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Register a new userConstraining cosmologies with fundamental constants I. Quintessence and K-Essence
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Rodger Thompson Prof.
Publication date
2012
fields
Physics
and research's language is
English
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Many cosmological models invoke rolling scalar fields to account for the observed acceleration of the expansion of the universe. These theories generally include a potential V(phi) which is a function of the scalar field phi. Although V(phi) can be represented by a very diverse set of functions, recent work has shown the under some conditions, such as the slow roll conditions, the equation of state parameter w is either independent of the form of V(phi) or is part of family of solutions with only a few parameters. In realistic models of this type the scalar field couples to other sectors of the model leading to possibly observable changes in the fundamental constants such as the fine structure constant alpha and the proton to electron mass ratio mu. This paper explores the limits this puts on the validity of various cosmologies that invoke rolling scalar fields. We find that the limit on the variation of mu puts significant constraints on the product of a cosmological parameter w+1 times a new physics parameter zeta_mu^2, the coupling constant between mu and the rolling scalar field. Even when the cosmologies are restricted to very slow roll conditions either the value of zeta_mu must be at the lower end of or less than its expected values or the value of w+1 must be restricted to values vanishingly close to 0. This implies that either the rolling scalar field is very weakly coupled with the electromagnetic field, small zeta_mu, very weakly coupled with gravity, w+1 ~ 0 or both. These results stress that adherence to the measured invariance in mu is a very significant test of the validity of any proposed cosmology and any new physics it requires. The limits on the variation of mu also produces a significant tension with the reported changes in the value of alpha.
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This investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar $phi$ with respect to the natural log of the scale factor $a$, $beta(phi)=frac{d phi}{d ln(a)}$. Once the beta function is specified, modulo a boundary condition, the evolution of the scalar $phi$ as a function of the scale factor is completely determined. A rolling scalar field cosmology is defined by its action which can contain a range of physically motivated dark energy potentials. The beta function is chosen so that the associated beta potential is an accurate, but not exact, representation of the appropriate dark energy model potential. The basic concept is that the action with the beta potential is so similar to the action with the model potential that solutions using the beta action are accurate representations of solutions using the model action. The beta function provides an extra equation to calculate analytic functions of the cosmologies parameters as a function of the scale factor that are that are not calculable using only the model action. As an example this investigation uses a quintessence cosmology to demonstrate the method for power and inverse power law dark energy potentials. An interesting result of the investigation is that the Hubble parameter H is almost completely insensitive to the power of the potentials and that $Lambda$CDM is part of the family of quintessence cosmology power law potentials with a power of zero.
We summarize the attempts by our group and others to derive constraints on variations of fundamental constants over cosmic time using quasar absorption lines. Most upper limits reside in the range 0.5-1.5x10-5 at the 3sigma level over a redshift range of approximately 0.5-2.5 for the fine-structure constant, alpha, the proton-to-electron mass ratio, mu, and a combination of the proton gyromagnetic factor and the two previous constants, gp(alpha^2/mu)^nu, for only one claimed variation of alpha. It is therefore very important to perform new measurements to improve the sensitivity of the numerous methods to at least <0.1x10-5 which should be possible in the next few years. Future instrumentations on ELTs in the optical and/or ALMA, EVLA and SKA pathfinders in the radio will undoutedly boost this field by allowing to reach much better signal-to-noise ratios at higher spectral resolution and to perform measurements on molecules in the ISM of high redshift galaxies.
This paper uses the beta function formalism to extend the analysis of quintessence cosmological parameters to the logarithmic and exponential dark energy potentials. The previous paper (Thompson 2018) demonstrated the formalism using power and inverse power potentials. The essentially identical evolution of the Hubble parameter for all of the quintessence cases and LambdaCDM is attributed to the flatness of the quintessence dark energy potentials in the dark energy dominated era. The Hubble parameter is therefore incapable of discriminating between static and dynamic dark energy. Unlike the other three potentials considered in the two papers the logarithmic dark energy potential requires a numerical integration in the formula for the superpotential rather than being an analytic function. The dark energy equation of state and the fundamental constants continue to be good discriminators between static and dynamical dark energy. A new analysis of quintessence with all four of the potentials relative the swampland conjectures indicates that the conjecture on the change in the scalar field is satisfied but that the conjecture on the change of the potential is not.
We explore the possibility that a scalar field with appropriate Lagrangian can mimic a perfect fluid with an affine barotropic equation of state. The latter can be thought of as a generic cosmological dark component evolving as an effective cosmological constant plus a generalized dark matter. As such, it can be used as a simple, phenomenological model for either dark energy or unified dark matter. Furthermore, it can approximate (up to first order in the energy density) any barotropic dark fluid with arbitrary equation of state. We find that two kinds of Lagrangian for the scalar field can reproduce the desired behaviour: a quintessence-like with a hyperbolic potential, or a purely kinetic k-essence one. We discuss the behaviour of these two classes of models from the point of view of the cosmological background, and we give some hints on their possible clustering properties.
The values of the fundamental constants such as $mu = m_P/m_e$, the proton to electron mass ratio and $alpha$, the fine structure constant, are sensitive to the product $sqrt{zeta_x^2(w+1)}$ where $zeta_x$ is a coupling constant between a rolling scalar field responsible for the acceleration of the expansion of the universe and the electromagnetic field with x standing for either $mu$ or $alpha$. The dark energy equation of state $w$ can assume values different than $-1$ in cosmologies where the acceleration of the expansion is due to a scalar field. In this case the value of both $mu$ and $alpha$ changes with time. The values of the fundamental constants, therefore, monitor the equation of state and are a valuable tool for determining $w$ as a function of redshift. In fact the rolling of the fundamental constants is one of the few definitive discriminators between acceleration due to a cosmological constant and acceleration due to a quintessence rolling scalar field. $w$ is often given in parameterized form for comparison with observations. In this manuscript the predicted evolution of $mu$, is calculated for a range of parameterized equation of state models and compared to the observational constraints on $Delta mu / mu$. We find that the current limits on $Delta mu / mu$ place significant constraints on linear equation of state models and on thawing models where $w$ deviates from $-1$ at late times. They also constrain non-dynamical models that have a constant $w$ not equal to $-1$. These constraints are an important compliment to geometric tests of $w$ in that geometric tests are sensitive to the evolution of the universe before the epoch of observation while fundamental constants are sensitive to the evolution of the universe after the observational epoch. Abstract truncated.
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