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Measurements for the expansion rate of the universe disagree. Indeed, local measurements suggest a higher value of the Hubble constant than those performed through the cosmic microwave background. This fact led to a very interesting debate within the scientific community. The paper is not devoted to give solutions to the problem of “Hubble tension”. The aim of this paper is, on the contrary, to deduce the ${\mathrm{\Omega }}_{0m}{h}^2$ cosmological parameter from a theoretical point of view, using only two experimental data: the temperature of CMB today and the temperature of photons near the decoupling time.

We propose a new method for calculating the redshift in galaxies, according to which the amount of redshift in the spectrum of each galaxy consists of two parts: about 2/3 of the redshift is due to the speed of the galaxy moving away from us, and about 1/3 is due to the fact that photons moving in the expanding Universe acquire an additional (non-Doppler) redshift. The additional reddening of photons in the spectrum of the galaxy is due to photons coming to us from the past, when the gravitational potential of the universe was lower, and consequently, the frequencies of atomic spectra were also lower than at present. A scheme of a laboratory experiment is proposed that will allow direct measurement of a non-Doppler (additional) part of the cosmological redshift and demonstrate the very fact of the expansion of the universe in real time in about 15 min. The experiment also makes it possible to measure the expansion rate of the universe and its current gravitational potential. These results will help to significantly refine modern ideas about the age of the universe, and about the amount of dark energy and dark matter in it.

The estimation of the Hubble constant in the past few decades has increasingly become more accurate with the advancement of new techniques. However, its value seems to depend on the epoch at which the measurements are made. The Planck estimate of the Hubble constant from the observations of the cosmic microwave background radiation in the early universe is about $67\mathrm{\text{km}}\backslash \mathrm{\text{s}}\backslash \mathrm{\text{Mpc}}$, whereas that obtained from the distance indicators at the current epoch is $\sim 73-74\mathrm{\text{km}}\backslash \mathrm{\text{s}}\backslash \mathrm{\text{Mpc}}$. This discrepancy between the two groups of measurement is termed as the Hubble tension which has gained much attention in the past few decades with growing significance as measurements from both, the early and the late universe, studies continue to produce results with increasing precision. In this work, we propose a modification to gravity by considering a finite range gravitational field as an alternate explanation for this discrepancy in the value of the Hubble constant.

Using comoving distance $d_c$ and angular diameter distance $d_A$, we recalculate parameters describing kinematical state of the universe, still combining the kinematical model of universe but not relying on dynamical equations for gravity. Comoving distance $d_c$ comes from Hubble data $H(z)$ and is more reliable. Angular diameter distance $d_A$ comes from SZE (Sunyaev–Zel’dovich Effect) and X-ray data, and needs calibration. In low redshift case, we use expansion of relation between luminosity distance and redshift about redshift $z$; in high redshift case, we take variable substitution $y=1/(1+z)$, and expand the relation between luminosity distance and redshift about variable $y$ in order to reduce computational errors. Finally, we get the more precise value of Hubble parameter $H_0=69.13\pm 0.24$ km ⋅ s${}^{-1}\cdot {\mathrm{\text{Mpc}}}^{-1}$, corresponding to $0.4\%$ uncertainty in $68.3\%$ confidence region, also deceleration factor $q_0=-0.57\pm 0.04$ and acceleration rate $j_0=1.28\pm 0.33$, and their statistical values and probability graph. We compare the values of $H_0$, $q_0$ and $j_0$ with those obtained from other observation data and model.

This Essay explores consequences of a dark nonlinear electromagnetic sector in a universe with a net dark charge for matter. The cosmological dynamics can be described by a Lemaître model and can be understood, thanks to a screening mechanism driven by the electromagnetic nonlinearities that suppress the dark force on small scales. Only at low redshift, when the screening scale enters the Hubble horizon, do cosmological structures commence to feel the dark repulsion. This repulsive force enhances the local value of the Hubble constant, thus providing a promising scenario for solving the Hubble tension. Remarkably, the dark electromagnetic interaction can have a crucial impact on peculiar velocities, i.e. introducing a bias in their reconstruction methods, and having the potential to explain the presence of a dark flow.

In this paper, we generalize the Phenomenologically Emergent Dark Energy (PEDE) model, famous for solving the long standing Hubble tension, with our Modified Emergent Dark Energy (MEDE) scenario. This new model introduces one additional parameter ‘$\alpha$’ that, depending on the value assumed by the analysis, can recover $\mathrm{\Lambda }$CDM (if $\alpha =0$), PEDE (if $\alpha =1$). We perform a robust observational analysis of MEDE using various observational datasets including cosmic microwave background (CMB) radiation, baryon acoustic oscillations (BAO) distance measurements, a local value of the Hubble constant (R19) and the Pantheon sample of Supernovae Type Ia. We find that when $\alpha$ is free to vary, the $H_0$ tension is alleviated but not solved like in PEDE, and the $\mathrm{\Lambda }$CDM is always preferred by the data when R19 is excluded, as confirmed by the bayesian evidence analysis.

Gravitational waves from binary black-hole mergers can be used to provide distance and angular location information of these sources, which, upon comparison with galaxy catalogs, can be used to measure the Hubble Constant. For a given galaxy catalog, and binary merger rates associated with each galaxy, a Fisher information approach can be used to estimate the measurement error for the Hubble Constant from the dark siren approach. In this paper, we validate the predictions from the Fisher information approach by carrying out a series of Monte Carlo simulations. Except in situations with very low event rates, the Fisher information approach is shown to predict the statistical errors of the Bayesian approach with good accuracy.

The standard ΛCDM cosmological model now seems to face some puzzles. One of the most serious problems is the so-called Hubble tension; the values of the Hubble constant H₀ obtained by local measurements look inconsistent with that inferred from Cosmic Microwave Background (CMB). Although introducing extra energy components such as the extra radiation or Early Dark Energy appears to be promising, such extra components could alter the abundance of light elements synthesized by Big Bang Nucleosynthesis (BBN). We perform a Monte Carlo simulation to evaluate the effect of those extra component scenarios to solve the Hubble tension on the BBN prediction.

The actual knowledge of the structure and future evolution of our universe is based on the use of cosmological models, which can be tested through the so-called ‘probes’, namely astrophysical phenomena, objects or structures with peculiar properties that can help to discriminate among different cosmological models. Among all the existing probes, of particular importance are the Supernovae Ia (SNe Ia) and the Gamma Ray Bursts (GRBs): the former are considered among the best standard candles so far discovered but suffer from the fact that can be observed until redshift z = 2.26, while the latter are promising standardizable candles which have been observed up to z = 9.4, surpassing even the farthest quasar known to date, which is at z = 7.64. The standard candles can be used to test the cosmological models and to give the expected values of cosmological parameters, in particular the Hubble constant value. The Hubble constant is affected by the so-called “Hubble constant tension”, a discrepancy in more than 4 σ between its value measured with local probes and its value measured through the cosmological probes. The increase in the number of observed SNe Ia, as well as the future standardization of GRBs through their correlations, will surely be of help in alleviating the Hubble constant tension and in explaining the structure of the universe at higher redshifts. A promising class of GRBs for future standardization is represented by the GRBs associated with Supernovae Ib/c, since these present features similar to the SNe Ia class and obey a tight correlation between their luminosity at the end of the plateau emission in X-rays and the time at the end of the plateau in the rest-frame.