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Register a new userConstructing and solving cosmologies of early universes with dark energy and matter. I
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Authors
Alexandre T.Filippov
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The main purpose of this paper is to advance a unified theory of dark matter, dark energy, and inflation first formulated in 2008. Our minimal affine extension of the GR has geodesics coinciding with the pseudo Riemannian ones, up to parameterizations. It predicts a `sterile massive vecton and depends on two new dimensional constants, which can be measured in the limit of small vecton velocity. In a special gauge, this velocity has an upper limit near which it grows to infinity. The linearized vecton theory is similar to the scalar models of inflation except the fact of internal anisotropy of the vecton. For this reason we study general solutions of scalar analogs of the vecton theory without restricting the curvature parameter and anisotropy by using previously derived exact solutions as functions of the metric. It is shown that the effects of curvature and anisotropy fast decrease in expanding universes. Our approach can be applied to anisotropic universes, which is demonstrated on an exactly solvable strongly anisotropic cosmology. To characterize different cosmological scenarios in detail we introduce three characteristic functions, two of which are small and almost equal during inflation and grow near the exit. Instead of the potential it is possible to use one of the two characteristic functions. This allows to approximately derive flat isotropic universes with `prescribed scenarios, which is the essence of our constructive cosmology of early universes. The most natural application of our approach is in analytically constructing characteristic functions of inflationary models with natural exits. However, the general construction can be applied to other problems, e.g., to evolution of contracting universes.
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We show that several integrable (i.e., exactly solvable) scalar cosmologies considered by Fre, Sagnotti and Sorin (Nuclear Physics textbf{B 877}(3) (2013), 1028--1106) can be generalized to include cases where the spatial curvature is not zero and, besides a scalar field, matter or radiation are present with an equation of state $p^{(m)} = w, rho^{(m)}$; depending on the specific form of the self-interaction potential for the field, the constant $w$ can be arbitrary or must be fixed suitably.
We suggest a Lorentz non-invariant generalization of the unimodular gravity theory, which is classically equivalent to general relativity with a locally inert (devoid of local degrees of freedom) perfect fluid having an equation of state with a constant parameter $w$. For the range of $w$ near $-1$ this dark fluid can play the role of dark energy, while for $w=0$ this dark dust admits spatial inhomogeneities and can be interpreted as dark matter. We discuss possible implications of this model in the cosmological initial conditions problem. In particular, this is the extension of known microcanonical density matrix predictions for the initial quantum state of the closed cosmology to the case of spatially open Universe, based on the imitation of the spatial curvature by the dark fluid density. We also briefly discuss quantization of this model necessarily involving the method of gauge systems with reducible constraints and the effect of this method on the treatment of recently suggested mechanism of vacuum energy sequestering.
The cosmological energy density $rho_{_{_Lambda}}$ at the Planck scale $M_{rm pl}$ drives inflation and simultaneously reduces its value to create the pair-energy density $rho_{_{_M}}$ via the continuous pair productions of massive fermions and antifermions. The decreasing $rho_{_{_Lambda}}$ and increasing $rho_{_{_M}}$, in turn, slows down the inflation to its end when the pair production rate $Gamma_M$ is larger than the Hubble rate $H$ of inflation. A large number of massive pairs is produced and reheating epoch starts. In addition to the Einstein equation and energy-conservation law, we introduce the Boltzmann-type rate equation describing the number of pairs produced from (annihilating to) the spacetime, and reheating equation describing massive unstable pairs decay to relativistic particles and thermodynamic laws. This forms a close set of four independent differential equations uniquely determining $H$, $rho_{_Lambda}$, $rho_{_M}$ and radiation-energy density $rho_{_R}$, given the initial conditions at inflation end. Numerical solutions demonstrate three episodes of preheating, massive pairs dominate and genuine reheating. Results show that $rho_{_Lambda}$ can efficiently convert to $rho_{_M}$ by producing massive pairs, whose decay accounts for reheating $rho_{_R}$, temperature and entropy of the Big-Bang Universe. The stable massive pairs instead account for cold dark matter. Using CMB and baryon number-to-entropy ratio measurements, we constrain the effective mass of pairs, Yukawa coupling and degeneracies of relativistic particles. As a result, the obtained inflation $e$-folding number, reheating scale, temperature and entropy are in terms of the tensor-to-scalar ratio in the theoretically predicated range $0.042lesssim r lesssim 0.048$, consistently with current observations.
Evidence to the case that classical gravitation provides the clue to make sense out of quantum gravity is presented. The key observation is the existence in classical gravitation of child universe solutions or almost solutions, almost because of some singularity problems. The difficulties of these child universe solutions due to their generic singularity problems will be very likely be cured by quantum effects, just like for example almost instanton solutions are made relevant in gauge theories with breaking of conformal invariance. Some well motivated modifcations of General Relativity where these singularity problems are absent even at the classical level are discussed. High energy density excitations, responsible for UV divergences in quantum field theories, including quantum gravity, are likely to be the source of child universes which carry them out of the original space time. This decoupling could prevent these high UV excitations from having any influence on physical amplitudes. Child universe production could therefore be responsible for UV regularization in quantum field theories which take into account semiclassically gravitational effects. Child universe production in the last stages of black hole evaporation, the prediction of absence of tranplanckian primordial perturbations, connection to the minimum length hypothesis and in particular the connection to the maximal curvature hypothesis are discussed. Some discussion of superexcited states in the case these states are Kaluza Klein excitations is carried out. Finally, the posibility of obtaining string like effects from the wormholes associated with the child universes is discussed.
In this paper, we study the changes of quantum effects of a growing universe by using Wheeler-DeWitt equation (WDWE) together with de Broglie-Bohm quantum trajectory approach. From WDWE, we obtain the quantum modified Friedmann equations which have additional terms called quantum potential compared to standard Friedmann equations. The quantum potential governs the behavior of the early universe, providing energy for inflation, while it decreases rapidly as the universe grows. The quantum potential of the grown-up universe is much smaller than that required for accelerating expansion. This indicates that quantum effects of our universe cannot be treated as a candidate for dark energy.
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