arXiv subjects

Andre Maeder

Publications and source records attributed to Andre Maeder.

At least 37 records · Page 2Linked to original sources

arXiv2021

Reparametrization Invariance and Some of the Key Properties of Physical Systems

In this paper, we argue in favor of first-order homogeneous Lagrangians in the velocities. The relevant form of such Lagrangians is discussed and justified physically and geometrically. Such Lagrangian systems possess Reparametrization Invariance (RI) and explain the observed common Arrow of Time as related to the non-negative mass for physical particles. The extended Hamiltonian formulation, which is generally covariant and applicable to reparametrization-invariant systems, is emphasized. The connection between the explicit form of the extended Hamiltonian $\boldsymbol{H}$ and the meaning of the process parameter $λ$ is illustrated. The corresponding extended Hamiltonian $\boldsymbol{H}$ defines the classical phase space-time of the system via the Hamiltonian constraint $\boldsymbol{H}=0$ and guarantees that the Classical Hamiltonian $H$ corresponds to $p_{0}$ -- the energy of the particle when the coordinate time parametrization is chosen. The Schrödinger's equation and the principle of superposition of quantum states emerge naturally. A connection is demonstrated between the positivity of the energy $E=cp_{0}>0$ and the normalizability of the wave function by using the extended Hamiltonian that is relevant for the proper-time parametrization

math-ph↗

arXiv2021

Scale Invariance, Horizons, and Inflation

Maxwell equations and the equations of General Relativity are scale invariant in empty space. The presence of charge or currents in electromagnetism or the presence of matter in cosmology are preventing scale invariance. The question arises on how much matter within the horizon is necessary to kill scale invariance. The scale invariant field equation, first written by Dirac in 1973 and then revisited by Canuto et al. in 1977, provides the starting point to address this question. The resulting cosmological models show that, as soon as matter is present, the effects of scale invariance rapidly decline from ρ=0 to ρ_c and are forbidden for densities above ρ_c. The absence of scale invariance in this case is consistent with considerations about causal connection. Below ρ_c, scale invariance appears as an open possibility, which also depends on the occurrence of inflation in the scale invariant context. In the present approach, we identify the scalar field of the empty space in the Scale Invariant Vacuum (SIV) context to the scalar field ϕin the energy density expression of the vacuum at inflation. This leads to some constraints on the potential. This identification also solves the so-called ``cosmological constant problem''. In the framework of scale invariance,an inflation with a large number of e-foldings is also predicted. We conclude that scale invariance for models with densities below ρ_c is an open possibility; the final answer may come from high redshift observations, where differences from the LCDM models appear.

gr-qc↗

arXiv2020

Grids of stellar models with rotation: V. Models from 1.7 to 120 Msun at zero metallicity

Understanding the nature of the first stars is key to understanding the early universe. With new facilities such as JWST we may soon have the first observations of the earliest stellar populations, but to understand these observations we require detailed theoretical models. Here we compute a grid of stellar evolution models using the Geneva code with the aim to improve our understanding of the evolution of zero-metallicity stars, with particular interest in how rotation affects surface properties, interior structure, and metal enrichment. We produce a range of models of initial masses (Mini) from 1.7 Msun to 120 Msun, focusing on massive models of 9 Msun < Mini < 120 Msun. Our grid includes models with and without rotation, with rotating models having an initial velocity of 40% of the critical velocity. We find that rotation strongly impacts the evolution of the first stars, mainly through increased core size and stronger H-burning shells during core He-burning. Without radiative mass loss, angular momentum builds at the surface in rotating models, thus models of initial masses Mini > 60 Msun reach critical rotation on the main sequence and experience mass loss. We find that rotational mixing strongly affects metal enrichment, but does not always increase metal production as we see at higher metallicities. This is because rotation leads to an earlier CNO boost to the H shell during He-burning, which may hinder metal enrichment depending on initial mass and rotational velocity. Electronic tables of this new grid of Population III models are publicly available.

astro-ph.SR↗

arXiv2020

Revisiting the Cosmological Constant Problem within Quantum Cosmology

A new perspective on the Cosmological Constant Problem (CCP) is proposed and discussed within the multiverse approach of Quantum Cosmology. It is assumed that each member of the ensemble of universes has a characteristic scale $a$ that can be used as integration variable in the partition function. An averaged characteristic scale of the ensemble is estimated by using only members that satisfy the Einstein field equations. The averaged characteristic scale is compatible with the Planck length when considering an ensemble of solutions to the Einstein field equations with an effective cosmological constant. The multiverse ensemble is split in Planck-seed universes with vacuum energy density of order one; thus, $ \tildeΛ\approx 8π$ in Planck units and $a$-derivable universes. For~$a$-derivable universe with a characteristic scale of the order of the observed Universe $a\approx 8\times10^{60}$, the cosmological constant $Λ=\tildeΛ/a^{2}$ is in the range $10^{-121}$--$10^{-122}$, which is close in magnitude to the observed value $10^{-123}$. We point out that the smallness of $Λ$ can be viewed to be natural if its value is associated with the entropy of the Universe. This approach to the CCP reconciles the Planck-scale huge vacuum energy--density predicted by QFT considerations, as valid for Planck-seed universes, with the observed small value of the cosmological constant as relevant to an $a$-derivable universe as~observed.

gr-qc↗

arXiv2020

Scale-Invariant Dynamics of Galaxies, MOND, Dark Matter, and the Dwarf Spheroidals

The Scale-Invariant Vacuum (SIV) theory is based on Weyl's Integrable Geometry, endowed with a gauge scalar field. The main difference between MOND and the SIV theory is that the first considers a global dilatation invariance of space and time, where the scale factor $λ$ is a constant, while the second opens the likely possibility that $λ$ is a function of time. The key equations of the SIV framework are used here to study the relationship between the Newtonian gravitational acceleration due to baryonic matter $g_{\mathrm{bar}}$ and the observed kinematical acceleration $g_{\mathrm{obs}}$. The relationship is applied to galactic systems of the same age where the Radial Acceleration Relation (RAR), between the $g_{\mathrm{obs}}$ and $g_{\mathrm{bar}}$ accelerations, can be compared with observational data. The SIV theory shows an excellent agreement with observations and with MOND for baryonic gravities $g_{\mathrm{bar}}>10^{-11.5}$ m s$^{-2}$. Below this value, SIV still fully agrees with the observations, as well as with the horizontal asymptote of the RAR for dwarf spheroidals, while this is not the case for MOND. These results support the view that there is no need for dark matter and that the RAR and related dynamical properties of galaxies can be interpreted by a modification of gravitation.

gr-qc↗

arXiv2019

Grids of stellar models with rotation IV. Models from 1.7 to 120 Msun at a metallicity Z = 0.0004

The effects of rotation on stellar evolution are particularly important at low metallicity, when mass loss by stellar winds diminishes and the surface enrichment due to rotational mixing becomes relatively more pronounced than at high metallicities. Here we investigate the impact of rotation and metallicity on stellar evolution. Using a similar physics as in our previous large grids of models at Z=0.002 and Z=0.014, we compute stellar evolution models with the Geneva code for rotating and nonrotating stars with initial masses (Mini) between 1.7 and 120 Msun and Z=0.0004 (1/35 solar). This is comparable to the metallicities of the most metal poor galaxies observed so far, such as I Zw 18. Concerning massive stars, both rotating and nonrotating models spend most of their core-helium burning phase with an effective temperature higher than 8000 K. Stars become red supergiants only at the end of their lifetimes, and few RSGs are expected. Our models predict very few to no classical Wolf-Rayet stars as a results of weak stellar winds at low metallicity. The most massive stars end their lifetimes as luminous blue supergiants or luminous blue variables, a feature that is not predicted by models with higher metallicities. Interestingly, due to the behavior of the intermediate convective zone, the mass domain of stars producing pair-instability supernovae is smaller at Z=0.0004 than at Z=0.002. We find that during the main sequence phase, the ratio between nitrogen and carbon abundances (N/C) remains unchanged for nonrotating models. However, N/C increases by factors of 10-20 in rotating models at the end of the MS. Cepheids coming from stars with Mini > 4-6 Msun are beyond the core helium burning phase and spend little time in the instability strip. Since they would evolve towards cooler effective temperatures, these Cepheids should show an increase of the pulsation period as a function of age.

astro-ph.SR↗

arXiv2019

Evolution of the early Universe in the scale invariant theory

Analytical solutions are obtained for the early cosmological phases in the scale invariant models with curvature k=0. They complete the analytical solutions already found in the matter--dominated era by (Jesus 2018). The physical properties in the radiative era are derived from the conservation laws and compared to those of current standard models. The critical runs of the temperature T(MeV) and of the expansion rate H of the scale invariant models with low densities, Omega_m=0.04, are quite similar at the time of nucleosynthesis to those of standard models with Omega_m=0.30, leading to the same freezing number ratio of neutrons to protons.These results are consistent with the fact that the scale invariant models appear to not require the presence of dark matter.

astro-ph.CO↗

arXiv2019

The growth of the density fluctuations in the scale-invariant theory: one more challenge for dark matter

The growth of the density fluctuations is considered to be an important cosmological test. In the standard model, for a matter dominated universe, the growth of the density perturbations evolves with redshift z like (1/{1+z))^s with s=1. This is not fast enough to form galaxies and to account for the observed present-day inhomogeneities. This problem is usually resolved by assuming that at the recombination epoch the baryons settle down in the potential well of the dark matter previously assembled during the radiation era of the universe. This view is challenged in the present paper by using the recently proposed model of a scale-invariant framework for cosmology that enlarges the invariance group subtending the theory of the gravitation. From the continuity equation, the Euler and Poisson equations written in the scale-invariant framework, the equation governing the growth of the density fluctuations is obtained. Starting from δ= 10^{-5} at a redshift around 1000, numerical solutions for various density background are obtained. The growth of density fluctuations is much faster than in the standard EdS model. The s values are in the range from 2.7 to 3.9 for Ω_m between 0.30 and 0.02. This enables the density fluctuations to enter the nonlinear regime with δ> 1 long before the present time, typically at redshifts of about 10, without requiring the presence of dark matter.

astro-ph.CO↗

arXiv2018

The acceleration relation in galaxies and scale invariant dynamics: another challenge for dark matter

A relation between the centripetal acceleration g_obs in galaxies and the gravity due to the baryon distribution g_bar has been found by McGaugh (2016) and Lelli et al.(2017). It also summarizes properties such as the Tully-Fisher and Faber-Jackson relations. Below about g_bar= 10E-10 m s^(-2), the observed relation deviates from the 1:1 line, g_obs being much larger than g_bar. The acceleration relation is followed by late and early type galaxies, and also by the dwarf spheroidals where the deviations from the 1:1 line are the largest ones. These deviations are currently attributed to dark matter. We show that the scale invariant theory, with the assumption of the scale invariance of the empty space, correctly predicts the observed deviations in the acceleration relation. The large deviations (up to a factor 400) and the flattening of the acceleration relation observed for the dwarf spheroidal galaxies are also well described. The presence of dark matter is no longer necessary in the scale invariant context, which also accounts why dark matter usually appears to dominate in galactic regions with low baryonic gravities.

astro-ph.GA↗

arXiv2017

Supernovae from rotating stars

The present paper discusses the main physical effects produced by stellar rotation on presupernovae, as well as observations which confirm these effects and their consequences for presupernova models. Rotation critically influences the mass of the exploding cores, the mass and chemical composition of the envelopes and the types of supernovae, as well as the properties of the remnants and the chemical yields. In the formation of gamma-ray bursts, rotation and the properties of rotating stars appear as the key factor. In binaries, the interaction between axial rotation and tidal effects often leads to interesting and unexpected results. Rotation plays a key role in shaping the evolution and nucleosynthesis in massive stars with very low metallicities (metallicity below about the Small Magellanic Cloud metallicity down to Population III stars). At solar and higher metallicities, the effects of rotation compete with those of stellar winds. In close binaries, the synchronisation process can lock the star at a high rotation rate despite strong mass loss and thus both effects, rotation and stellar winds, have a strong impact. In conclusion, rotation is a key physical ingredient of the stellar models and of presupernova stages, and the evolution both of single stars and close binaries. Moreover, important effects are expected along the whole cosmic history.

astro-ph.SR↗

arXiv2017

Dynamical effects of the scale invariance of the empty space: The fall of dark matter ?

The hypothesis of the scale invariance of the macroscopic empty space, which intervenes through the cosmological constant, has led to new cosmological models. They show an accelerated cosmic expansion and satisfy several major cosmological tests. No unknown particles are needed. Developing the weak field approximation, we find that the here derived equation of motion corresponding to Newton's equation also contains a small outwards acceleration term. The new term is particularly significant for very low density systems. A modified virial theorem is derived and applied to clusters of galaxies. For the Coma and Abell 2029 clusters, the dynamical masses are about a factor of 5 to 10 smaller than in the standard case. This tends to let no room for dark matter in these clusters. Then, the two-body problem is studied and an equation corresponding to the Binet equation is obtained. The results are applied to the rotation curve of the outer layers of the Milky Way. Starting backwards from the present rotation curve, we calculate the past evolution of the galactic rotation and find that, in the early stages, it was steep and Keplerian. Thus, the flat rotation curves of galaxies appears as an age effect, a result consistent with recent observations of distant galaxies by Genzel et al. (2017) and Lang et al. (2017). Finally, in an Appendix we also study the long-standing problem of the increase with age of the vertical velocity dispersion in the Galaxy. The observed increase appears to result from the new small acceleration term in the equation of the harmonic oscillator describing stellar motions around the galactic plane. Thus, we tend to conclude that neither the dark energy, nor the dark matter seem to be needed in the proposed theoretical context.

astro-ph.GA↗

arXiv2017

Scale invariant cosmology and CMB temperatures as a function of redshifts

Cosmological models assuming the scale invariance of the macroscopic empty space show an accelerated expansion, without calling for some unknown particles. Several comparisons between models and observations (tests on distances, m-z diagram, Omega_Lambda vs. Omega_m plot, age vs. H_0, H(z) vs. z, transition braking-acceleration) have indicated an impressive agreement {Maeder 2017}. We pursue the tests with the CMB temperatures T(CMB) as a function of redshifts z. CO molecules in DLA systems provide the most accurate excitation temperatures T(exc) up to z ~ 2.7. Such data need corrections for local effects, like particle collisions, optical depths, UV radiation, etc. We estimate these corrections as a function of the (CO/H_2) ratios from far UV observations of CO molecules in the Galaxy. The results show that it is not sufficient to apply theoretical collisional corrections to get the proper values of T(CMB) vs.z. Thus, the agreement often found with the standard model may be questioned. The T(CMB)vs. z relation needs further careful attention and the same for the scale invariant cosmology in view of its positive tests.

astro-ph.CO↗

arXiv2017

An alternative to the LCDM model: the case of scale invariance

The hypothesis is made that, at large scales where General Relativity may be applied, the empty space is scale invariant. This establishes a relation between the cosmological constant and the scale factor of the scale invariant framework. This relation brings major simplifications in the scale invariant equations for cosmology, which now contain a new term, depending on the derivative of the scale factor, that opposes to gravity and produces an accelerated expansion. The displacements due to the acceleration term make a high contribution Omega_l to the energy-density of the Universe, satisfying an equation of the form Omega_m+Ω_k+Omega_l = 1. The models do not demand the existence of unknown particles. There is a family of flat models with different density parameters Omega_m < 1. Numerical integrations of the cosmological equations for different values of the curvature and density parameter k and Omega_m are performed. The presence of even tiny amounts of matter in the Universe tends to kill scale invariance. The point is that for Omega_m = 0.3 the effect is not yet completely killed. The models with non-zero density start explosively with first a braking phase followed by a continuously accelerating expansion. Several observational properties are examined, in particular the distances, the m--z diagram, the Omega_m vs. lambda plot. Comparisons with observations are also performed for the Hubble constant H_0 vs. Omega_m, for the expansion history in the plot H(z)/(z+1) vs. redshift z and for the transition redshift from braking to acceleration. These first dynamical tests are satisfied by the scale invariant models, which thus deserve further studies.

astro-ph.CO↗

arXiv2016

Scale invariant cosmology III: dynamical models and comparisons with observations

We examine the properties of the scale invariant cosmological models, also making the specific hypothesis of the scale invariance of the empty space at large scales. Numerical integrations of the cosmological equations for different values of the curvature parameter k and of the density parameter Omega_m are performed. We compare the dynamical properties of the models to the observations at different epochs. The main numerical data and graphical representations are given for models computed with different curvatures and density parameters. The models with non-zero density start explosively with first a braking phase followed by a continuously accelerating expansion. The comparison of the models with the recent observations from supernovae SN Ia, BAO and CMB data from Planck 2015 shows that the scale invariant model with k=0 and Omega_m=0.30 very well fits the observations in the usual Omega_m vs. Omega_Lambda plane and consistently accounts for the accelerating expansion or dark energy. The expansion history is compared to observations in the plot H(z) vs. redshift z, the parameters q_0 is also examined, as well the recent data about the redshift z_trans of the transition between braking and acceleration. These dynamical tests are fully satisfied by the scale invariant models. The past evolution of matter and radiation density is studied, it shows small differences with respect to the standard case. These first comparisons are encouraging further investigations on scale invariant cosmology with the assumption of scale invariance of the empty space at large scales.

gr-qc↗

arXiv2016

Scale invariant cosmology I: the vacuum and the cosmological constant

The source of the acceleration of the expansion of the Universe is still unknown. We examine some consequences of the possible scale invariance of the empty space at large scales. The central hypothesis of this work is that, at macroscopic and large scales where General Relativity may be applied, the empty space in the sense it is used in the Minkowski metric, is also scale invariant. It is shown that if this applies, the Einstein cosmological constant and the scale factor of the scale invariant framework are related by two differential equations.

gr-qc↗

arXiv2016

Scale invariant cosmology II: model equations and properties

We want to establish the basic properties of a scale invariant cosmology, that also accounts for the hypothesis of scale invariance of the empty space at large scales. We write the basic analytical properties of the scale invariant cosmological models. The hypothesis of scale invariance of the empty space at large scale brings interesting simplifications in the scale invariant equations for cosmology. There is one new term, depending on the scale factor of the scale invariant cosmology, that opposes to gravity and favours an accelerated expansion. We first consider a zero-density model and find an accelerated expansion, going like t square. In models with matter present, the displacements due to the new term make a significant contribution Omega_l to the energy-density of the Universe, satisfying an equation of the form Omega_m + Omega_k + Omega_l = 1. Unlike the Friedman's models, there is a whole family of flat models (k=0) with different density parameters Omega_m smaller than 1. We examine the basic relations between the density and geometrical properties, as well as the conservation laws. The models containing matter have an inflexion point, with first a braking phase followed by an accelerated expansion phase. The scale invariant models have interesting properties and deserve further investigations.

gr-qc↗

arXiv2016

Nucleosynthesis in the first massive stars

The nucleosynthesis in the first massive stars may be constrained by observing the surface composition of long-lived very iron-poor stars born around 10 billion years ago from material enriched by their ejecta. Many interesting clues on physical processes having occurred in the first stars can be obtained just based on nuclear aspects. Two facts are particularly clear, 1) in these first massive stars, mixing must have occurred between the H-burning and the He-burning zone during their nuclear lifetimes; 2) only the outer layers of these massive stars have enriched the material from which the very iron-poor stars, observed today in the halo, have formed. These two basic requirements can be obtained by rotating stellar models at very low metallicity. In the present paper, we discuss the arguments supporting this view and illustrates the sensitivity of the results concerning the [Mg/Al] ratio on the rate of the reaction Na(23)(p,γ)Mg(24).

astro-ph.SR↗

arXiv2015

Impact of rotation on stellar models

After a brief recall of the main impacts of stellar rotation on the structure and the evolution of stars, four topics are addressed: 1) the links between magnetic fields and rotation; 2) the impact of rotation on the age determination of clusters; 3) the exchanges of angular momentum between the orbit of a planet and the star due to tides; 4) the impact of rotation on the early chemical evolution of the Milky Way and the origin of the Carbon-Enhanced-Metal-Poor stars.

astro-ph.SR↗