, $f({\cal G}, \Box^{-1} {\cal G})$ and $f(T, \Box^{-1} T)$ gravity where $R$ is the Ricci curvature scalar, $\cal G$ is the Gauss-Bonnet topological invariant, $T$ the torsion scalar and the operator $\Box^{-1}$ gives rise to non-locality. After selecting their functional form by using Noether Symmetries, we find out exact solutions in a cosmological background. It is possible to reduce the dynamics of selected models and to find analytic solutions for the equations of motion. As a general feature of the approach, it is possible to address the accelerated expansion of the Hubble flow at various epochs, in particular the dark energy issues, by taking into account non-locality corrections to the gravitational Lagrangian. On the other hand, it is possible to search for gravitational non-local effects also at astrophysical scales. In this perspective, we search for symmetries of $f(R, \Box^{-1} R)$ gravity also in a spherically symmetric background and constrain the free parameters, Specifically, by taking into account the S2 star orbiting around the Galactic Centre SgrA$^*$, it is possible to study how non-locality affects stellar orbits around such a massive self-gravitating object., Comment: 43 pages, 5 figures, to appear in Int. J. Mod. Phys. D

We review the possible violation of the Equivalence Principle at finite temperature T in the framework of curvature based Extended Theories of Gravity. Specifically, we first show how it is possible to derive Equivalence Principle violation from Quantum Field Theory at non-vanishing T. Subsequently, we exhibit how this result can be precisely recovered by following an alternative path that envisages the employment of generalized Einstein equations with a temperature-dependent energy-momentum tensor. Finally, we adopt the latter formalism in the context of some Extended Gravity models to quantify the amount of Equivalence Principle violation. Specifically, Brans-Dicke Theory, Standard Model Extension and Conformal Gravity are considered in details.

For an observation time {equal to} the universe age, the Heisenberg principle fixes the value of the smallest measurable mass at $m_{\rm H}=1.35 \times 10^{-69}$ kg and prevents to probe the masslessness for any particle using a balance. The corresponding reduced Compton length to $m_{\rm H}$ is $\lambdabar_{\rm H}$, and represents the length limit beyond which masslessness cannot be proved using a metre ruler. In turns, $\lambdabar_{\rm H}$ is equated to the luminosity distance $d_{\rm H}$ which corresponds to a red shift $z_{\rm H}$. When using the Concordance-Model parameters, we get $d_{\rm H} = 8.4$ Gpc and $z_{\rm H}=1.3$. Remarkably, $d_{\rm H}$ falls quite short to the radius of the {\it observable} universe. According to this result, tensions in cosmological parameters could be nothing else but due to comparing data inside and beyond $z_{\rm H}$. Finally, in terms of quantum quantities, the expansion constant $H_0$ reveals to be one order of magnitude above the smallest measurable energy, divided by the Planck constant, Comment: A different view on the Hubble tension. To appear in final form on Foundations of Physics by Springer, as follow-on of Capozziello S., Benetti M., Spallicci A.D.A.M., 2020, Found. Phys., 50, 893

We consider extensions of General Relativity based on the non-local function $f(R, \Box^{-1} R)$, where $R$ is the Ricci curvature scalar and the non-locality is due to the term $\Box^{-1} R$. We focus on cosmological minisuperspaces and select viable models by the Noether Symmetry Approach. Then we find viable exact solutions pointing out the role of non-locality in cosmology., Comment: 13 pages

We test the validity of a possible schematization of DNA structure and dynamics based on the Chern-Simons theory, that is a topological field theory mostly considered in the context of effective gravity theories. By means of the expectation value of the Wilson Loop, derived from this analogue gravity approach, we find the point-like curvature of genomic strings in KRAS human gene and COVID-19 sequences, correlating this curvature with the genetic mutations. The point-like curvature profile, obtained by means of the Chern-Simons currents, can be used to infer the position of the given mutations within the genetic string. Generally, mutations take place in the highest Chern-Simons current gradient locations and subsequent mutated sequences appear to have a smoother curvature than the initial ones, in agreement with a free energy minimization argument., Comment: 25 Pages. Accepted for publication in European Physicsl Journal Plus

The geometric trinity of gravity offers a platform in which gravity can be formulated in three analogous approaches, namely curvature, torsion and nonmetricity. In this vein, general relativity can be expressed in three dynamically equivalent ways which may offer insights into the different properties of these decompositions such as their Hamiltonian structure, the efficiency of numerical analyses, as well as the classification of gravitational field degrees of freedom. In this work, we take a $3+1$ decomposition of the teleparallel equivalent of general relativity and the symmetric teleparallel equivalent of general relativity which are both dynamically equivalent to curvature based general relativity. By splitting the spacetime metric and corresponding tetrad into their spatial and temporal parts as well as through finding the Gauss-like equations, it is possible to set up a general foundation for the different formulations of gravity. Based on these results, general $3$-tetrad and $3$-metric evolution equations are derived. Finally through the choice of the two respective connections, the metric $3+1$ formulation for general relativity is recovered as well as the tetrad $3+1$ formulation of the teleparallel equivalent of general relativity and the metric $3+1$ formulation of symmetric teleparallel equivalent of general relativity. The approach is capable, in principle, of resolving common features of the various formulations of general relativity at a fundamental level and pointing out characteristics that extensions and alternatives to the various formulations can present., Comment: 23 pages

Inflationary models derived from $f(R)$ gravity, where the scalaron rolls down with a constant rate from the top to the minimum of the effective potential, are considered. Specifically, we take into account three $f(R)$ models \textit{i.e.}\,Starobinsky $R^{2}$, $R^{2p}$ and the logarithmic corrected models. We compare the inflationary parameters derived from the models with the observational data of CMB anisotropies \textit{i.e.} the Planck and Keck/array datasets in order to find observational constraints on the parameters space. We find that although our $f(R)$ constant-roll models for $\gamma=0$ show observationally acceptable values of $r$, they do not predict favoured values of the spectral index. In particular, we have $n_{s}>1$ for the Starobinsky $R^{2}$ and $R^{2p}$ models and $0.996

Loop Quantum Cosmology (LQC) is a theory which renders the Big Bang initial singularity into a quantum bounce, by means of short range repulsive quantum effects at the Planck scale. In this work, we are interested in reproducing the effective Friedmann equation of LQC, by considering a generic $f(R,P,Q)$ theory of gravity, where $R=g^{\mu\nu}R_{\mu\nu}$ is the Ricci scalar, $P=R_{\mu\nu}R^{\mu\nu}$, and $Q=R_{\alpha\beta\mu\nu}R^{\alpha\beta\mu\nu}$ is the Kretschmann scalar. An order reduction technique allows us to work in $f(R,P,Q)$ theories which are perturbatively close to General Relativity, and to deduce a modified Friedmann equation in the reduced theory. Requiring that the modified Friedmann equation mimics the effective Friedmann equation of LQC, we are able to derive several functional forms of $f(R,P,Q)$. We discuss the necessary conditions to obtain viable bouncing cosmologies for the proposed effective actions of $f(R,P,Q)$ theory of gravity., Comment: v1: 15 pages; v2: 16 pages. Matches published version in EPJC

We derive gravitational waves in a theory with non-local curvature corrections to the Hilbert-Einstein Lagrangian. In addition to the standard two massless tensor modes, with plus and cross polarizations, helicity 2 and angular frequency $\omega_{1}$, we obtain a further scalar massive mode with helicity 0 and angular frequency $\omega_{2}$, whose polarization is transverse. It is a breathing mode, which, at the lowest order of an effective parameter $\gamma$, presents a speed difference between nearly null and null plane waves. Finally, the quasi-Lorentz $E(2)$-invariant class for the non-local gravity is type $N_{3}$, according to the Petrov classification. This means that the presence (or absence) of gravitational wave modes is observer-independent., Comment: 22 pages, accepted for publication in Classical and Quantum Gravity

We propose two model independent methods to obtain constraints on the transition and equivalence redshifts $z_{tr}$, $z_{eq}$. In particular, we consider $z_{tr}$ as the onset of cosmic acceleration, whereas $z_{eq}$ the redshift at which the densities of dark energy and pressureless matter are equated. With this prescription, we expand the Hubble and deceleration parameters up to two hierarchical orders and show a linear correlation between transition and equivalence, from which we propose exclusion plots where $z_{eq}$ is not allowed to span. To this end, we discuss how to build up cosmographic expansions in terms of $z_{tr}$ and compute the corresponding observable quantities directly fitting the luminosity and angular distances and the Hubble rate with cosmic data. We make our computations through Monte Carlo fits involving type Ia supernova, baryonic acoustic oscillation and Hubble most recent data catalogs. We show at $1\sigma$ confidence level the $\Lambda$CDM predictions on $z_{tr}$ and $z_{eq}$ are slightly confirmed, although at $2\sigma$ confidence level dark energy expectations cannot be excluded. Finally, we theoretically interpret our outcomes and discuss possible limitations of our overall approach., Comment: 17 pages, 11 figures, 3 tables, Accepted for publication in MNRAS

The measurement of the epicyclic frequencies is a widely used astrophysical technique to infer information on a given self-gravitating system and on the related gravity background. We derive their explicit expressions in static and spherically symmetric wormhole spacetimes. We discuss how these theoretical results can be applied to: (1) detect the presence of a wormhole, distinguishing it by a black hole; (2) reconstruct wormhole solutions through the fit of the observational data, once we have them. Finally, we discuss the physical implications of our proposed epicyclic method., Comment: 11 pages, 6 figures, 2 tables; accepted for publication on Phys. Rev. D on 23/06/2021

Lovelock gravity in $D$-dimensional space-times is considered adopting Cartan's structure equations. In this context, we find out exact solutions in cosmological and spherically symmetric backgrounds. In the latter case, we also derive horizons and the corresponding Bekenstein--Hawking entropies. Moreover, we focus on the topological Chern--Simons theory, providing exact solutions in 5 dimensions. Specifically, it is possible to show that Anti-de Sitter invariant Chern--Simons gravity can be framed within Lovelock--Zumino gravity in 5 dimensions, for particular choices of Lovelock parameters., Comment: 23 pages. Accepted for publication in JCAP

General Relativity and the $\Lambda$CDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. All extended theories and scenarios are first examined under the light of theoretical consistency, and then are applied to various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology are able to offer recently. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature. This work is a Review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. Its realization was performed in the framework of the COST European Action ``Cosmology and Astrophysics Network for Theoretical Advances and Training Actions''., Comment: 543 pages

It is well known that General Relativity cannot be considered under the standard of a perturbatively renormalizable quantum field theory, but asymptotic safety is taken into account as a possibility for the formulation of gravity as a non-perturbative renormalizable theory. Recently, the entropy argument has however stepped into the discussion claiming for a "no-go" to the asymptotic safety argument. In this paper, we present simple counter-examples, considering alternative theories of gravity, to the entropy argument as further indications, among others, on the possible flows in the assumptions on which the latter is based on. We consider different theories, namely curvature based extensions of General Relativity as $f(R)$, $f(\mathcal{G})$, extensions of Teleparallel Gravity as $f(T)$, and Horava-Lifshitz gravity, working out the explicit spherically symmetric solutions in order to make a comparison between power counting and the entropy argument. Even in these cases, inconsistencies are found., Comment: 13 pages. Accepted for publication in "Universe"

We consider thermal effects in the propagation of gravitational waves on a cosmological background. In particular, we consider scalar field cosmologies and study gravitational modes near cosmological singularities. We point out that the contribution of thermal radiation can heavily affect the dynamics of gravitational waves giving enhancement or dissipation effects both at quantum and classical level.These effects are considered both in General Relativity and in modified theories like $F(R)$ gravity which can be easily reduced to scalar-tensor cosmology. The possible detection and disentanglement of standard and scalar gravitational modes on the stochastic background are also discussed., Comment: 21 pages, accepted for publication in Physics of the Dark Universe

We discuss the emergence of black hole shadow and photon-sphere in the context of $f(R)$ gravity. It is shown that the shadow is exponentially sensitive to linear instabilities of metric coming from some $f(R)$ solutions. Thus, the instabilities of photon circular trajectories, delimiting the black hole photon-sphere, are double exponentialized. Specifically we individuate two Lyapunov exponents, rather than only one, related to two different sources of chaos in geodesic orbits as a sort of butterfly effect. Such a result violates the black hole chaos bound proposed by Maldacena, Shenker and Stanford for General Relativity. We also explore the impact of the black hole metric instabilities in $f(R)$ gravity on the quasi-normal modes. In the framework of Extended Theories of Gravity, our analysis suggests a new paradigm to deal with black hole shadow and gravitational waves observations coming from black hole merging in the ringdown phase., Comment: 16 pages, 2 figures, accepted for publication in Phys. Lett. B

We study a single field inflationary model modified by a non-minimal coupling term between the Ricci scalar $R$ and the scalar field $\varphi$ in the context of constant-roll inflation. The first-order formalism is used to analyse the constant-roll inflation instead of the standard methods used in the literature. In principle, the formalism considers two functions of the scalar field, $W=W(\varphi)$ and $Z=Z(\varphi)$, which lead to the reduction of the equations of motion to first-order differential equations. The approach can be applied to a wide range of cosmological situations since it directly relates the function $W$ with Hubble parameter $H$. We perform the inflationary analysis for power-law and exponential couplings, separately. Then, we investigate the features of constant-roll potentials as inflationary potentials. Finally, we compare the inflationary parameters of the models with the observations of CMB anisotropies in view of realize a physically motivated model., Comment: 15 pages, 6 figures, Accepted for publication in Int. J. Mod. Phys. D

The debate on gravity theories to extend or modify General Relativity is very active today because of the issues related to ultra-violet and infra-red behavior of Einstein's theory. In the first case, we have to address the Quantum Gravity problem. In the latter, dark matter and dark energy, governing the large scale structure and the cosmological evolution, seem to escape from any final fundamental theory and detection. The state of art is that, up to now, no final theory, capable of explaining gravitational interaction at any scale, has been formulated. In this perspective, many research efforts are devoted to test theories of gravity by space-based experiments. Here we propose straightforward tests by the GINGER experiment, which, being Earth based, requires little modeling of external perturbation, allowing a thorough analysis of the systematics, crucial for experiments where sensitivity breakthrough is required. Specifically, we want to show that it is possible to constrain parameters of gravity theories, like scalar-tensor or Horava-Lifshitz gravity, by considering their post-Newtonian limits matched with experimental data. In particular, we use the Lense-Thirring measurements provided by GINGER to find out relations among the parameters of theories and finally compare the results with those provided by LARES and Gravity Probe-B satellites., Comment: 15 pages, 3 figures, accepted for publication in EPJP

We study the frequency shift of photons generated by rotating gravitational sources in the framework of curvature based Extended Theories of Gravity. The discussion is developed considering the weak-field approximation. Following a perturbative approach, we analyze the process of exchanging photons between Earth and a given satellite, and we find a general relation to constrain the free parameters of gravitational theories. Finally, we suggest the Moon as a possible laboratory to test theories of gravity by future experiments which can be, in principle, based also on other Solar System bodies., Comment: 10 pages

Effects from nonstandard corrections to Newtonian gravity, at large scale, can be investigated using the cosmological structure formation. In particular, it is possible to show if and how a logarithmic correction (as that induced from nonlocal gravity) modifies the clustering properties of galaxies and of clusters of galaxies. The thermodynamics of such systems can be used to obtain important information about the effects of such modification on clustering. We will compare its effects with observational data and it will be demonstrated that the observations seem to point to a characteristic scale where such a logarithmic correction might be in play at galactic scales. However, at larger scales such statistical inferences are much weaker, so that a fully reliable statistical evidence for this kind of corrections cannot be stated without further investigations and the use of more varied and precise cosmological and astrophysical probes., Comment: 19 pages, 8 figures, accepted for publication in EPJC

Static and spherically symmetric wormhole solutions can be reconstructed in the framework of curvature based Extended Theories of Gravity. In particular, extensions of the General Relativity, in metric and curvature formalism give rise to modified gravitational potentials, constituted by the classical Newtonian potential and Yukawa-like corrections, whose parameters can be, in turn, gauged by the observations. Such an approach allows to reconstruct the spacetime out of the wormhole throat considering the asymptotic flatness as a physical property for the related gravitational field. Such an argument can be applied for a large class of curvature theories characterising the wormholes through the parameters of the potentials. According to this procedure, possible wormhole solutions could be observationally constrained. On the other hand, stable and traversable wormholes could be a direct probe for this class of Extended Theories of Gravity., Comment: 9 pages; 2 figures; 1 Table; accepted on EPJ C

The sensitivity to angular rotation of the top class Sagnac gyroscope GINGERINO is carefully investigated with standard statistical means, using 103 days of continuous operation and the available geodesic measurements of the Earth angular rotation rate. All features of the Earth rotation rate are correctly reproduced. The sensitivity of fractions of frad/s is attained for long term runs. This excellent sensitivity and stability put Sagnac gyroscopes at the forefront for fundamental physics, in particular for tests of general relativity and Lorentz violation, where the sensitivity plays the key role to provide reliable data for deeper theoretical investigations. The achieved sensitivity overcomes the conventionally expected one for Sagnac ring laser gyroscopes., Comment: 13 pages, 7 figures, regular paper

We develop a model-independent procedure to single out static and spherically symmetric wormhole solutions based on the general relativistic Poynting-Robertson effect and the extension of the ray-tracing formalism in generic static and spherically symmetric wormhole metrics. Simulating the flux emitted by the Poynting-Robertson critical hypersurface (i.e., a stable structure where gravitational and radiation forces attain equilibrium) or also from another X-ray source in these general geometrical environments toward a distant observer, we are able to reconstruct, only locally to the emission region, the wormhole solutions which are in agreement with the high-energy astrophysical observational data. This machinery works only if wormhole evidences have been detected. Indeed, in our previous paper we showed how the Poynting-Robertson critical hypersurfaces can be located in regions of strong gravitational field and become valuable astrophysical probe to observationally search for wormholes' existence. As examples, we apply our method to selected wormhole solutions in different extended theories of gravity by producing lightcurves, spectra, and images of an accretion disk. In addition, the present approach may constitute a procedure to also test the theories of gravity. Finally, we discuss the obtained results and draw the conclusions., Comment: 17 pages, 4 figures, 2 Tables. Paper accepted on Physical Review D

We apply the Noether Symmetry Approach to point-like teleparallel Lagrangians in view to derive minisuperspaces suitable for Quantum Cosmology. Adopting the Arnowitt-Deser-Misner formalism, we find out related Wave Functions of the Universe. Specifically, by means of appropriate changes of variables suggested by the existence of Noether symmetries, it is possible to obtain the cosmological Hamiltonians whose solutions are classical trajectories interpretable as observable universes., Comment: 15 Pages, 1 figure

We derive exact traversable wormhole solutions in the framework of $f(R)$ gravity with no exotic matter and with stable conditions over the geometric fluid entering the throat. For this purpose, we propose power-law $f(R)$ models and two possible approaches for the shape function $b(r)/r$. The first approach makes use of an inverse power law function, namely $b(r)/r\sim r^{-1-\beta}$. The second one adopts Pad\'e approximants, used to characterize the shape function in a model-independent way. We single out the $P(0,1)$ approximant where the fluid perturbations are negligible within the throat, if the sound speed vanishes at $r=r_0$. The former guarantees an overall stability of the geometrical fluid into the wormhole. Finally we get suitable bounds over the parameters of the model for the above discussed cases. In conclusion, we find that small deviations from General Relativity give stable solutions., Comment: 11 pages, 2 figures

The gravitino problem is investigated in the framework of Extended Gravity cosmologies. In particular, we consider $f(R)$ gravity, the most natural extension of the Hilbert-Einstein action, and $f(\cal T)$ gravity, the extension of teleparallel equivalent gravity. Since in these theories the expansion laws of the Universe are modified, as compared to the standard $\Lambda$CDM cosmology, it follows that also the thermal history of particles gets modified. We show that $f(R)$ models allow to avoid the late abundance of gravitinos. In particular, we found that for an appropriate choice of the parameters characterizing the $f(R)$ model, the gravitino abundance turns out to be independent of the reheating temperature. A similar behavior is achieved also in the context of $f(\cal T)$ gravity. In this perspective, we can conclude that geometric corrections to standard General Relativity (and to Teleparallel Equivalent of General Relativity) can improve shortcomings both in cosmology and in unified theories beyond the Standard Model of particles., Comment: 7 pages

The total red shift $z$ might be recast as a combination of the expansion red shift and a static shift due to the energy-momentum tensor non-conservation of a photon propagating through Electro-Magnetic (EM) fields. If massive, the photon may be described by the de Broglie-Proca (dBP) theory which satisfies the Lorentz(-Poincar\'e) Symmetry (LoSy) but not gauge-invariance. The latter is regained in the Standard-Model Extension (SME), associated with LoSy Violation (LSV) that naturally dresses photons of a mass. The non-conservation stems from the vacuum expectation value of the vector and tensor LSV fields. The final colour (red or blue) and size of the static shift depend on the orientations and strength of the LSV and EM multiple fields encountered along the path of the photon. Turning to cosmology, for a zero $\Omega_{\Lambda}$ energy density, the discrepancy between luminosity and red shift distances of SNeIa disappears thanks to the recasting of $z$. Massive photons induce an effective dark energy acting `optically' but not dynamically., Comment: Version accepted by Eur. Phys. J. C

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 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 DM 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., Comment: 64 pages 16 Figures. In print on Frontiers in Astronomy and Space Sciences, for the Research Topic: "When Planck, Einstein and Vera Rubin Meet. Dark Matter: What is it ? Where is it?"

We propose a covariant and geometric framework to introduce space distances as they are used by astronomers. In particular, we extend the definition of space distances from the one used between events to non-test-bodies with horizons and singularities so that the definition extends through the horizons and it matches the protocol used to measure them. The definition we propose can be used in standard General Relativity although it extends directly to Weyl geometries to encompass a number of modified theories, extended theories in particular., Comment: 12 pages, 4 figures

Non-local gravity cosmologies are considered under the standard of Noether Symmetry Approach. In particular, we focus on non-local theories whose gravitational actions depend on curvature and Gauss-Bonnet scalar invariants. Specific functional forms of the related point-like Lagrangians are selected by Noether symmetries and we solve the corresponding field equations finding out exact cosmological solutions., Comment: 12 pages, 46 references

We consider f(Q) extended symmetric teleparallel cosmologies, where Q is the non-metricity scalar, and constrain its functional form through the order reduction method. By using this technique, we are able to reduce and integrate the field equations and thus to select the corresponding models giving rise to bouncing cosmology. The selected Lagrangian is then used to develop the Hamiltonian formalism and to obtain the Wave Function of the Universe which suggests that classical observable universes can be recovered according to the Hartle Criterion., Comment: 11 pages, 1 figure, 68 references

We discuss non-minimally coupled cosmologies involving different geometric invariants. Specifically, actions containing a non-minimally coupled scalar field to gravity described, in turn, by curvature, torsion and Gauss--Bonnet scalars are considered. We show that couplings, potentials and kinetic terms are determined by the existence of Noether symmetries which, moreover, allows to reduce and solve dynamics. The main finding of the paper is that different non-minimally coupled theories, presenting the same Noether symmetries, are dynamically equivalent. In other words, Noether symmetries are a selection criterion to compare different theories of gravity., Comment: 16 pages. Accepted for publication in "International Journal of Modern Physics D"

In the framework of Teleparallel Gravity, we derive a charged non-vacuum solution for a physically symmetric tetrad field with two unknown functions of radial coordinate. The field equations result in a closed-form adopting particular metric potentials and a suitable anisotropy function combined with the charge. Under these circumstances, it is possible to obtain a set of configurations compatible with observed pulsars. Specifically, boundary conditions for the interior spacetime are applied to the exterior Reissner-Nordstr\"om metric to constrain the radial pressure that has to vanish through the boundary. Starting from these considerations, we are able to fix the model parameters. The pulsar $\textit {PSR J 1614--2230}$, with estimated mass $M= 1.97 \pm 0.04\, M_{\circledcirc},$ and radius $R= 9.69 \pm 0.2$ km is used to test numerically the model. The stability is studied, through the causality conditions and adiabatic index, adopting the Tolman-Oppenheimer-Volkov equation. The mass-radius $(M,R)$ relation is derived. Furthermore, the compatibility of the model with other observed pulsars is also studied. We reasonably conclude that the model can represent realistic compact objects., Comment: 21 pages, 14 figures, accepted for publication in EPJC

A large fraction of Gamma-Ray Bursts (GRBs) lightcurves (LCs) shows X-ray plateaus. We analyze all GRBs with known redshifts presenting plateaus observed by \emph{The Neil Gehrels Swift Observatory} from its launch until August 2019. The fundamental plane relation between the rest-frame time and X-ray luminosity at the end of the plateau emission and the peak prompt luminosity holds for all the GRB classes when selection biases and cosmological evolutions are applied. We have discovered two important findings: 1) a new class of Long GRBs with good data coverage: the Platinum Sample; 2) the Platinum, the SNe-LGRB and the KN-SGRB samples, the second sample composed of GRBs associated spectroscopically with the SNe Ib,c, the third sample composed by 8 GRBs associated with Kilonovae or where there could have been such an association, yield the smallest intrinsic scatter, $\sigma_{platinum,GRB-SNe}=0.22 \pm 0.10$ and $\sigma_{KN-SGRB}=0.24 \pm 0.12$. The highest correlation coefficients yield for the SN-LGRB-ABC sample, which are GRBs spectroscopically associated with SNe Ib/c or with a clear optical bump in the LC resembling the SNe Ib/c, ($R^{2}_{SN-LGRB-ABC}=0.95$), for the SN-LGRBs ($R^{2}_{SN-LGRB}=0.91$) and the KN-SGRBs ($R^{2}_{KN-SGRB}=0.90$) when the redshift evolution is considered. These category planes are reliable candidates to be used as cosmological tools. Furthermore, the distance from the Gold fundamental plane is a crucial discriminant among classes. In fact, we find that the distributions of the distances of the SNe-LGRB, SNe-LGRB-ABC, KN-SGRBs and SGRBs samples from the Gold fundamental plane are statistically different from the distribution of the Gold GRBs' distances from the Gold fundamental plane with and without considering evolution cases., Comment: ApJ accepted, to be published 25th november, 19 Pages, 9 Figures, 6 Tables. Press Release has been issued by https://www.riken.jp/press/2020/20201119_3/index.html and http://www.oa.uj.edu.pl/AOM/aom20nov.en.html

The teleparallel equivalent of higher order Lagrangians like $L_{\Box R}=-R+a_{0}R^{2}+a_{1}R\Box R$ can be obtained by means of the boundary term $B=2\nabla_{\mu}T^{\mu}$. In this perspective, we derive the field equations in presence of matter for higher-order teleparallel gravity considering, in particular, sixth-order theories where the $\Box$ operator is linearly included. In the weak field approximation, gravitational wave solutions for these theories are derived. Three states of polarization are found: the two standard $+$ and $\times$ polarizations, namely 2-helicity massless transverse tensor polarizations, and a 0-helicity massive, with partly transverse and partly longitudinal scalar polarization. Moreover, these gravitational waves exhibit four oscillation modes related to four degrees of freedom: the two classical $+$ and $\times$ tensor modes of frequency $\omega_{1}$, related to the standard Einstein waves with $k^{2}_{1}=0$; two mixed longitudinal-transverse scalar modes for each frequencies $\omega_{2}$ and $\omega_{3}$, related to two different 4-wave vectors, $k^{2}_{2}=M_{2}^{2}$ and $k^{2}_{3}=M^{2}_{3}$. The four degrees of freedom are the amplitudes of each individual mode, i.e. $\hat{\epsilon}^{(+)}\left(\omega_{1}\right)$, $\hat{\epsilon}^{(\times)}\left(\omega_{1}\right)$, $\hat{B}_{2}\left(\mathbf{k}\right)$, and $\hat{B}_{3}\left(\mathbf{k}\right)$., Comment: 27 pages, accepted for publication in Classical and Quantum Gravity

We apply Gaussian processes (GP) in order to impose constraints on teleparallel gravity and its $f(T)$ extensions. We use available $H(z)$ observations from (i) cosmic chronometers data (CC); (ii) Supernova Type Ia (SN) data from the compressed Pantheon release together with the CANDELS and CLASH Multi-Cycle Treasury programs; and (iii) baryonic acoustic oscillation (BAO) datasets from the Sloan Digital Sky Survey. For the involved covariance functions, we consider four widely used choices, namely the square exponential, Cauchy, Mat\'{e}rn and rational quadratic kernels, which are consistent with one another within 1$\sigma$ confidence levels. Specifically, we use the GP approach to reconstruct a model-independent determination of the Hubble constant $H_0$, for each of these kernels and dataset combinations. These analyses are complemented with three recently announced literature values of $H_0$, namely (i) Riess $H_0^{\rm R} = 74.22 \pm 1.82 \,{\rm km\, s}^{-1} {\rm Mpc}^{-1}$; (ii) H0LiCOW Collaboration $H_0^{\rm HW} = 73.3^{+1.7}_{-1.8} \,{\rm km\, s}^{-1} {\rm Mpc}^{-1}$; and (iii) Carnegie-Chicago Hubble Program $H_0^{\rm TRGB} = 69.8 \pm 1.9 \,{\rm km\, s}^{-1} {\rm Mpc}^{-1}$. Additionally, we investigate the transition redshift between the decelerating and accelerating cosmological phases through the GP reconstructed deceleration parameter. Furthermore, we reconstruct the model-independent evolution of the dark energy equation of state, and finally reconstruct the allowed $f(T)$ functions. As a result, the $\Lambda$CDM model lies inside the allowed region at 1$\sigma$ in all the examined kernels and datasets, however a negative slope for $f(T)$ versus $T$ is slightly favored., Comment: 36 pages, 16 figures

The detection of gravitational wave modes and polarizations could constitute an extremely important signature to discriminate among different theories of gravity. According to this statement, it is possible to prove that higher-order non-local gravity has formally the same gravitational spectrum of higher-order local gravity. In particular, we consider the cases of $f \left( R, \Box R, \Box^2 R, \cdots, \Box^n R \right) = R + \sum_{i=1}^n \alpha_i R \Box^i R$ gravity, linear with respect to both $R$ and $\Box^i R$ and $ f \left( R, \Box R \right) = R + \alpha \left(\Box R\right)^2 $ gravity, quadratic with respect to $\Box R$, where it is demonstrated the graviton amplitude changes if compared with General Relativity. We also obtain the gravitational spectrum of higher-order non-local gravity $ f \left( R, \Box^{-1} R, \Box^{-2} R, \cdots, \Box^{-n} R \right) = R + \sum_{i=1}^n \alpha_i R \Box^{-i} R$. In this case, we have three state of polarization and $n+3$ oscillation modes. More in detail, it is possible to derive two transverse tensor $(+)$ and $(\times)$ standard polarization modes of frequency $\omega_{1}$, massless and with 2-helicity; $n+1$ further scalar modes of frequency $\omega_{2},\dots,\omega_{n+2}$, massive and with 0-helicity, each of which has the same mixed polarization, partly longitudinal and partly transverse., Comment: 15 pages, to appear in Physics. Lett. B

Very recently a compact object with a mass in the range $2.50\div 2.67\, M_{\odot}$ has been discovered via gravitational waves detection of a compact binary coalescence. The mass of this object makes it among the heaviest neutron star never detected or the lightest black hole ever observed. Here we show that a neutron star with this observed mass, can be consistently explained with the mass-radius relation obtained by Extended Theories of Gravity. Furthermore, equations of state, consistent with LIGO observational constraints, are adopted. We consider also the influence of rotation and show that masses of rotating neutron stars can exceed $2.6 M_\odot$ for some equations of state compatible with LIGO data., Comment: 8 pages, 3 figures

The current cosmological probes have provided a fantastic confirmation of the standard $\Lambda$ Cold Dark Matter cosmological model, that has been constrained with unprecedented accuracy. However, with the increase of the experimental sensitivity a few statistically significant tensions between different independent cosmological datasets emerged. While these tensions can be in portion the result of systematic errors, the persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the need for new physics. In this Letter of Interest we will focus on the $4.4\sigma$ tension between the Planck estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we will list a few interesting new physics models that could solve this tension and discuss how the next decade experiments will be crucial., Comment: Snowmass2021 - Letter of Interest

A precise measurement of the curvature of the Universe is of primeval importance for cosmology since it could not only confirm the paradigm of primordial inflation but also help in discriminating between different early Universe scenarios. The recent observations, while broadly consistent with a spatially flat standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model, are showing tensions that still allow (and, in some cases, even suggest) a few percent deviations from a flat universe. In particular, the Planck Cosmic Microwave Background power spectra, assuming the nominal likelihood, prefer a closed universe at more than 99\% confidence level. While new physics could be in action, this anomaly may be the result of an unresolved systematic error or just a statistical fluctuation. However, since a positive curvature allows a larger age of the Universe, an accurate determination of the age of the oldest objects provides a smoking gun in confirming or falsifying the current flat $\Lambda$CDM model., Comment: Snowmass2021 - Letter of Interest

The standard $\Lambda$ Cold Dark Matter cosmological model provides a wonderful fit to current cosmological data, but a few tensions and anomalies became statistically significant with the latest data analyses. While these anomalies could be due to the presence of systematic errors in the experiments, they could also indicate the need for new physics beyond the standard model. In this Letter of Interest we focus on the tension of the Planck data with weak lensing measurements and redshift surveys, about the value of the matter energy density $\Omega_m$, and the amplitude or rate of the growth of structure ($\sigma_8,f\sigma_8$). We list a few interesting models for solving this tension, and we discuss the importance of trying to fit with a single model a full array of data and not just one parameter at a time., Comment: Snowmass2021 - Letter of Interest

The standard $\Lambda$ Cold Dark Matter cosmological model provides an amazing description of a wide range of astrophysical and astronomical data. However, there are a few big open questions, that make the standard model look like a first-order approximation to a more realistic scenario that still needs to be fully understood. In this Letter of Interest we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances present between the different cosmological probes, as the Hubble constant $H_0$ value, the $\sigma_8 - S_8$ tension, and the anomalies present in the Planck results. Finally, we will give an overview of upgraded experiments and next-generation space-missions and facilities on Earth, that will be of crucial importance to address all these questions., Comment: Snowmass2021 - Letter of Interest

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 $F(R,{\cal G})$, with $R$ the Ricci scalar and $\cal G$ 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 $F(R,{\cal G})$ models can lead gravity from ultraviolet to infrared scales. Specifically, we will take into account a cosmographic approach for this purpose., Comment: 16 pages, 2 figures. Accepted for publication on Physical Review D

General properties of vacuum solutions of $f(R)$ gravity are obtained by the condition that the divergence of the Weyl tensor is zero and $f''\neq 0$. Specifically, a theorem states that the gradient of the curvature scalar, $\nabla R$, is an eigenvector of the Ricci tensor and, if it is time-like, the space-time is a Generalized Friedman-Robertson-Walker metric; in dimension four, it is Friedman-Robertson-Walker., Comment: 9 pages, accepted for publication in Int. Jou. Mod. Phys. D

The uncertainty on measurements, given by the Heisenberg principle, is a quantum concept usually not taken into account in General Relativity. From a cosmological point of view, several authors wonder how such a principle can be reconciled with the Big Bang singularity, but, generally, not whether it may affect the reliability of cosmological measurements. In this letter, we express the {Compton mass} as a function of the cosmological redshift. The cosmological application of the indetermination principle unveils the differences of the Hubble-Lema\^{i}tre constant value, $H_0$, as measured from the Cepheids estimates and from the Cosmic Microwave Background radiation constraints. In conclusion, the $H_0$ tension could be related to the effect of indetermination derived in comparing a kinematic with a dynamic measurement., Comment: 7 pages, 1 figure, accepted for publication in Foundations of Physics