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A critical discussion on the $H_0$ Hubble constant tension is presented by considering both early and late-type observations. From recent precise measurements, discrepancies emerge when comparing results for some cosmological quantities obtained at different redshifts. We highlight the most relevant measurements of $H_0$ and propose potential ideas to solve its tension. These solutions concern the exploration of new physics beyond the $\Lambda$CDM model or the evaluation of $H_0$ by other methods. In particular, we focus on the role of the look-back time., Comment: 33 pages, 7 figures

A critical discussion on the $H_0$ Hubble constant tension is presented by considering both early and late-type observations. From recent precise measurements, discrepancies emerge when comparing results for some cosmological quantities obtained at different redshifts. We highlight the most relevant measurements of $H_0$ and propose potential ideas to solve its tension. These solutions concern the exploration of new physics beyond the $\Lambda$CDM model or the evaluation of $H_0$ by other methods. In particular, we focus on the role of the look-back time., Comment: 33 pages, 7 figures

The Hubble tension is investigated taking into account the cosmological look-back time. Specifically, considering a single equation, widely used in standard cosmology, it is possible to recover both values of the Hubble constant $H_0$ reported by the SH0ES and Planck collaborations: the former is obtained through cosmological ladder methods (e.g. Cepheids, Supernovae Type IA) and the latter through measurements of the Cosmic Microwave Background. Also, other values obtained in the literature are achieved with the same approach. We conclude that the Hubble tension can be removed if the look-back time is correctly referred to the redshift where the measurement is performed., Comment: 8 pages, 1 figure, accepted for publication in Physics of the Dark Universe

The Hubble tension is investigated taking into account the cosmological look-back time. Specifically, considering a single equation, widely used in standard cosmology, it is possible to recover both values of the Hubble constant $H_0$ reported by the SH0ES and Planck collaborations: the former is obtained through cosmological ladder methods (e.g. Cepheids, Supernovae Type IA) and the latter through measurements of the Cosmic Microwave Background. Also, other values obtained in the literature are achieved with the same approach. We conclude that the Hubble tension can be removed if the look-back time is correctly referred to the redshift where the measurement is performed., Comment: 8 pages, 1 figure, accepted for publication in Physics of the Dark Universe

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)

Gamma-Ray Bursts (GRBs), observed up to $z=9.4$, can be employed as standardized candles, extending the distance ladder beyond Supernovae Type Ia (SNe Ia, $z=2.26$). We standardize GRBs using the 3D fundamental plane relation among the rest-frame end time of the X-ray plateau emission, its corresponding luminosity, and the peak prompt luminosity. Combining SNe Ia and GRBs, we constrain the matter content $\Omega_{\text{M}}= 0.299 \pm 0.009$ assuming a flat $\Lambda$CDM cosmology with and without correcting for selection biases and redshift evolution. Using a similar 3D correlation in optical, we find that our optical GRB sample is as efficacious in the determination of $\Omega_{\text{M}}$ as the X-ray sample. We trimmed our GRB samples to achieve tighter planes to be used to simulate additional GRBs. We determined how many GRBs are needed to be used as standalone probes to achieve a comparable precision on $\Omega_{\text{M}}$ to the one obtained by SNe Ia only. {\bf We achieve the error measurements derived using SNe Ia in (Conley et al. 2011) with 142 GRBs in optical considering the errorbars on the variables halved and in Betoule et al. (2014) with 284 optical GRBs, by considering that the error bars on the variables halved. Using a doubled sample (obtained by future machine learning approaches that allow both a lightcurve reconstruction and the estimates of GRBs for which the GRB is unknown) compared to our current one, with errorbars halved we will reach the same precision of (Scolnic et al. 2018) with 390 GRBs which will be uses as efficient standalone probes as SNe Ia by 2054., Comment: 31 pages, 17 figures, 10 tables, submitted to MNRAS

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)

The photon is commonly believed being the only free massless particle. Deviations from the Amp\`ere-Maxwell law, due to a photon mass, real for the de Broglie-Proca theory, or effective for the Lorentz-Poincar\'e Symmetry Violation (LSV) in the Standard-Model Extension (SME) were sought in six years of MMS satellite data. In a minority of cases, out of which $76\%$ in modulus and $65\%$ in Cartesian components for the highest time resolution burst data and best tetrahedron configurations in the solar wind and peripheries, deviations have been found. After currents error analysis, the minimal photon mass would be $1.74 \times 10^{-53}$ kg while the minimal LSV parameter $|\vec{k}^{\rm AF}|$ value would be $4.95 \times 10^{-11}$ m$^{-1}$. These values are compared with actual limits and discussed., Comment: We have further defined the plasma regions, updated Fig. 3, enlarged the discussion and added references. Thanks for the comments received

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)

The photon, main messenger for reading the universe, is the only free massless particle in the Standard-Model (SM). Deviations from the Amp\`ere-Maxwell law, due to a photon mass, real for the de Broglie-Proca theory, or effective for the Lorentz-Poincar\'e Symmetry Violation (LSV) in the SM Extension (SME), were sought in six years data of the Magnetospheric Multi-Scale (MMS) mission, a four-satellite constellation, crossing mostly turbulent regions of magnetic reconnection and collecting about 95\% of the data outside the quieter solar wind. We examined 3.8 million data points from the solar wind, magnetosheath, and magnetosphere regions. Beyond the upper limits on which we duly report, in a minority of cases, for the highest time resolution burst data and best tetrahedron configurations ($2.2\%$ in modulus and $4.8\%$ in Cartesian components for all regions, but $21\%$ in modulus and $29.9\%$ in Cartesian components in the solar wind), deviations have been found. The deviations might be due to unaccounted experimental errors or to non-Maxwellian terms. Possibly, we are at the boundaries of measurability for non-dedicated missions. We discuss our experimental results versus more stringent but model-based limits., Comment: We have updated the figures and clarified the results. Thanks for the comments received

Following results presented in Spallicci et al. (Eur Phys J Plus 137, 2022) by the same authors, we investigate the observed red shift $z$, working under the hypothesis that it 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, due to Extended Theories of Electromagnetism (ETE). We have tested this prediction considering the novel Pantheon+ Catalogue, composed by 1701 light curves collected by 1550 SNe Ia, and 16 BAO data, for different cosmological models characterised by the absence of a dark energy component. In particular, we shall derive which values of $z_{\rm S}$ match the observations, comparing the new results with the ones obtained considering the older Pantheon Catalogue. We find interesting differences in the resulting $z_{\rm S}$ distributions, highlighted in the text. Later, we also add a discussion regarding Extended Theories of Gravity and how to incorporate them in our methodology., Comment: 7 Figures, 8 Tables, 18 Pages. Follow up of arXiv:2202.02731

Cosmological probes at any redshift are necessary to reconstruct consistently the cosmic history. Studying properly the tension on the Hubble constant, $H_0$, obtained by Supernovae Type Ia (SNe Ia) and the Planck measurements of the Cosmic Microwave Background Radiation would require complete samples of distance indicators at any epoch. Gamma-Ray Bursts (GRBs) are necessary for the aforementioned task because of their huge luminosity that allows us to extend the cosmic ladder at very high redshifts. However, using GRBs alone as standard candles is challenging because their luminosity varies widely. To this end, we choose a reliable correlation for GRBs with a very small intrinsic scatter: the so-called fundamental plane correlation for GRB afterglows corrected for selection biases and redshift evolution. We choose a well-defined sample: the platinum sample, composed of 50 Long GRBs. To further constrain cosmological parameters, we use Baryon Acoustic Oscillations (BAOs) given their reliability as standard rulers. Thus, we have applied GRBs, SNe Ia, and BAOs in a binned analysis in redshifts so that GRBs' contribution is fully included in the last redshift bin, which reaches $z=5$. We use the fundamental plane correlation together with SNe Ia and BAOs, to constrain $H_0$ and the density matter today, $\Omega_{M}$. This methodology allows us to assess the role of GRBs combined with SNe Ia and BAOs. We have obtained results for $H_0$ and $\Omega_{M}$ using GRBs+ SNe Ia+BAOs with better precision than the SNe Ia alone for every bin, thus confirming the beneficial role of BAOs and GRBs added together. In addition, consistent results between GRBs+ SNe Ia +BAOs are obtained when compared with the SNe Ia +BAOs, showing the importance of GRBs since the distance ladder is extended up to $z=5$ with a similar precision obtained with other probes without including the GRBs., Comment: 32 Pages, 9 Figures, 7 Tables, accepted for publication by PASJ

Gamma-Ray Bursts (GRBs), can be employed as standardized candles, extending the distance ladder beyond Supernovae Type Ia (SNe Ia, $z=2.26$). We standardize GRBs using the 3D fundamental plane relation (the Dainotti relation) among the rest-frame end time of the X-ray plateau emission, its corresponding luminosity, and the peak prompt luminosity. Combining SNe Ia and GRBs, we constrain $\Omega_{\text{M}}= 0.299 \pm 0.009$ assuming a flat $\Lambda$CDM cosmology with and without correcting GRBs for selection biases and redshift evolution. Using a 3D optical Dainotti correlation, we find this sample is as efficacious in the determination of $\Omega_{\text{M}}$ as the X-ray sample. We trimmed our GRB samples to achieve tighter planes to simulate additional GRBs. We determined how many GRBs are needed as standalone probes to achieve a comparable precision on $\Omega_{\text{M}}$ to the one obtained by SNe Ia only. We reach the same error measurements derived using SNe Ia in 2011 and 2014 with 142 and 284 simulated optical GRBs, respectively, considering the errorbars on the variables halved. These error limits will be reached in 2038 and in 2047, respectively. Using a doubled sample (obtained by future machine learning approaches allowing a lightcurve reconstruction and the estimates of GRB redhifts when z is unknown) compared to the current sample, with errorbars halved we will reach the same precision as SNe Ia in 2011 and 2014, now and in 2026, respectively. If we consider the current SNe precision, this will be reached with 390 optical GRBs by 2054., Comment: 31 pages, 17 figures, 10 tables

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)

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?"

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?"

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