On Some Mathematical Connections between the Cyclic Universe, Inflationary Universe, p-Adic Inflation, p-Adic Cosmology and Various Sectors of Number Theory

This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmology. In Section 2, we have described some equations concerning cosmic evolution in a Cyclic Universe. In Section 3, we have described some equations concerning the cosmological perturbations in a Big Crunch/Big Bang space-time, the M-theory model of a Big Crunch/Big Bang transition and some equations concerning the solution of a braneworld Big Crunch/Big Bang Cosmology. In Section 4, we have described some equations concerning the generating ekpyrotic curvature perturbations before the Big Bang, some equations concerning the effective five-dimensional theory of the strongly coupled heterotic string as a gauged version of N=1five-dimensional supergravity with four-dimensional boundaries, and some equations concerning the colliding branes and the origin of the Hot Big Bang. In Section 5, we have described some equations regarding the “null energy condition” violation concerning the inflationary models and some equations concerning the evolution to a smooth universe in an ekpyrotic contracting phase with w>1. In Section 6, we have described some equations concerning the approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory. In Section 7, we have described various equations concerning the p-adic minisuperspace model, zeta strings, zeta nonlocal scalar fields and p-adic and adelic quantum cosmology. In Section 8, we have shown various and interesting mathematical connections between some equations concerning the p-adic inflation, the p-adic quantum cosmology, the zeta strings and the brane collisions in string and M-theory. Furthermore, in each section, we have shown the mathematical connections with various sectors of Number Theory, principally the Ramanujan’s modular equations, the Aurea Ratio and the Fibonacci’s numbers.

Classical Cosmology II. The Einstein Ring

The Einstein ring is usually explained in the framework of the gravitational lens. Conversely here we apply the framework of the expansion of a superbubble (SB) in order to explain the spherical appearance of the ring. Two classical equations of motion for SBs are derived in the presence of a linear and a trigonometric decrease for density. A relativistic equation of motion with an inverse square dependence for the density is derived. The angular distance, adopting the minimax approximation, is derived for three relativistic cosmologies: the standard, the flat and the wCDM. We derive the relation between redshift and Euclidean distance, which allows fixing the radius of the Einstein ring. The details of the ring are explained by a simple version of the theory of images.

The Tension Cosmology, Largest Cosmic Structures and Explosions of Supernovae from SST

Here, using the Scale-Symmetric Theory (SST) we explain the cosmological tension and the origin of the largest cosmic structures. We show that a change in value of strong coupling constant for cold baryonic matter leads to the disagreement in the galaxy clustering amplitude, quantified by the parameter S8. Within the same model we described the Hubble tension. We described also the mechanism that transforms the gravitational collapse into an explosion—it concerns the dynamics of virtual fields that lead to dark energy. Our calculations concern the Type Ia supernovae and the core-collapse supernovae. We calculated the quantized masses of the progenitors of supernovae, emitted total energy during explosion, and we calculated how much of the released energy was transferred to neutrinos. Value of the speed of sound in the strongly interacting matter measured at the LHC confirms that presented here model is correct. Our calculations show that the Universe is cyclic.

Time Dilation Cosmology 2

This paper is a further elaboration of the author’s Time Dilation Cosmology (TDC) holographic model that ties gravitation and celestial mechanics and kinematics directly to time dilation, resolving all the major conundrums in astrophysics, and ties astrophysics directly to quantum physics. It begins with a brief summary of the TDC model and contains the new derivation for the time dilation version of the formula for summing relativistic velocities, Einstein’s gravitational constant and the time dilation versions for the Lorentz factor and the Euclidean norm of the 3d velocity vector, the two of which can then be used in the Four-velocity formula. It is demonstrated how orbital curvature is manifested as the resultant of two time dilation-manifested velocities. It also explains why an interferometer cannot distinguish free fall from zero gravity and further elaborates on the author’s previous explanations of how spiral galaxies are formed, and contains mathematical proof that Black Holes are actually Magnetospheric Eternally Collapsing Objects (MECOs) that are massless spacetime vortices.

Combining optical and X-ray observations of galaxy clusters to constrain cosmological parameters

Galaxy clusters present unique advantages for cosmological study.Here we collect a new sample of 10 lensing galaxy clusters with X-ray observations to constrain cosmological parameters.The redshifts of the lensing clusters lie between 0.1 and 0.6,and the redshift range of their arcs is from 0.4 to 4.9.These clusters are selected carefully from strong gravitational lensing systems which have both X-ray satellite observations and optical giant luminous arcs with known redshifts.Giant arcs usually appear in the central region of clusters,where mass can be traced with luminosity quite well.Based on gravitational lensing theory and a cluster mass distribution model,we can derive a ratio using two angular diameter distances.One is the distance between lensing sources and the other is that between the deflector and the source. Since angular diameter distance relies heavily on cosmological geometry,we can use these ratios to constrain cosmological models.Moreover,X-ray gas fractions of galaxy clusters can also be a cosmological probe.Because there are a dozen parameters to be fitted,we introduce a new analytic algorithm,Powell＇s UOBYQA（Unconstrained Optimization By Quadratic Approximation） ,to accelerate our calculation.Our result demonstrates that this algorithm is an effective fitting method for such a continuous multi-parameter constraint.We find an interesting fact that these two approaches are separately sensitive toΩΛandΩM.By combining them,we can get reasonable fitting values of basic cosmological parameters：ΩM=0.26 ＋0.04 -0.04,andΩΛ=0.82 ＋0.14 -0.16.

The Evolving Absolute Magnitude of Type 1a Supernovae and Its Critical Impact on the Cosmological Parameters

In this work, a computer optimization model has been developed that allows one to load the initial data of observations of supernovae 1a into a table and, in simple steps, by searching for the best fit between observations and theory, obtain the values of the parameters of cosmological models. The optimization is carried out assuming that the absolute magnitude of supernovae is not constant, but evolves with time. It is assumed that the dependence of the absolute magnitude on the redshift is linear: M = M( z = 0) + εc z, where εc is the evolution coefficient of the absolute magnitude of type 1a supernovae. In the case of a flat universe ( ΩM + ΩΛ = 1 ), the best fit between theory and observation is εc = 0.304. In this case, for the cosmological parameters we obtain ΩΛ = 0.000, ΩM =1.000. Naturally, this result exactly coincides with the simulation result for the model with zero cosmological constant ( εc = 0.304, q0 = 0.500 ). Within the framework of the ΛCDM model, without restriction on space curvature ( ΩM + ΩΛ+ ΩK = 1 ), we obtain the following values: εc = 0.304, ΩΛ = 0.000, ΩM = 1.000, ΩK =0.000. Those, this case also leads to a flat model of the Universe ( ΩK =0.000 ). In this work, the critical influence of the absolute magnitude M of type 1a supernovae on the cosmological parameters is also shown. In particular, it was found that a change in this value by only 0.4m (from -19.11 to -18.71) leads to a change in the parameters from ΩΛ = 0.7 and ΩM = 0.3 to ΩΛ = 0 and ΩM =1.

Decisive Role of Gravitational Parameter G in Cosmology

In 1937, P. Dirac proposed the Large Number Hypothesis and the Hypothesis of the variable gravitational “constant”, and later added the notion of continuous creation of Matter in the World. The Hypersphere World-Universe Model (WUM) follows these ideas, albeit introducing a different mechanism of Matter creation. In this paper, we show that Gravitational parameter G that can be measured directly makes measurable all Cosmological parameters, which cannot be measured directly.

Cosmological Constraints on Neutrino Masses in Light of JWST Red and Massive Candidate Galaxies

The overabundance of the red and massive candidate galaxies observed by the James Webb Space Telescope(JWST)implies efficient structure formation or large star formation efficiency at high redshift z~10.In the scenario of a low or moderate star formation efficiency,because massive neutrinos tend to suppress the growth of structure of the universe,the JWST observation tightens the upper bound of the neutrino masses.Assuming A cold dark matter cosmology and a star formation efficiency∈[0.05,0.3](flat prior),we perform joint analyses of Planck+JWST and Planck+BAO+JWST,and obtain improved constraints∑m_(ν)<0.196 eV and ∑m_(ν)+<0.111 eV at 95% confidence level,respectively.Based on the above assumptions,the inverted mass ordering,which implies ∑m_(ν)≥0.1 eV,is excluded by Planck+BAO+JWST at 92.7% confidence level.

Quantifying the Tension between Cosmological Models and JWST Red Candidate Massive Galaxies

We develop a Python tool to estimate the tail distribution of the number of dark matter halos beyond a mass threshold and in a given volume in a light-cone.The code is based on the extended Press-Schechter model and is computationally efficient,typically taking a few seconds on a personal laptop for a given set of cosmological parameters.The high efficiency of the code allows a quick estimation of the tension between cosmological models and the red candidate massive galaxies released by the James Webb Space Telescope,as well as scanning the theory space with the Markov Chain Monte Carlo method.As an example application,we use the tool to study the cosmological implication of the candidate galaxies presented in Labbéet al.The standard Λcold dark matter(ΛCDM)model is well consistent with the data if the star formation efficiency can reach~0.3 at high redshift.For a low star formation efficiency ε~0.1,theΛCDM model is disfavored at~2σ-3σconfidence level.

Prospects of the Multi-channel Photometric Survey Telescope in the Cosmological Application of Type Ia Supernovae

The Multi-channel Photometric Survey Telescope(Mephisto)is a real-time,three-color photometric system designed to capture the color evolution of stars and transients accurately.This telescope system can be crucial in cosmological distance measurements of low-redshift(low-z,z■0.1)Type Ia supernovae(SNe Ia).To optimize the capabilities of this instrument,we perform a comprehensive simulation study before its official operation is scheduled to start.By considering the impact of atmospheric extinction,weather conditions,and the lunar phase at the observing site involving the instrumental features,we simulate light curves of SNe Ia obtained by Mephisto.The best strategy in the case of SN Ia cosmology is to take the image at an exposure time of 130 s with a cadence of 3 days.In this condition,Mephisto can obtain hundreds of high-quality SNe Ia to achieve a distance measurement better than 4.5%.Given the on-time spectral classification and monitoring of the Lijiang 2.4 m Telescope at the same observatory,Mephisto,in the whole operation,can significantly enrich the well-calibrated sample of supernovae at low-z and improve the calibration accuracy of high-z SNe Ia.

The Extremal Universe Exact Solution from Einstein’s Field Equation Gives the Cosmological Constant Directly

Einstein’s field equation is a highly general equation consisting of sixteen equations. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into today standard model of modern cosmology: The Λ-CDM model. However, this is naturally not the only solution to Einstein’s field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant;instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.

Cosmology of a Chaplygin Gas Model Under f(T)Gravity and Evolution of Primordial Perturbations

This paper reports a detailed study of generalized Chaplygin gas(GCG)with power law form of scale factor and truncated form of the scale factor using binomial expansion in both interacting and non-interacting scenarios along with its cosmological consequences,studied in terms of equation of state(EoS)parameter.In the non-interacting scenario,the EoS parameter behaves as quintessence in both forms of the scale factor.In the interacting scenario,the EoS parameter behaves as phantom and for the truncated form of the scale factor,it violates the constraints of the positive parameterα.The cosmological implementation of GCG interacting with pressureless dark matter is investigated in the framework of f(T)modified gravity,where T is the torsion scalar in teleparallelism.The interaction term is directly proportional to the GCG density with positive coupling constant.In f(T)gravity,the EoS is behaving like phantom.The stability of the reconstructed model is investigated and it is found to be stable against small gravitational perturbations,i.e.,the squared speed of sound is non-negative and an increasing function of cosmic time t.We have observed that our reconstructed f(T)model satisfies one of the sufficient conditions of a realistic reconstructed model and it is consistent with the CMB constraints and primordial nucleosynthesis.Cosmology of primordial perturbations has also been analyzed and the self-interacting potential has been found to be an increasing function of cosmic time t.

Cosmological parameters for spatially flat dust filled Universe in Brans-Dicke theory

We have investigated late time acceleration for a spatially fiat dust filled Universe in Brans- Dicke theory in the presence of a positive cosmological constant A. Expressions for Hubble＇s constant, luminosity distance and apparent magnitude have been obtained for our model. The theoretical results are compared with observed values of the latest 287 high redshift （0.3 ≤ z ≤1.4） Type Ia supernova data taken from the Union 2.1 compilation to estimate present values of matter and dark energy parame- ters, （Ωm）0 and （ΩA）0. We have also estimated the present value of Hubble＇s constant H0 in light of an updated sample of Hubble parameter measurements including 19 independent data points. The results are found to be in good agreement with recent astrophysical observations. We also calculated various physical parameters such as matter and dark energy densities, present age of the Universe and decelera- tion parameter. The value for Brans-Dicke-coupling constant ω is set to be 40 000 based on accuracy of solar system tests and recent experimental evidence.

Time Dilation Cosmology

This model ties gravitation and celestial mechanics and kinematics directly to time dilation. It is a new theory of cosmology and the evolution of galaxies. Space and time are not two separate things, but two aspects of a single thing, “spacetime”. Whatever affects space, affects time, and vice-versa. If time speeds up, space must contract to maintain the speed of light, c, and when space thickens into a mass, it is harder to evolve forward, and time appears to slow. If spatial events are spinning as time passes, then the forward direction of time is spinning. This is Einstein’s curvature in the forward direction of time. Herein, the basis is outlined for time dilation cosmology in a spacetime/quantum continuum, including the time dilation-based derivation of the mass of the Cosmic Microwave Background Radiation (CMBR), and time dilation formulas are derived for stellar system orbital, and galactic rotation, velocities, the force in time in Newtons, the Hamiltonian, the Hubble shift, the empirical gravitational constant, G, and other formulas, showing their direct relationship to the difference in the rate of time between the far distant observer’s invariant 1 s/s rate of time and the slower rate of time at the coordinate point, proving the universe is not composed of separate bodies moving through space, but is an evolving 3-dimensional holographic continuum containing varying densities evolving forward in the forward direction of time, the 4th dimension, at apparently different rates of time, the velocities merely being compensation for those slower rates of time in a continuum evolving forward overall at c, which is why light propagates at c, even from a moving source. As per General Relativity, if there is no rate of time difference between coordinate points, there is no gravitational attraction between those points, and no gravitationally induced velocity. This model resolves all the major conundrums in astrophysics, eliminating Dark Energy and Dark Matter, and ties astrophysics directly to quantum physics.

Measurements of the Cosmological Parameters &Omega;_mand <i>H</i>₀

From Baryon Acoustic Oscillation measurements with Sloan Digital Sky Survey SDSS DR14 galaxies, and the acoustic horizon angle measured by the Planck Collaboration, we obtain Ωm=0.2724±0.0047, and h+0.020&sdot;∑mv=0.7038±0.0060, assuming flat space and a cosmological constant. We combine this result with the 2018 Planck “TT, TE, EE + lowE + lensing” analysis, and update a study of ∑mv with new direct measurements of σ8, and obtain ∑mv=0.27±0.08 eV assuming three nearly degenerate neutrino eigenstates. Measurements are consistent with Ωk=0, and Ωde(a)=ΩΛ constant.

Redshift drift reconstruction for some cosmological models from observations

Redshift drift is a tool to directly probe the expansion history of the uni- verse. Based on the Friedmann-Robertson-Walker framework, we reconstruct the ve- locity drift and deceleration factor for several cosmological models using observa- tional H（z） data from the differential ages of galaxies and baryon acoustic oscillation peaks, luminosity distance of Type Ia supernovae, cosmic microwave background shift parameter, and baryon acoustic oscillation distance parameter. They can, for the first time, provide an objective and quantifiable measure of the redshift drift. We find that reconstructed velocity drift with different peak values and corresponding redshifts can potentially provide a method to distinguish the quality of competing dark energy mod- els at low redshifts. Better fitting between models and observational data indicate that current data are insufficient to distinguish the quality of these models. However, by comparing with the simulated velocity drift from Liske et al, we find that the Dvali- Gabadadze-Porrati model is inconsistent with the data at high redshift, which origi- nally piqued the interest of researchers in the topic of redshift drift. Considering the deceleration factor, we are able to give a stable instantaneous estimation of a transition redshift of zt ~ 0.7 from joint constraints, which incorporates a more complete set of values than the previous study that used a single data set.

Confidence Level Estimator of Cosmological Parameters

Cosmological Models frequently suggest the existence of physical, quantities, e.g. dark energy, we cannot yet observe and measure directly. Their values are obtained indirectly setting them equal to values and accuracy of the associated model parameters which best fit model and observation. Apparently results are so accurate that some researchers speak of precision cosmology. The accuracy attributed to these indirect values of the physical quantities however does not include the uncertainty of the model used to get them. We suggest a Confidence Level Estimator to be attached to these indirect measurements and apply it to current cosmological models.

Cosmological Inconstant, Supernovae 1a and Decelerating Expansion

In 1998, two groups of astronomers, one led by Saul Perlmutter and the other by Brian Schmidt, set out to determine the deceleration—and hence the total mass/energy—of the universe by measuring the recession speeds of type la supernovae (SN1a), came to an unexpected conclusion: ever since the universe was about 7 billion years old, its expansion rate has not been decelerating. Instead, the expansion rate has been speeding up. To justify this acceleration, they suggested that the universe does have a mysterious dark energy and they have emerged from oblivion the cosmological constant, positive this time, which is consistent with the image of an inflationary universe. To explain the observed dimming of high-redshift SN1a they have bet essentially on their distance revised upwards. We consider that an accelerated expansion leads right to a “dark energy catastrophe” (i.e., the chasm between the current cosmological vacuum density value of 10 GeV/m3 and the vacuum energy density proposed by quantum field theory of ~10122 GeV/m3). We suppose rather that the universe knows a slowdown expansion under the positive pressure of a dark energy, otherwise called a variable cosmological constant. The dark luminosity of the latter would be that of a “tired light” which has lost energy with distance. As for the low brilliance of SN1a, it is explained by two physical processes: The first relates to their intrinsic brightness—supposedly do not vary over time—which would depend on the chemical conditions which change with the temporal evolution;the second would concern their apparent luminosity. Besides the serious arguments already known, we strongly propose that their luminosity continually fades by interactions with cosmic magnetic fields, like the earthly PVLAS experiment which loses much more laser photons than expected by crossing a magnetic field. It goes in the sense of a “tired light” which has lost energy with distance, and therefore, a decelerated expansion of the universe. Moreover, we propose the “centrist” principle to complete the hypothesis of the cosmological principle of homogeneity and isotropy considered verified. Without denying the Copernican principle, he is opposed to a “spatial” theoretical construction which accelerates the world towards infinity. The centrist principle gives a “temporal” and privileged vision which tends to demonstrate the deceleration of expansion.

On Dark Gravitational Wave Standard Sirens as Cosmological Inference and Forecasting the Constraint on Hubble Constant using Binary Black Holes Detected by Deci-hertz Observatory

Gravitational wave(GW) signals from compact binary coalescences can be used as standard sirens to constrain cosmological parameters if their redshift can be measured independently by electromagnetic signals.However,mergers of stellar binary black holes(BBHs) may not have electromagnetic counterparts and thus have no direct redshift measurements.These dark sirens may be still used to statistically constrain cosmological parameters by combining their GW measured luminosity distances and localization with deep redshift surveys of galaxies around it.We investigate this dark siren method to constrain cosmological parameters in detail by using mock BBH and galaxy samples.We find that the Hubble constant can be constrained well with an accuracy■ 1% with a few tens or more of BBH mergers at redshift up to 1 if GW observations can provide accurate estimates of their luminosity distance(with relative error of■ 0.01) and localization(■ 0.1 deg^(2)),though the constraint may be significantly biased if the luminosity distance and localization errors are larger.We also introduce a simple method to correct this bias and find it is valid when the luminosity distance and localization errors are modestly large.We further generate mock BBH samples,according to current constraints on BBH merger rate and the distributions of BBH properties,and find that the Deci-hertz Observatory(DO) in a half year observation period may detect about one hundred BBHs with signal-to-noise ratio■■30,relative luminosity distance error■ 0.02 and localization error ■0.01 deg^(2).By applying the dark standard siren method,we find that the Hubble constant can be constrained to the~0.1%-1% level using these DO BBHs,an accuracy comparable to the constraints obtained by using electromagnetic observations in the near future,thus it may provide insight into the Hubble tension.We also demonstrate that the constraint on the Hubble constant applying this dark siren method is robust and does not depend on the choice of the prior for the properties of BBH host galaxies.

A critique of supernova data analysis in cosmology

Observational astronomy has shown significant growth over the last decade and has made important contributions to cosmology. A major paradigm shift in cosmology was brought about by observations of Type Ia supernovae. The notion that the universe is accelerating has led to several theoretical challenges. Unfortunately, although high-quality supernovae data-sets are being produced, their statistical anal- ysis leaves much to be desired. Instead of using the data to directly test the model, several studies seem to concentrate on assuming the model to be correct and limiting themselves to estimating model parameters and internal errors. As shown here, the important purpose of testing a cosmological theory is thereby vitiated.