CosmoVerse seminar: Emmanuel Saridakis

(Late-time) “solutions” to H0 and S8 tensions through modified gravity.
We discuss some possible late-time alleviations of H0 and S8 tensions in the context of modified theories of gravity. In particular, we examine how torsional and non-metric theories can lead to weaker gravity at “intermediate” scales, in a suitable way in order to lead to faster expansion and less matter clustering (and we show why this is not possible in simple curvature-based modifications).
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1:09:20 “A purely algebraic theory is required to describe reality." (Einstein, January, 1955). On the “dark” invariance: 0.in RT the main invariant is the 4-interval (a mathematical description of the constant c), however, it could offer another invariant value based on another physical constant. 1.Comparing with Einstein's equations of 1915, we find a=-c^3/16πG. Strictly speaking, in order to determine the constant a, it was necessary to make a transition to the Poisson equation. Thus, a rigorous derivation of Einstein's equations can be given. The transition to the non-relativistic limit allows us to determine a constant factor for the integral of the gravitational field according to: R[(0)^0]=(4πG/c^2)p; Δφ=-pc^3/4a=4πGр. And a=(1/16π)m(pl)w(pl). 2.Therefore, the Poisson equation can be written as: ∆g(00)=8πGT(00)/c^4, where g(00) is the time component of the metric tensor (for a weakly curved metric the time component of the energy-momentum tensor: T(00)~=pc^2). This equation is true only in the non-relativistic case, but it is applicable to the case of a homogeneous and isotropic Universe, when Einstein's equations have only solutions with a time-varying space-time metric. Then the energy density of the gravitational field: g^2/8πG=T(00)=pc^2 [~=(ħ/8πc^3)w(relic)^4= =1600 quanta/cm^3, which is in order of magnitude consistent with the observational-measured data (~500 quanta/cm^3)], where the critical density value determining the nature of the model is: p=(3/8π)H^2/G. Hence it follows: g~πcH. 3.Expansion is a special kind of motion, and it seems that the Universe is a non-inertial frame of reference that performs variably accelerated motion along a phase trajectory, and thereby creates a phase space. And according to the strong equivalence principle: g=|a*|=πcH [=r(pl)w(relic)^2], and w(relic)^2=πw(pl)H. Thus H=1,72*10^-20sec^-1! 4.Intra-metagalactic gravitational potential: |ф0|=πGmpl/λ(relic)=[Gm(pl)/2c]w(relic), where the constant Gm(pl)/2c is a quantum of the inertial flow Ф(i) = (½)S(pl)w(pl) = h/4πm(pl) (magnetic flux is quantized: = h/2e, Josephson’s const; and the mechanical and magnetic moments are proportional).Thus, the phenomenon can be interpreted as gravity/inertial induction. {The basic formula QG of the quantum expression of the Newtonian gravitational potential is: ф(G)=-Ф(i)w, where w is the frequency of the quanta of the gravitational (~ vibrational) field.} 5.From Kepler's third law follows: M/t=v^3/G, where M/t=I(G)=[gram•sec^-1] is the gravitational current. By the way, in SR: I(G)=inv; this follows from the Lorentz transformations: m=m(0)/√(1-v^2/c^2) and t=t(0)/√(1-v^2/c^2). Hence, obviously, we have I(G)=m/t=m(0)/t(0)=inv. However, а*=-2πcа/M(universe), what is F=M(universe)а*=-2πса=-с^4/8G=-(⅛)F(pl). 6.In the case of the Universe: I(G)=M(universe)H=m(pl)w(pl)/8π=c^3/8πG=-2a (~ the "dark" const~inv), where M(universe)=E/c^2 is the full mass of the Universe, and the total energy E is spent on creating a phase-quantized space-time: m(pl)w(pl)=8πM(Universe)H { w(relic)^2=πw(pl)H. 7.That is: Δφ=-pc^3/4a= рс^3/2M(universe)H^2. And Δφ=4π[с^3/Gm(pl)w(pl)]H^2= 4πH^2; which is evidence of a phenomenon: spontaneous Lorentz transformations. Thus; Δφ(0)/Δφ=w(pl)^2/H^2~10^126, where Δφ(0)=4πw(pl)^2; the “best” prediction. Addition On the self repel: 0.“Giving the interval ds the size of time, we will denote it by dт: in this case, the constant k will have the dimension length divided by mass and in CGS units will be equal to 1,87*10^-27", Friedmann, (On the curvature of space, 1922). 1.[The ds, which is assumed to have the dimension of time, we denote by dт; then the constant k has the dimension Length Mass and in CGS-units is equal to 1, 87.10^ ± 27. See Laue, Die Relativitatstheorie, Bd. II, S. 185. Braunschweig 1921.] 2.Apparently, the following expression takes place: μ(0)ε(0)Gi=1, which means that Gi=с^2 where i is inertial constant, i=1,346*10^28[g/cm]; or k°=1/i=7,429*10^-29[cm/g]: k(Friedmann)/k°=8π; where k°=r(pl)/m(pl). 3.For clarity, let's draw an analogy. In electrodynamics, a circular conductor detects the properties of two conductors with currents flowing in opposite directions, since for each section of a conductor with a current on the opposite side there is a reverse current flow. Thus, the conductor is self-repelled by the magnetic force: F(m)=μ(0)I(e)^2, where I(e) is the electric current. 4.Then the force of inertia is: F(i)=(1/i)[I(G)^2], where I(G)=mw. That is, the expansion of the mechanical system is due to the inertial force of self-repelled (it is clear that this is not an anti-gravitational force). 5.In the case of the Universe; the gravitational current flowing along the phase trajectory: I(universe)=M(universe)H~m(pl)w(pl), respectively, the inertial force of self-expansion: F(i)=(1/i)I(universe)^2~F(pl). 6.It is clear that this approach is also valid for bodies moving in the same direction: then the inertial force of attraction will "appear", and this is not a gravitational, and even more so, not a "dark matter" effect. {For example, for clusters of galaxies; for stars orbiting the center of galaxies.} 7.The general formula for both cases: dF(i)=(1/4πi)[2I(1)I(2)](dl/r), where dl is the "element of length" of the trajectory of motion of the test body: a vector modulo equal to dl and coinciding in direction with the motion-current of the body, r is the distance between the trajectories of moving bodies. Thus, the three directions I(G), r, B(i) are perpendicular to each other in pairs: it follows that gravity/inertial (and electro/magnetic) actions are closely related to the structure of space-time and form a natural rectangular coordinate system. 8.Moreover, if "The geometry of space in general relativity theory turned out to be another field, therefore the geometry of space in GR is almost the same as the gravitational field.” (Smolin); then the gravity/inertial field is a dynamic 4-space.