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At least one dimensionless physical constant (i.e., a physically observable) must change for the cosmic time to make the varying speed of light (VSL) models phenomenologically feasible. Various physical constants and quantities also should be functions of cosmic time to satisfy all known local laws of physics, including special relativity, thermodynamics, and electromagnetism. Adiabatic condition is another necessary condition to keep the homogeneity and isotropy of three-dimensional space. To be a self-consistent theory, one should consider cosmic evolutions of physical constants and quantities when one derives Einstein's field equations and their solutions. All these conditions are well satisfied in the so-called minimally extended varying speed of light (meVSL) model. Unlike other VSL models, we show that the redshift-drift formula of the meVSL model is the same as a standard model. Therefore, we cannot use this as an experimental tool to verify the meVSL. Instead, one can still use the cosmological chronometers (CC) as a model-independent test of the meVSL. The current CC data cannot distinguish meVSL from the standard model (SM) when we adopt the best-fit values (or Gaussian prior) of the present values of $H_0$ and of $\Omega_{m0}$ from the Planck mission. However, the CC data prefer the meVSL when we choose Pantheon 22 data., Comment: version 3 to match the version accepted by MNRAS. 8 pages, 2 figures. arXiv admin note: text overlap with arXiv:2011.09274

The Robertson-Walker (RW) metric allows us to apply general relativity to model the behavior of the Universe as a whole (i.e., cosmology). We can properly interpret various cosmological observations, like the cosmological redshift, the Hubble parameter, geometrical distances, and so on, if we identify fundamental observers with individual galaxies. That is to say that the interpretation of observations of modern cosmology relies on the RW metric. The RW model satisfies the cosmological principle in which the 3-space always remains isotropic and homogeneous. One can derive the cosmological redshift relation from this condition. We show that it is still possible for us to obtain consistent results in a specific time-varying speed-of-light model without spoiling the success of the standard model. The validity of this model needs to be determined by observations., Comment: 13 pages

Cosmological observations provide more accurate values both for background evolution of the Universe and for the structure formation. These values are given by the so-called dark energy equation of state, $\omega$ and the growth index parameter, $\gamma$. From these observed parameters, one can reconstruct the model functions in scalar tensor gravity theories. However, there is a long standing debate about the (in)equality between conformally transformed frames in scalar tensor gravity models. We show that cosmological observables are frame dependent when they are described by frame independent parameter, redshift. Thus, if the cosmological observables are interpreted in one frame, then all of the observables should also be interpreted in that frame. This explicitly shows the conformal inequality of cosmological observables. Also, our method provides the model independent analysis for STG models about various observables in both frames., Comment: 14 pages, 5 figures

Even though there have been the various varying speed of light (VSL) cosmology models, they remain out of the mainstream because of their possible violation of physics laws built into fundamental physics. In order to be the VSL as a viable theory, it should inherit the success of special relativity including Maxwell equations and thermodynamics at least. Thus, we adopt that the speed of light, $\tilde c$ varies for the cosmic time not for the local time, i.e., $\tilde c[z]$ where $z$ is the cosmological redshift. When one describes the background FLRW universe, one can define the constant-time hypersurface by using physical quantities such as temperature, density, and $\tilde c$. It is because they evolve in time, and the homogeneity of the Universe demands that they must equal at the equal cosmic time. The variation of $\tilde c$ accompanies the joint variations of all related physical constants in order to satisfy the Lorentz invariance, thermodynamics, and Bianchi identity. We call this VSL model as a "minimally extended VSL (meVSL)". We derive cosmological observables of meVSL and obtain the constraints on the variation of $\tilde c$ by using the current observations. Interestingly, $z$ and all geometrical distances except the luminosity distance of meVSL are the same as those of general relativity. However, the Hubble parameter of meVSL is rescaled as $H = (1+z)^{-b/4} H^{(\rm GR)}$ which might be used as a solution for the tension of the Hubble parameter measurements. In this manuscript, we provide the main effects of meVSL on various cosmological observations including BBN, CMB, SZE, BAO, SNe, GWs, H, SL, and $\Delta \alpha$., Comment: 84 pages, 10 figures, 2 tables. To match the version accepted by JCAP

We reconstruct the viable f(G) gravity models from the observations and provide the analytic solutions that well describe our numerical results. In order to avoid unphysical challenges that occur during the numerical reconstruction, we generalize f(G) models into f(GA), which is the simple extension of f(G) models with the introduction of a constant A parameter. We employ several observational data together with the stability condition, which reads d2f/dG2 > 0 and must be satisfied in the late-time evolution of the universe, to give proper initial conditions for solving the perturbation equation. As a result, we obtain the analytic functions that match the numerical solutions. Furthermore, it might be interesting if one can find the physical origin of those analytic solutions and its cosmological implications., 17 pages, 9 figures

We consider the Einstein-Hilbert action without cosmological constant in 5-dimensions and implement the Kaluza-Klein (KK) reduction by compactifying the fifth direction on a circle of small but finite radius. For non-zero compactification radius, the 4- dimensional spectrum contains massless and massive KK modes. For the massive KK modes, we retain four KK tensor and one KK scalar modes after a gauge fixing. We treat those massive KK modes as stochastic sources of gravitational wave (GW) with characteristic dependences of the frequencies on the size of the extra dimension. Using the observational bounds on the size of the extra dimension and on the characteristic strain, we make an order estimation on the frequencies and amplitudes of the massive KK modes that can contribute to the GW., Comment: 27pages, 2tables

The recent astonishing realization of the negative absolute temperature (NAT) for motional degrees of freedom \cite{Braun_ea13} inspires its possible application to the early universe. The existence of the upper bound on the energy of the system is the sufficient requirement for a NAT and this might correspond to the Planck scale at the Big Bang model. It has been argued that standard inflation requires an initial patch that is smooth over distance scales a bit larger than the causal horizon at the onset of inflation. We show that this initial condition problem can be solved if the NAT fermion, dubbed ``NATON'', occupies the Universe before the standard inflation is ignited by providing mini inflation prior to the standard one. As long as NATON dominated era lasts until at least ten times older than the Planck time, it makes the Universe homogeneous enough to derive the successful standard inflation., Comment: 11pages, 7figures

The gravitational wave (GW) detection of a binary neutron star inspiral made by the Advanced LIGO and Advanced Virgo paves the unprecedented way for multi-messenger observations. The propagation speed of this GW can be scrutinized by comparing the arrival times between GW and neutrinos or photons. It provides the constraint on the mass of the graviton. f(R) gravity theories have the habitual non-zero mass gravitons in addition to usual massless ones. Previously, we show that the model independent f(R) gravity theories can be constructed from the both background evolution and the matter growth with one undetermined parameter. We show that this parameter can be constrained from the graviton mass bound obtained from GW detection. Thus, the GW detection provides the invaluable constraint on the validity of f(R) gravity theories., Comment: 6 pages, 2 figures, To match the version accepted by EPJC

The absence of compelling theoretical model requires the parameterizing the dark energy to probe its properties. The parametrization of the equation of state of the dark energy is a common method. We explore the theoretical optimization of the parametrization based on the Fisher information matrix. As a suitable parametrization, it should be stable at high redshift and should produce the determinant of the Fisher matrix as large as possible. For the illustration, we propose one parametrization which can satisfy both criteria. By using the proper parametrization, we can improve the constraints on the dark energy even for the same data. We also show the weakness of the so-called principal component analysis method., 7pages, 11 figures, 2 tables, To match the version accepted by ASS

Recently, the power spectrum (PS) multipoles using the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 (DR12) sample are analyzed \cite{160703150}. The based model for the analysis is the so-called TNS quasi-linear model and the analysis provides the multipoles up to the hexadecapole \cite{TNS}. Thus, one might be able to recover the real-space linear matter PS by using the combinations of multipoles to investigate the cosmology \cite{0407214}. We provide the analytic form of the ratio of quadrupole (hexadecapole) to monopole moments of the quasi-linear PS including the Fingers-of-God (FoG) effect to recover the real-space PS in the linear regime. One expects that observed values of the ratios of multipoles should be consistent with those of the linear theory at large scales. Thus, we compare the ratios of multipoles of the linear theory, including the FoG effect with the measured values. From these, we recover the linear matter power spectra in real-space. These recovered power spectra are consistent with the linear matter power spectra., 15 pages, 5 figures, To match the version to be published in JCAP

We investigate a spherical collapse model with and without the spatial curvature. We obtain the exact solutions of dynamical quantities such as the ratio of the scale factor to its value at the turnaround epoch and the ratio of the overdensity radius to its value at the turnaround time with general cosmological parameters. The exact solutions of the overdensity at the turnaround epoch for the different models are also obtained. Thus, we are able to obtain the nonlinear overdensity at any epoch for the given model. We obtain that the nonlinear overdensity of the Einstein de Sitter Universe is 18 pi^2(fr{1}{2pi} + fr{3}{4})^2 ~ 147 instead of the well known value 18 pi^2 ~ 178. In the open Universe, perturbations are virialized earlier than in flat Universe and thus clusters are denser at the virial epoch. Also the critical density threshold from the linear theory at the virialized epoch is obtained as fr{3}{20} (9pi+6)^{fr{2}{3}} ~ 1.58 instead of fr{3}{20} (12pi)^{fr{2}{3}} ~ 1.69. This value is same for the close and the open Universes. Because we obtain the analytic forms of dynamical quantities, we are able to estimate the abundances of both virialized and non-virialized clusters at any epoch. Also the temperature and luminosity functions are able to be computed at any epoch. Unfortunately, the current concordance model prefers the almost flat Universe and the above results might be restricted by the academic interests only. However, mathematical structure of the physical evolution equations of the curved space is identical with that of the dark energy with the equation of state w = -fr{1}{3}. Thus, we are able to extend these analytic solutions to the general dark energy model and they will provide the useful tools for probing the properties of dark energy., 11 pages, 4 figres, 1 table, Full version of abstract is available in the manuscript

Recent astrophysical observations of quasar absorption systems indicate that the fine structure constant $\alpha$ and the proton-electron mass ratio $\mu$ may have evolved through the history of the universe. Motivated by these observations, we consider the cosmological evolution of a quintessence-like scalar field $\phi$ coupled to gauge fields and matter which leads to effective modifications of the coupling constants and particle masses over time. We show that a class of models where the scalar field potential $V(\phi)$ and the couplings to matter $B(\phi)$ admit common extremum in $\phi$ naturally explains constraints on variations of both the fine structure constant and the proton-electron mass ratio., Comment: 9 pages, 4 figures, CosPA 2006 Proceeding. 9 pages, 4 figures, CosPA 2006 Proceeding will be published in the Mod. Phys. Lett. A

Recently, we find that the correction for the EdS assumption on the one-loop matter power spectrum for general dark energy models using the standard perturbation theory is not negligible \cite{LPB}. Thus, we investigate the same problem by obtaining the exact displacement vector and kernels up to the third order for the general dark energy models in the Lagrangian perturbation theory (LPT). Using these exact solutions, we investigate the present one-loop matter power spectrum in the $\Lambda$CDM model with $\Omega_{m0} = 0.25 (0.3)$ to obtain about 0.2 (0.18) \% error correction compared to that obtained from the EdS assumption for $k = 0.1 \rm{h\, Mpc}^{-1}$ mode. If we consider the total matter power spectrum, the correction is only 0.05 (0.03) \% for the same mode. It means that EdS assumption is a good approximation for $\Lambda$CDM model in LPT theory. However, one can use this method for general models where EdS assumption is improper., Comment: 7 pages, 3 figures

Recently, BICEP2 measurements of the cosmic microwave background (CMB) $B$-mode polarization has indicated the presence of primordial gravitational waves at degree angular scales, inferring the tensor-to-scalar ratio of $r=0.2$ and a running scalar spectral index. In this {\em Letter}, we show that the existence of the fluctuations of cosmological birefringence can give rise to CMB $B$-mode polarization that fits BICEP2 data with $r, to match the version to be published in Phys. Lett. B that sets an upper limit on cosmic birefringence. arXiv admin note: text overlap with arXiv:1307.6298

The cosmic microwave background and large scale structure are complementary probes to investigate the early and late time universe. After the current accomplishment of the high accuracies of CMB measurements, accompanying precision cosmology from LSS data is emphasized. We investigate the dynamical dark energy models which can produce the same CMB angular power spectra as that of the LCDM model with less than a sub-percent level accuracy. If one adopts the dynamical DE models using the so-called Chevallier-Polarski-Linder (CPL) parametrization, w = w0 + wa(1-a), then one obtains models (w0,wa)= (-0.8,-0.767), (-0.9,-0.375), (-1.1,0.355), (-1.2,0.688) named as M8, M9, M11, and M12, respectively. The differences of the growth rate, f which is related to the redshift space distortions (RSD) between different DE models and the LCDM model are about 0.2% only at z=0. The difference of f between M8 (M9, M11, M12) and the LCDM model becomes maximum at z ~ 0.25 with -2.4 (-1.2, 1.2, 2.5)%. This is a scale-independent quantity. One can investigate the one-loop correction of the matter power spectrum of each model using the standard perturbation theory in order to probe the scale-dependent quantity in the quasi-linear regime ({\it i.e.} k < 0.4 h/Mpc). The differences in the matter power spectra including the one-loop correction between M8 (M9, M11, M12) and the LCDM model for k= 0.4 h/Mpc scale are 1.8 (0.9, 1.2, 3.0)% at z=0, 3.0 (1.6, 1.9, 4.2)% at z=0.5, and 3.2 (1.7, 2.0, 4.5)% at z=1.0. The bigger departure from -1 of w0, the larger the difference in the power spectrum. Thus, one should use both the RSD and the quasi-linear observable in order to discriminate a viable DE model among a slew of models which are degenerated in CMB. Also we obtain the lower limit on w0 > -1.5 from the CMB acoustic peaks and this will provide the useful limitation on phantom models., 9 pages, 3 figures, add more references, change typo

We investigate the Lagrangian perturbation theory of a general dark energy models with a constant equation of state, \omega, and derive the fitting form of the fastest growing mode solutions up to the third order. These fitting forms are less than few % errors compared to the numerical calculation. We also correct the solutions of Einstein-de Sitter and the open universe with the proper initial conditions and the correct consideration for the growing mode solutions in order to compare with the general dark energy models. Even though these fitting forms are limited to the constant equation of state models, one can apply these to the time-varying \omega by interpolating between models with the constant \omega. These fitting forms can be used for the correct prediction for the two point correlation function and can give the proper predictions for the different dark energy models., Comment: 25 pages, 12 figures, To match the version accepted by Physical Review D

We study the imprint of a coupling of scalar dark energy to photon on the cosmic microwave background (CMB) polarization. The time-evolving field value as well as the perturbation of the scalar generically induce $B$-mode polarization. Future CMB data will find either a cosmic parity violation in temperature-polarization correlation due to the field value, or perturbation-induced $B$-mode polarization that is almost indistinguishable from that generated by gravitational lensing or primordial gravitational waves., matches version accepted for publication in PRD

In spite of their original discrepancy, both dark energy and modified theory of gravity can be parameterized by the effective equation of state (EOS) $\omega$ for the expansion history of the Universe. A useful model independent approach to the EOS of them can be given by so-called Chevallier-Polarski-Linder (CPL) parametrization where two parameters of it ($\omega_{0}$ and $\omega_{a}$) can be constrained by the geometrical observations which suffer from degeneracies between models. The linear growth of large scale structure is usually used to remove these degeneracies. This growth can be described by the growth index parameter $\gamma$ and it can be parameterized by $\gamma_{0} + \gamma_{a} (1 - a)$ in general. We use the scalar-tensor theories of gravity (STG) and show that the discernment between models is possible only when $\gamma_a$ is not negligible. We show that the linear density perturbation of the matter component as a function of redshift severely constrains the viable subclasses of STG in terms of $\omega$ and $\gamma$. From this method, we can rule out or prove the viable STG in future observations. When we use $Z(\phi) =1$, $F$ shows the convex shape of evolution in a viable STG model. The viable STG models with $Z(\phi) = 1$ are not distinguishable from dark energy models when we strongly limit the solar system constraint., Comment: 19 pages, 20 figures, 2 tables, submitted to JCAP

There have been the approximate analytic solution \cite{Silveria} and several approximate analytic forms \cite{0508156,Carroll,0303112} of the growth factor $D_{g}$ for the general dark energy models with the constant values of its equation of state $\omde$ after Heath found the exact integral form of the solution of $D_{g}$ for the Universe including the cosmological constant or the curvature term. Recently, we obtained the exact analytic solutions of the growth factor for both $\omde = -1$ or $-\fr{1}{3}$ \cite{SK1} and the general dark energy models with the constant equation of state $\omde$ \cite{SK3} independently. We compare the exact analytic solution of $D_{g}$ with the other well known approximate solutions. We also prove that the analytic solutions for $\omde = -1$ or $-\fr{1}{3}$ in Ref. \cite{SK1} are the specific solutions of the exact solutions of the growth factor for general $\omde$ models in Ref. \cite{SK3} even though they look quite different. We scrutinize the issue of using the well known parameterizations of the growth index and its parameter given in Ref. \cite{WS} to obtain the growth factor for general dark energy models. We also investigate the possible extensions of the exact solution of $D_{g}$ to the time-varying $\omde$ for the comparison with observations., Comment: 18 pages, 10 figures, 3 tables, To match the version accepted by Physical Review D

Three decades ago Heath found the integral form of the exact analytic growing mode solution of the linear density perturbation $\delta$ on sub-horizon scales including the cosmological constant or the curvature term. Recently, we obtained the exact analytic form of this solution in our previous work \cite{SK}. Interestingly, we are able to extend this solution for general dark energy models with the constant equation of state $\omega_{de}$ in a flat universe. This analytic solution provides the accurate and efficient tools for probing the properties of dark energy models such as the behavior of the growth factor and the growth index. We investigate the growth index and its parameter at any epoch with this exact solution for different dark energy models and find that the growth index is quite model dependent in the redshift space, $0.25 \leq z \leq 1.5$, so observations of the structure growth around this epoch would be very interesting. Also one may be able to rule out some dark energy models by using the analysis from this exact solution. Thus, the analytic solution for the growth factor provides the very useful tools for future observations to constrain the exact values of observational quantities at any epoch related to the growth factor in the dark energy models., Comment: 8pages, 3figures, 1Table, minor revisions to match version accepted by PLB (add Fig1)

We investigate a spherical overdensity model for the non-clustering dark energy (DE) with the constant equation of state, w in a flat universe. In this case, the exact solution for the evolution of the scale factor is obtained for general w. We also obtain the exact (when w = - 1/3) and the approximate (when w neq -1/3) solutions for the ratio of the overdensity radius to its value at the turnaround epoch (y) for general cosmological parameters. Also the exact and approximate solutions of the overdensity at the turnaround epoch (zeta) are obtained for general w. Thus, we are able to obtain the non-linear overdensity Delta = 1 + delta at any epoch for the given DE model. The non-linear overdensity at the virial epoch (Delta_{vir}) is obtained by using the virial theorem and the energy conservation. The non-linear overdensity of every DE model converges to that of the Einstein de Sitter universe ~ 147 when z_{vir}increases. We find that the observed quantities at high redshifts are insensitive to the different w models. The low-redshift cluster (z_{vir} ~ 0.04, i.e., z_{ta} ~ 0.7) shows the most model dependent feature and it should be a suitable object for testing DE models. Also as Omo increases, the model dependence of the observed quantities decreases. The error in the approximate solutions is at most 2% for a wide range of the parameter space. Even though the analytic forms of y and \zeta are obtained for the constant w, they can be generalized to the slowly varying w. Thus, these analytic forms of the scale factor, y, and zeta provide a very accurate and useful tool for measuring the properties of DE., Comment: 16 pages, 10 figures, 2 tables, Correct typos. Modify frames of figures

We investigate the effects of the nonminimal coupling between the scalar field dark energy (quintessence) and the dark matter on the two- point correlation function. It is well known that this coupling shifts the turnover scale as well as suppresses the amplitude of the matter power spectrum. However, these effects are too small to be observed when we limit the coupling strength to be consistent with observations. Since the coupling of quintessence to baryons is strongly constrained, species dependent coupling may arise. This results in a baryon bias that is dif- ferent from unity. Thus, we look over the correlation function in this coupled model. We find that even the non-coupled quintessence model gives the better fit to the correlation function compared to the cosmo- logical constant model. We are also able to observe the enhancement of the baryon acoustic oscillation (BAO) peak due to the increasing bias factor of baryon from this species dependent coupling. In order to avoid the damping effect of the BAO signature in the matter power spectrum due to nonlinear clustering, we consider the coupling effect on the BAO bump in the linear regime. This provides an alternative method to constrain the coupling of dark energy to dark matter., Comment: 10 pages, 5 figures, To match the version accepted by Physical Review D Rapid Communication

We investigate the modified gravity theories in terms of the effective dark energy models. We compare the cosmic expansion history and the linear growth in different models. We also study the evolution of linear cosmological perturbations in modified theories of gravity assuming the Palatini formalism. We find the stability of the superhorizon metric evolution depends on models. We also study the matter density fluctuation in the general gauge and show the differential equations in super and sub-horizon scales., Comment: 10 pages, CosPA 2007 Proceeding will be published in the Mod. Phys. Lett. A

We discuss the ratio of the angular diameter distances from the source to the lens, $D_{ds}$, and to the observer at present, $D_{s}$, for various dark energy models. It is well known that the difference of $D_s$s between the models is apparent and this quantity is used for the analysis of Type Ia supernovae. However we investigate the difference between the ratio of the angular diameter distances for a cosmological constant, $(D_{ds}/D_{s})^{\Lambda}$ and that for other dark energy models, $(D_{ds}/D_{s})^{\rm{other}}$ in this paper. It has been known that there is lens model degeneracy in using strong gravitational lensing. Thus, we investigate the model independent observable quantity, Einstein radius ($\theta_E$), which is proportional to both $D_{ds}/D_s$ and velocity dispersion squared, $\sigma_v^2$. $D_{ds}/D_s$ values depend on the parameters of each dark energy model individually. However, $(D_{ds}/D_s)^{\Lambda} - (D_{ds}/D_{s})^{\rm{other}}$ for the various dark energy models, is well within the error of $\sigma_v$ for most of the parameter spaces of the dark energy models. Thus, a single strong gravitational lensing by use of the Einstein radius may not be a proper method to investigate the property of dark energy. However, better understanding to the mass profile of clusters in the future or other methods related to arc statistics rather than the distances may be used for constraints on dark energy., Comment: 15 pages, 13 figures, Accepted in PRD

We revise the stability of the tracking solutions and briefly review the potentials of quintessence models. We discuss the evolution of linear perturbations for $V(\phi) = V_{0} \exp(\lambda \phi^2/2)$ potential in which the scalar field is non-minimally coupled to cold dark matter. We consider the effects of this coupling on both cosmic microwave background temperature anisotropies and matter perturbations. We find that the phenomenology of this model is consistent with current observations up to the coupling power $n_{c} \leq 0.01$ while adopting the current parameters measured by WMAP, $\Omega_{\phi}^{(0)}=0.76$, $\Omega_{cdm}^{(0)}=0.191$, $\Omega_{b}^{(0)}=0.049$, and $h=0.70$. Upcoming cosmic microwave background observations continuing to focus on resolving the higher peaks may put strong constraints on the strength of the coupling., Comment: 10 pages, 3 figures, the ICGA7 conference proceedings published by World Scientific

We discuss the evolution of linear perturbations in a quintessence model in which the scalar field is non-minimally coupled to cold dark matter. We consider the effects of this coupling on both cosmic microwave background temperature anisotropies and matter perturbations. Due to the modification of the scale of cold dark matter as $\rho_{c} = \rho_{c}^{(0)} a^{-3 + \xi}$, we can shift the turnover in the matter power spectrum even without changing the present energy densities of matter and radiation. This can be used to constrain the strength of the coupling. We find that the phenomenology of this model is consistent with current observations up to the coupling power $n_{c} \leq 0.01$ while adopting the current parameters measured by WMAP. Upcoming cosmic microwave background observations continuing to focus on resolving the higher peaks may put strong constraints on the strength of the coupling., Comment: 23 pages, 7 figures

We present the full set of power spectra of cosmic microwave background (CMB) temperature and polarization anisotropies due to the coupling between quintessence and pseudoscalar of electromagnetism. This coupling induces the rotation of the polarization plane of CMB photons, thus resulting in non-vanishing B mode and parity-violating TB and EB modes. Using the 2003 flight of BOOMERANG (B03) data, we give the most stringent constraint on the coupling strength. In some cases, the rotation-induced B mode can confuse the hunting for the gravitational lensing induced B mode., Comment: 9 pages, 5 eps figures. references updated, version accepted by PRL

We introduce a simple parametrization of the dark energy equation of state, \omega, which is motivated from theory and recent experimental data. The theory is related to the tracker solution to alleviate the fine tuning problem. Recent experimental data indicates that the present value of \omega is close to -1. We analyze the evolution of \omega from the separation of CMB peaks and the time variation of the fine structure constant, \alpha. We find that -1.00 \leq \omega^{(0)} \leq -0.971_{-0.027}^{+0.017} and 1.76_{-0.42}^{+0.29} \times 10^{-4} \leq (d \omega / dz)_{z=0} \leq 0.041_{-0.037}^{+0.016} at 95% confidence level (CL)., Comment: 17pages, 14figures

The cosmological evolution of a quintessence-like scalar field, phi, coupled to matter and gauge fields leads to effective modifications of the coupling constants and particle masses over time. We analyze a class of models where the scalar field potential V(phi) and the couplings to matter B(phi) admit common extremum in phi, as in the Damour-Polyakov ansatz. We find that even for the simplest choices of potentials and B(phi), the observational constraints on delta alpha/alpha coming from quasar absorption spectra, the Oklo phenomenon and Big Bang nucleosynthesis provide complementary constraints on the parameters of the model. We show the evolutionary history of these models in some detail and describe the effects of a varying mass for dark matter., Comment: 26 pages, 20 eps figures

We derive two classes of brane-world solutions arising in the presence of a bulk scalar field. For static field configurations, we adopt a time-dependent, factorizable metric ansatz that allows for radion stabilization. The solutions are characterized by a non-trivial warping along the extra dimension, even in the case of a vanishing bulk cosmological constant, and lead to a variety of inflationary, time-dependent solutions of the 3D scale factor on the brane. We also derive the constraints necessary for the stability of these solutions under time-dependent perturbations of the radion field, and we demonstrate the existence of phenomenologically interesting, stable solutions with a positive cosmological constant on the brane., Comment: 24 pages, latex, 4 eps figure