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Register a new userFundamental constants and cosmic vacuum: the micro and macro connection
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The idea that the vacuum energy density $rho_{Lambda}$ could be time dependent is a most reasonable one in the expanding Universe; in fact, much more reasonable than just a rigid cosmological constant for the entire cosmic history. Being $rho_{Lambda}=rho_{Lambda}(t)$ dynamical, it offers a possibility to tackle the cosmological constant problem in its various facets. Furthermore, for a long time (most prominently since Diracs first proposal on a time variable gravitational coupling) the possibility that the fundamental constants of Nature are slowly drifting with the cosmic expansion has been continuously investigated. In the last two decades, and specially in recent times, mounting experimental evidence attests that this could be the case. In this paper, we consider the possibility that these two groups of facts might be intimately connected, namely that the observed acceleration of the Universe and the possible time variation of the fundamental constants are two manifestations of the same underlying dynamics. We call it: the micro and macro connection, and on its basis we expect that the cosmological term in Einsteins equations, Newtons coupling and the masses of all the particles in the Universe, both the dark matter particles and the ordinary baryons and leptons, should all drift with the cosmic expansion. Here we discuss specific cosmological models realizing such possibility in a way that preserves the principle of covariance of General Relativity.
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We propose that the constants of Nature we observe (which appear as parameters in the classical action) are quantum observables in a kinematical Hilbert space. When all of these observables commute, our proposal differs little from the treatment given to classical parameters in quantum information theory, at least if we were to inhabit a constants eigenstate. Non-commutativity introduces novelties, due to its associated uncertainty and complementarity principles, and it may even preclude hamiltonian evolution. The system typically evolves as a quantum superposition of hamiltonian evolutions resulting from a diagonalization process, and these are usually quite distinct from the original one (defined in terms of the non-commuting constants). We present several examples targeting $G$, $c$ and $Lambda $, and the dynamics of homogeneous and isotropic Universes. If we base our construction on the Heisenberg algebra and the quantum harmonic oscillator, the alternative dynamics tends to silence matter (effectively setting $G$ to zero), and make curvature and the cosmological constant act as if their signs are reversed. Thus, the early Universe expands as a quantum superposition of different Milne or de Sitter expansions for all material equations of state, even though matter nominally dominates the density, $rho $, because of the negligible influence of $Grho $ on the dynamics. A superposition of Einstein static universes can also be obtained. We also investigate the results of basing our construction on the algebra of $SU(2)$, into which we insert information about the sign of a constant of Nature, or whether its action is switched on or off. In this case we find examples displaying quantum superpositions of bounces at the initial state for the Universe.
We study particle production and the corresponding entropy increase in the context of cosmology with dynamical vacuum. We focus on the particular form that has been called running vacuum model (RVM), which is known to furnish a successful description of the overall current observations at a competitive level with the concordance $Lambda$CDM model. It also provides an elegant global explanation of the cosmic history from a non-singular initial state in the very early universe up to our days and further into the final de Sitter era. The model has no horizon problem and provides an alternative explanation for the early inflation and its graceful exit, as well as a powerful mechanism for generating the large entropy of the current universe. The energy-momentum tensor of matter is generally non-conserved in such context owing to particle creation or annihilation. We analyze general thermodynamical aspects of particle and entropy production in the RVM. We first study the entropy of particles in the comoving volume during the early universe and late universe. Then, in order to obtain a more physical interpretation, we pay attention to the entropy contribution from the cosmological apparent horizon, its interior and its surface. On combining the inner volume entropy with the entropy on the horizon, we elucidate with detailed calculations whether the evolution of the entropy of the RVM universe satisfies the Generalized Second Law of Thermodynamics. We find it is so and we prove that the essential reason for it is the existence of a positive cosmological constant.
We compute the time variation of the fundamental constants (such as the ratio of the proton mass to the electron mass, the strong coupling constant, the fine structure constant and Newtons constant) within the context of the so-called running vacuum models (RVMs) of the cosmic evolution. Recently, compelling evidence has been provided showing that these models are able to fit the main cosmological data (SNIa+BAO+H(z)+LSS+BBN+CMB) significantly better than the concordance $Lambda$CDM model. Specifically, the vacuum parameters of the RVM (i.e. those responsible for the dynamics of the vacuum energy) prove to be nonzero at a confidence level $gtrsim3sigma$. Here we use such remarkable status of the RVMs to make definite predictions on the cosmic time variation of the fundamental constants. It turns out that the predicted variations are close to the present observational limits. Furthermore, we find that the time variation of the dark matter particles should be crucially involved in the total mass variation of our Universe. A positive measurement of this kind of effects could be interpreted as strong support to the micro and macro connection (viz. the dynamical feedback between the evolution of the cosmological parameters and the time variation of the fundamental constants of the microscopic world), previously proposed by two of us (HF and JS).
The spectrum of relic gravitational wave (RGW) contains high-frequency divergences, which should be removed. We present a systematic study of the issue, based on the exact RGW solution that covers the five stages, from inflation to the acceleration, each being a power law expansion. We show that the present RGW consists of vacuum dominating at $f>10^{11}$Hz and graviton dominating at $f<10^{11}$Hz, respectively. The gravitons are produced by the four cosmic transitions, mostly by the inflation-reheating one. We perform adiabatic regularization to remove vacuum divergences in three schemes: at present, at the end of inflation, and at horizon-exit, to the 2-nd adiabatic order for the spectrum, and the 4-th order for energy density and pressure. In the first scheme a cutoff is needed to remove graviton divergences. We find that all three schemes yield the spectra of a similar profile, and the primordial spectrum defined far outside horizon during inflation is practically unaffected. We also regularize the gauge-invariant perturbed inflaton and the scalar curvature perturbation by the last two schemes, and find that the scalar spectra, the tensor-to-scalar ratio, and the consistency relation remain unchanged.
This is a summary of presentations delivered at the OC1 parallel session Primordial Gravitational Waves and the CMB of the 12th Marcel Grossmann meeting in Paris, July 2009. The reports and discussions demonstrated significant progress that was achieved in theory and observations. It appears that the existing data provide some indications of the presence of gravitational wave contribution to the CMB anisotropies, while ongoing and planned observational efforts are likely to convert these indications into more confident statements about the actual detection.
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