New full relativistic escape velocity and new Hubble related equation for the universe

The escape velocity derived from general relativity coincides with the Newtonian one. However, the Newtonian escape velocity can only be a good approximation when v ≪ c is sufficient to break free of the gravitational field of a massive body, as it ignores higher-order terms of the relativistic kinetic energy Taylor series expansion. Consequently, it does not work for a gravitational body with a radius at which v is close to c such as a black hole. To address this problem, we revisit the concept of relativistic mass, abandoned by Einstein, and derive what we call a full relativistic escape velocity. This approach leads to a new escape radius, where ve = c equal to a half of the Schwarzschild radius. Furthermore, we show that one can derive the Friedmann equation for a critical universe from the escape velocity formula from general relativity theory. We also derive a new equation for a flat universe based on our full relativistic escape velocity formula. Our alternative to the Friedmann formula predicts exactly twice the mass density in our (critical) universe as the Friedmann equation after it is calibrated to the observed cosmological redshift. Our full relativistic escape velocity formula also appears more consistent with the uniqueness of the Planck mass (particle) than the general relativity theory: whereas the general relativity theory predicts an escape velocity above c for the Planck mass at a radius equal to the Planck length, our model predicts an escape velocity c in this case.

Leaps and bounds towards scale separation

In a broad class of gravity theories, the equations of motion for vacuum compactifications give a curvature bound on the Ricci tensor minus a multiple of the Hessian of the warping function. Using results in so-called Bakry-Émery geometry, we put rigorous general bounds on the KK scale in gravity compactifications in terms of the reduced Planck mass or the internal diameter. We reexamine in this light the local behavior in type IIA for the class of supersymmetric solutions most promising for scale separation. We find that the local O6-plane behavior cannot be smoothed out as in other local examples; it generically turns into a formal partially smeared O4.

An approach to Grand Unification

Around the time of the completion of the Standard Model of particle physics in the 1970s, schemes were put forward for unifying the three gauge interactions (electric, strong and weak) using the renormalization equations at an energy approaching the Planck mass. Though these looked promising, the exact unification never materialised, and doubts have been raised about whether this Grand Unification can be achieved. It may be possible, however, to create Grand Unification at the Planck mass if we start with a radical examination of the nature of the colour model of quarks.

On the Trans-Planckian Censorship Conjecture and the generalized non-minimal coupling

We investigate the Trans-Planckian Censorship Conjecture (TCC) and the arising bounds on the inflationary cosmology caused by that conjecture. In that investigation, we analyze TCC bounds for both Jordan and Einstein frames in the presence of a generic non-minimal coupling (to gravity) term. That term allows us to use the functional freedom it brings to the inflationary Lagrangian as an effective Planck mass. In this sense, we argue one should consider the initial field value of the effective Planck mass for the TCC. We show that as a result, one can remove the TCC upper bounds without the need to produce a new process or go beyond the standard inflation mechanism, with the generalized non-minimal coupling, and for Higgs-like symmetry-breaking potentials.

Regular braneworlds with nonlinear bulk-fluids

We construct a regular five-dimensional brane-world with localised gravity on a flat 3-brane. The matter content in the bulk is parametrised by an analog of a non-linear fluid with equation of state $$p=\gamma \rho ^\lambda $$ p = γ ρ λ between the ‘pressure’ p and the ‘density’ $$\rho $$ ρ dependent on the 5th dimension. For $$\gamma $$ γ negative and $$\lambda >1$$ λ > 1 , the null energy condition is satisfied and the geometry is free of singularities within finite distance from the brane, while the induced four-dimensional Planck mass is finite.

Gravity, the origin of the mass in the Cosmos

The most accepted theory for the evolution of the Cosmos is the Big Bang theory, which suggests that, at the beginning, the entire mass-energy of the Cosmos was concentrated within an extremely small, dense and hot singularity. Here, we present a new physical formula that, although obtained in an extremely simple way, has significant implications in Cosmology. This equation indicates that the mass of the Cosmos has grown proportionally with time. This growth equates to a Planck mass for each unit of Planck Time, which is, the mass of 200000 suns per second. Finally the total energy of the Cosmos is demonstrated to be zero.

Reheating in small-field inflation on the brane: the swampland criteria and observational constraints in light of the PLANCK 2018 results

We study cosmological inflation and its dynamics in the framework of the Randall–Sundrum II brane model. In particular, we analyze in detail four representative small-field inflationary potentials, namely Natural inflation, Hilltop inflation, Higgs-like inflation, and Exponential SUSY inflation, each characterized by two mass scales. We constrain the parameters for which a viable inflationary Universe emerges using the latest PLANCK results. Furthermore, we investigate whether or not those models in brane cosmology are consistent with the recently proposed Swampland Criteria, and give predictions for the duration of reheating as well as for the reheating temperature after inflation. Our results show that (i) the distance conjecture is satisfied, (ii) the de Sitter conjecture and its refined version may be avoided, and (iii) the allowed range for the five-dimensional Planck mass, $$M_5$$ M 5 , is found to be $$10^5\,\text {TeV}\lesssim M_5\lesssim 10^{12}\,\text {TeV}$$ 10 5 TeV ≲ M 5 ≲ 10 12 TeV . Our main findings indicate that non-thermal leptogenesis cannot work within the framework of RS-II brane cosmology, at least for the inflationary potentials considered here.

Gravity, the origin of the mass in the Cosmos.

The most accepted theory for the evolution of the Cosmos is the Big Bang theory, which suggests that, at the beginning, the entire mass-energy of the Cosmos was concentrated within an extremely small, dense and hot singularity. Here, we present a new physical formula that, although obtained in an extremely simple way, has significant implications in Cosmology. This equation indicates that the mass of the Cosmos has grown proportionally with time. This growth equates to a Planck mass for each unit of Planck Time, which is, the mass of 200000 suns per second. Finally the total energy of the Cosmos is demonstrated to be zero.

Gravity, the origin of the mass in the Cosmos.

The most accepted theory for the evolution of the Cosmos is the Big Bang theory, which suggests that, at the beginning, the entire mass-energy of the Cosmos was concentrated within an extremely small, dense and hot singularity. Here, we present a new physical formula that, although obtained in an extremely simple way, has significant implications in Cosmology. This equation indicates that the mass of the Cosmos has grown proportionally with time. This growth equates to a Planck mass for each unit of Planck Time, which is, the mass of 200000 suns per second. Finally the total energy of the Cosmos is demonstrated to be zero.