Search

Detecting or placing upper limits on spacetime variations of fundamental constants requires quantifying every potential source of uncertainty. We continue our previous study into the impact of continuum variations on measurements of the fine structure constant, here in the context of quasar absorption systems. An automated (hence objective and reproducible) continuum modelling method is reported in an accompanying paper. We apply the method to the $z_{abs}=1.7975$ absorption system towards the quasar PHL957. Multiple continuum fits are generated, and for each, we derive independent models of the system, each giving its own measurement of the fine structure constant $\alpha$. This process isolates and quantifies the error contribution associated with continuum placement uncertainty. This source of uncertainty, ignored in many previous measurements, arises in two ways: (i) slight local continuum tilt uncertainty generates small line shifts, and (ii) different continuum estimates produce slightly different kinematic structures in the absorption system model. Taking continuum placement uncertainty into account, the new PHL957 measurement we obtain is $\Delta\alpha/\alpha= -0.53^{+5.45}_{-5.51} \times 10^{-6}$. This measurement assumes terrestrial magnesium isotopic abundances. Recommendations are provided for future $\alpha$ measurements. Finally, we also note the potential importance of the effects identified here for future redshift drift experiments., Comment: 10 pages, 3 figures. Submitted to Open Journal of Astrophysics

Searches for variations of fundamental constants require a comprehensive understanding of measurement errors. This paper examines a source of error that is usually overlooked: the impact of continuum placement error. We investigate the problem using a high resolution, high signal to noise spectrum of the white dwarf G191$-$B2B. Narrow photospheric absorption lines allow us to search for new physics in the presence of a gravitational field approximately $10^4$ times that on Earth. Modelling photospheric lines requires knowing the underlying spectral continuum level. We describe the development of a fully automated, objective, and reproducible continuum estimation method. Measurements of the fine structure constant are produced using several continuum models. The results show that continuum placement variations result in small systematic shifts in the centroids of narrow photospheric absorption lines which impact significantly on fine structure constant measurements. This effect should therefore be included in the error budgets of future measurements. Our results suggest that continuum placement variations should be investigated in other contexts, including fine structure constant measurements in stars other than white dwarfs. The analysis presented here is based on NiV absorption lines in the photosphere of G191$-$B2B. Curiously, the inferred measurement of the fine structure constant obtained in this paper using NiV (the least negative of our measurements is $\Delta\alpha/\alpha = -1.462 \pm 1.121 \times 10^{-5}$) is inconsistent with the most recent previous G191$-$B2B photospheric measurement using FeV ($\Delta\alpha/\alpha = 6.36 \pm 0.35_{stat} \pm 1.84_{sys} \times 10^{-5}$). Given both measurements are derived from the same spectrum, we presume (but in this work are unable to check) that this 3.2$\sigma$ difference results from unknown laboratory wavelength systematics., Comment: Main paper comprises 11 pages, 4 figures, 1 table. 41 pages in total including appendices. Submitted to Open Journal of Astrophysics. arXiv admin note: substantial text overlap with arXiv:2212.00434

Chemical evolution models predict a gradual build-up of $^{13}$C in the universe, based on empirical nuclear reaction rates and assumptions on the properties of stellar populations. However, old metal-poor stars within the Galaxy contain more $^{13}$C than is predicted, suggesting that further refinements to the models are necessary. Gas at high redshift provides important supplementary information at metallicities $-2\lesssim$ [Fe/H] $\lesssim-1$, for which there are only a few measurements in the Galaxy. We obtained new, high-quality, VLT/ESPRESSO observations of the QSO B1331+170 and used them to measure $^{12}$C/$^{13}$C in the damped Lyman-$\alpha$ system (DLA) at $z_{abs}=1.776$, with [Fe/H]=-1.27. AI-VPFIT, an Artificial Intelligence tool based on genetic algorithms and guided by a spectroscopic information criterion, was used to explore different possible kinematic structures of the carbon gas. Three hundred independent AI-VPFIT models of the absorption system were produced using pre-set $^{12}$C/$^{13}$C values, ranging from 4 to 500. Our results show that $^{12}$C/$^{13}$C$=28.5^{+51.5}_{-10.4}$, suggesting a possibility of $^{13}$C production at low metallicity., Comment: 11 pages, 6 figures. Three appendices. To appear in MNRAS

Searches for spacetime variations of fundamental constants have entered an era of unprecedented precision. New, high quality quasar spectra require increasingly refined analytic methods. In this article, a continuation in a series to establish robust and unbiased methodologies, we explore how convergence criteria in non-linear least squares optimisation impact on quasar absorption system measurements of the fine structure constant alpha. Given previous claims for high-precision constraints, we critically examine the veracity of a so-called ``blinding'' approach, in which alpha is fixed at the terrestrial value during the model building process, releasing it as a free parameter only after the ``final'' absorption system kinematic structure has been obtained. We show that this approach results in an extended flat canyon in chi squared-alpha space, such that convergence is unlikely to be reached, even after as many as 1000 iterations. The fix is straightforward: alpha must be treated as a free parameter from the earliest possible stages of absorption system model building. The implication of the results presented here is that all previous measurements that have used initially-fixed alpha should be reworked., Comment: 10 pages, 13 figures. Submitted for publication

We report unbiased AI measurements of the fine structure constant alpha in two proximate absorption regions in the spectrum of the quasar HE0515-4414. The data are high resolution, high signal to noise, and laser frequency comb calibrated, obtained using the ESPRESSO spectrograph on the VLT. The high quality of the data and proximity of the regions motivate a differential comparison, exploring the possibility of spatial variations of fundamental constants, as predicted in some theories. We show that if the magnesium isotopic relative abundances are terrestrial, the fine structure constants in these two systems differ at the 7-sigma level. A 3-sigma discrepancy between the two measurements persists even for the extreme non-terrestrial case of 100% ^{24}Mg, if shared by both systems. However, if Mg isotopic abundances take independent values in these two proximate systems, one terrestrial, the other with no heavy isotopes, both can be reconciled with a terrestrial alpha, and the discrepancy between the two measurements falls to 2-sigma. We discuss varying constant and varying isotope interpretations and resolutions to this conundrum for future high precision measurements., Comment: 6 pages, 3 figures

This article reviews the two major recent developments that significantly improved cosmological measurements of fundamental constants derived from high resolution quasar spectroscopy. The first one is the deployment of astronomical Laser Frequency Combs on high resolution spectrographs and the second one is the development of spectral analysis tools based on Artificial Intelligence methods. The former all but eliminated the previously dominant source of instrumental uncertainty whereas the latter established optimal methods for measuring the fine structure constant ($\alpha$) in quasar absorption systems. The methods can be used on data collected by the new ESPRESSO spectrograph and the future ANDES spectrograph on the Extremely Large Telescope to produce unbiased $\Delta\alpha/\alpha$ measurements with unprecedented precision., Comment: 10 pages, part of the HACK100 conference proceedings

Searches for variations of fundamental constants require accurate measurement errors. There are several potential sources of errors and quantifying each one accurately is essential. This paper addresses one source of uncertainty relating to measuring the fine structure constant on white dwarf surfaces. Detailed modelling of photospheric absorption lines requires knowing the underlying spectral continuum level. Here we describe the development of a fully automated, objective, and reproducible continuum estimation method, based on fitting cubic splines to carefully selected data regions. Example fits to the Hubble Space Telescope spectrum of the white dwarf G191-B2B are given. We carry out measurements of the fine structure constant using two continuum models. The results show that continuum placement variations result in small systematic shifts in the centroids of narrow photospheric absorption lines which impact significantly on fine structure constant measurements. This effect must therefore be included in the overall error budget of future measurements. Our results also suggest that continuum placement variations should be investigated in other contexts, including fine structure constant measurements in stars other than white dwarfs, quasar absorption line measurements of the fine structure constant, and quasar measurements of cosmological redshift drift., Comment: 10 pages, 4 figures. 4 additional files provided as supplementary material. Submitted to MNRAS 1 Dec 2022

The high resolution spectrograph ESPRESSO on the VLT allows measurements of fundamental constants at unprecedented precision and hence enables tests for spacetime variations predicted by some theories. In a series of recent papers, we developed optimal analysis procedures that both exposes and eliminates the subjectivity and bias in previous quasar absorption system measurements. In this paper we analyse the ESPRESSO spectrum of the absorption system at z_{abs}=1.15 towards the quasar HE0515-4414. Our goal here is not to provide a new unbiased measurement of fine structure constant, alpha, in this system (that will be done separately). Rather, it is to carefully examine the impact of blinding procedures applied in the recent analysis of the same data by Murphy (2022) and prior to that, in several other analyses. To do this we use supercomputer Monte Carlo AI calculations to generate a large number of independently constructed models of the absorption complex. Each model is obtained using AI-VPFIT, with alpha fixed until a "final" model is obtained, at which point alpha is then released as a free parameter for one final optimisation. The results show that the "measured" value of alpha is systematically biased towards the initially-fixed value i.e. this process produces meaningless measurements. The implication is straightforward: to avoid bias, all future measurements must include alpha as a free parameter from the beginning of the modelling process., Comment: 17 pages, 7 figures, and 5 tables. Submitted to MNRAS 1 Dec 2022

In this paper we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant $H_0$, the $\sigma_8$--$S_8$ tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the $5.0\,\sigma$ tension between the {\it Planck} CMB estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the {\it Planck} CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density $\Omega_m$, and the amplitude or rate of the growth of structure ($\sigma_8,f\sigma_8$). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the $H_0$--$S_8$ tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals.[Abridged], Comment: Contribution to Snowmass 2021. 224 pages, 27 figures. Accepted for publication in JHEAp

Recent advances in spectroscopic instrumentation and calibration methods dramatically improve the quality of quasar spectra. Supercomputer calculations show that, at high spectral resolution, procedures used in some previous analyses of spacetime variations of fundamental constants are likely to generate spurious measurements, biased systematically towards a null result. Developments in analysis methods are also summarised and a prescription given for the analysis of new and forthcoming data., Comment: 17 pages, 6 figures, accepted for publication in "The Universe". Contribution for the AlteCosmoFun'21 conference volume, 6-10 September 2022, Szczecin, Poland

The parent paper to this Addendum describes the optimisation theory on which VPFIT, a non-linear least-squares program for modelling absorption spectra, is based. In that paper, we show that Voigt function derivatives can be calculated analytically using Taylor series expansions and look-up tables, for the specific case of one column density parameter for each absorption component. However, in many situations, modelling requires more complex parameterisation, such as summed column densities over a whole absorption complex, or common pattern relative ion abundances. This Addendum provides those analytic derivatives., Comment: 4 pages, 2 figures. Submitted to MNRAS 23 Dec 2021, accepted 24 Dec 2021

This paper describes the optimisation theory on which VPFIT, a non-linear least-squares program for modelling absorption spectra, is based. Particular attention is paid to precision. Voigt function derivatives have previously been calculated using numerical finite difference approximations. We show how these can instead be computed analytically using Taylor series expansions and look-up tables. We introduce a new optimisation method for an efficient descent path to the best-fit, combining the principles used in both the Gauss-Newton and Levenberg-Marquardt algorithms. A simple practical fix for ill-conditioning is described, a common problem when modelling quasar absorption systems. We also summarise how unbiased modelling depends on using an appropriate information criterion to guard against over- or under-fitting. The methods and the new implementations introduced in this paper are aimed at optimal usage of future data from facilities such as ESPRESSO/VLT and HIRES/ELT, particularly for the most demanding applications such as searches for spacetime variations in fundamental constants and attempts to detect cosmological redshift drift., Comment: 15 pages, 7 figures, to appear in MNRAS

Modifications were made to the Sloan Digital Sky Survey's Baryonic Oscillations Spectroscopic Survey (SDSS/BOSS) optical fibres assigned to quasar targets in order to improve the signal-to-noise ratio in the Lyman-alpha forest. However, the penalty for these modifications is that quasars observed in this way require additional flux correction procedures in order to recover the correct spectral shapes. In this paper we describe such a procedure, based on the geometry of the problem and other observational parameters. Applying several correction methods to four SDSS quasars with multiple observations permits a detailed check on the relative performances of the different flux correction procedures. We contrast our method (which takes into account a wavelength dependent seeing profile) with the BOSS pipeline approach (which does not). Our results provide independent confirmation that the geometric approach employed in the SDSS pipeline works well, although with room for improvement. By separating the contributions from four effects we are able to quantify their relative importance. Most importantly, we demonstrate that wavelength dependence has a significant impact on the derived spectral shapes and thus should not be ignored., Comment: 24 pages, 17 figures, submitted to A&A

High resolution spectra of quasar absorption systems provide the best constraints on temporal or spatial changes of fundamental constants in the early universe. An important systematic that has never before been quantified concerns model non-uniqueness. The absorption structure is generally complicated, comprising many blended lines. This characteristic means any given system can be fitted equally well by many slightly different models, each having a different value of \alpha, the fine structure constant. We use AI Monte Carlo modelling to quantify non-uniqueness. Extensive supercomputer calculations are reported, revealing new systematic effects that guide future analyses: (i) Whilst higher signal to noise and improved spectral resolution produces a smaller statistical uncertainty for \alpha, model non-uniqueness adds a significant additional uncertainty. (ii) Non-uniqueness depends on the line broadening mechanism used. We show that modelling the spectral data using turbulent line broadening results in far greater non-uniqueness, hence this should no longer be done. Instead, for varying \alpha studies, it is important to use the more physically appropriate compound broadening. (iii) We have studied two absorption systems in detail. Generalising thus requires caution. Nevertheless, if non-uniqueness is present in all or most quasar absorption systems, it seems unavoidable that attempts to determine the existence (or non-existence) of spacetime variations of fundamental constants is best approached using a statistical sample., Comment: 17 pages, 11 figures

Robust model-fitting to spectroscopic transitions is a requirement across many fields of science. The corrected Akaike and Bayesian information criteria (AICc and BIC) are most frequently used to select the optimal number of fitting parameters. In general, AICc modelling is thought to overfit (too many model parameters) and BIC underfits. For spectroscopic modelling, both AICc and BIC lack in two important respects: (a) no penalty distinction is made according to line strength such that parameters of weak lines close to the detection threshold are treated with equal importance as strong lines and (b) no account is taken of the way in which spectral lines impact on narrow data regions. In this paper we introduce a new information criterion that addresses these shortcomings, the "Spectral Information Criterion" (SpIC). Spectral simulations are used to compare performances. The main findings are (i) SpIC clearly outperforms AICc for high signal to noise data, (ii) SpIC and AICc work equally well for lower signal to noise data, although SpIC achieves this with fewer parameters, and (iii) BIC does not perform well (for this application) and should be avoided. The new method should be of broader applicability (beyond spectroscopy), wherever different model parameters influence separated small ranges within a larger dataset and/or have widely varying sensitivities., Comment: 13 pages, 7 figures

New observations of the quasar HE0515$-$4414 have been made using the HARPS spectrograph on the ESO 3.6m telescope, aided by the Laser Frequency Comb (LFC). We present three important advances for $\alpha$ measurements in quasar absorption spectra from these observations. Firstly, the data have been wavelength calibrated using LFC and ThAr methods. The LFC wavelength calibration residuals are six times smaller than when using the standard ThAr calibration. We give a direct comparison between $\alpha$ measurements made using the two methods. Secondly, spectral modelling was performed using Artificial Intelligence (fully automated, all human bias eliminated), including a temperature parameter for each absorption component. Thirdly, in contrast to previous work, additional model parameters were assigned to measure $\alpha$ for each individual absorption component. The increase in statistical uncertainty from the larger number of model parameters is small and the method allows a substantial advantage; outliers that would otherwise contribute a significant systematic, possibly corrupting the entire measurement, are identified and removed, permitting a more robust overall result. The $z_{abs} = 1.15$ absorption system along the HE0515$-$4414 sightline yields 40 new $\alpha$ measurements. We constrain spatial fluctuations in $\alpha$ to be $\Delta\alpha/\alpha \leq 9 \times 10^{-5}$ on scales $\approx 20\;{\rm km\,s}^{-1}$, corresponding to $\approx25\;$kpc if the $z_{abs} = 1.15$ system arises in a $1\;$Mpc cluster. Collectively, the 40 measurements yield $\Delta\alpha/\alpha=-0.27\pm2.41\times10^{-6}$, consistent with no variation., Comment: Published in MNRAS, 500 1 1. 10 pages, 7 figures. Online supplementary material is available upon request

Exploring the possibility that fundamental constants of Nature might vary temporally or spatially constitutes one of the key science drivers for the European Southern Observatory's ESPRESSO spectrograph on the VLT and for the HIRES spectrograph on the ELT. High-resolution spectra of quasar absorption systems permit accurate measurements of fundamental constants out to high redshifts. The quality of new data demands completely objective and reproducible methods. We have developed a new fully automated Artificial Intelligence-based method capable of deriving optimal models of even the most complex absorption systems known. The AI structure is built around VPFIT, a well-developed and extensively-tested non-linear least-squares code. The new method forms a sophisticated parallelised system, eliminating human decision-making and hence bias. Here we describe the workings of such a system and apply it to synthetic spectra, in doing so establishing methods of importance for future analyses of VLT and ELT data. The results show that modelling line broadening for high-redshift absorption components should include both thermal and turbulent components. Failing to do so means it is easy to derive the wrong model and hence incorrect parameter estimates. We also argue that model non-uniqueness can be significant, such that it is not feasible to expect to derive an unambiguous estimate of the fine structure constant alpha from one or a small number of measurements. No matter how optimal the modelling method, it is a fundamental requirement to use a large sample of measurements to meaningfully constrain temporal or spatial alpha variation., Comment: Accepted by MNRAS, 1 April 2021

Observations of the redshift z=7.085 quasar J1120+0641 have been used to search for variations of the fine structure constant, alpha, over the redshift range 5.5 to 7.1. Observations at z=7.1 probe the physics of the universe when it was only 0.8 billion years old. These are the most distant direct measurements of alpha to date and the first measurements made with a near-IR spectrograph. A new AI analysis method has been employed. Four measurements from the X-SHOOTER spectrograph on the European Southern Observatory's Very Large Telescope (VLT) directly constrain any changes in alpha relative to the value measured on Earth (alpha_0). The weighted mean strength of the electromagnetic force over this redshift range in this location in the universe is da/a = (alpha_z - alpha_0)/alpha_0 = (-2.18 +/- 7.27) X 10^{-5}, i.e. we find no evidence for a temporal change from the 4 new very high redshift measurements. When the 4 new measurements are combined with a large existing sample of lower redshift measurements, a new limit on possible spatial variation of da/a is marginally preferred over a no-variation model at the 3.7 sigma level., Comment: Accepted for publication in Science Advances

We study a special running vacuum model (RVM) with $\Lambda = 3 \alpha H^2+3\beta H_0^4 H^{-2}+\Lambda_0$, where $\alpha$, $\beta$ and $\Lambda_0$ are the model parameters and $H$ is the Hubble one. This RVM has non-analytic background solutions for the energy densities of matter and radiation, which can only be evaluated numerically. From the analysis of the CMB power spectrum and baryon acoustic oscillation along with the prior of $\alpha>0$ to avoid having a negative dark energy density, we find that $\alpha<2.83\times 10^{-4}$ and $\beta=(-0.2^{+3.9}_{-4.5})\times 10^{-4}$ (95$\%$ C.L.). We show that the RVM fits the cosmological data comparably to the $\Lambda$CDM. In addition, we relate the fluctuation amplitude $\sigma_8$ to the neutrino mass sum $\Sigma m_\nu$., Comment: 16 pages, 6 figures, accepted for publication in EPJC

We concentrate on the cosmological properties in the Tsujikawa model (TM) of viable $f(R)$ gravity with the dynamical background evolution and linear perturbation theory by using the CosmoMC package. We study the constraints of the cosmological variables along with the model parameter from the current observational data. In particular, we show that the matter density fluctuation is suppressed and the constraint of the neutrino mass sum is relaxed in the TM, which are similar to other viable $f(R)$ models. In addition, we discuss the parameters of the deceleration and equation of state for dark energy in the TM and compare them with those in the $\Lambda$CDM model., Comment: 15 pages, 8 figures, accepted publication in Physics of the Dark Universe

We study the matter power spectra in the viable $f(R)$ gravity models with the dynamical background evolution and linear perturbation theory by using the CosmoMC package. We show that these viable $f(R)$ models generally shorten the age of the universe and suppress the matter density fluctuation. We examine the allowed ranges of the model parameters and the constraints of the cosmological variables from the current observational data, and find that the dynamical evolution of $\rho_{DE}(z)$ plays an important role to constrain the neutrino masses., Comment: 16 pages, 4 figures, to be published at EPJC

We investigate the power spectra of the CMB temperature and matter density in the running vacuum model (RVM) with the time-dependent cosmological constant of $\Lambda = 3 \nu H^2 + \Lambda_0$, where $H$ is the Hubble parameter. In this model, dark energy decreases in time and decays to both matter and radiation. By using the Markov chain Monte Carlo method, we constrain the model parameter $\nu$ as well as the cosmological observables. Explicitly, we obtain $\nu \leq 1.54 \times 10^{-4}$ (68\% confidence level) in the RVM with the best-fit $\chi^2_{\mathrm{RVM}} = 13968.8$, which is slightly smaller than $\chi^2_{\Lambda \mathrm{CDM}} = 13969.8$ in the $\Lambda$CDM model of $\nu=0$., Comment: 13 pages, 3 figures, to be published in Chinese Physics C

We study quintessential inflation using a generalized exponential potential $V(\phi)\propto exp(-\lambda \phi^n/Mpl^n), n>1$, the model admits slow-roll inflation at early times and leads to close-to-scaling behaviour in the post inflationary era with an exit to dark energy at late times. We present detailed investigations of the inflationary stage in the light of the Planck 2015 results, study post-inflationary dynamics and analytically confirm the existence of an approximately scaling solution. Additionally, assuming that standard massive neutrinos are non-minimally coupled, makes the field $\phi$ dominant once again at late times giving rise to present accelerated expansion of the Universe. We derive observational constraints on the field and time-dependent neutrino masses. In particular, for $n=6 (8)$, the parameter $\lambda$ is constrained to be,$\log \lambda > -7.29 (-11.7)$; the model produces the spectral index of the power spectrum of primordial scalar (matter density) perturbations as $ n_s = 0.959 \pm 0.001 (0.961 \pm 0.001)$ and tiny tensor-to-scalar ratio, $r<1.72 \times 10^{-2} (2.32 \times 10^{-2})$ respectively. Consequently, the upper bound on possible values of the sum of neutrino masses $\Sigma m_{\nu} \lesssim 2.5$ eV significantly enhances compared to that in the standard $\Lambda$CDM model., Comment: 14 pages,2 tables and six figures.Minor changes in reference section, to appear in JCAP

We examine the running vacuum model with $\Lambda (H) = 3 \nu H^2 + \Lambda_0$, where $\nu$ is the model parameter and $\Lambda_0$ is the cosmological constant. From the data of the cosmic microwave background radiation, weak lensing and baryon acoustic oscillation along with the time dependent Hubble parameter $H(z)$ and weighted linear growth $f (z)\sigma_8(z)$ measurements, we find that $\nu=(1.37^{+0.72}_{-0.95})\times 10^{-4}$ with the best fitted $\chi^2$ value slightly smaller than that in the $\Lambda$CDM model., Comment: 15 pages, 1 figure, revised version accepted by JCAP

We discuss the linear perturbation equations with the synchronous gauge in a minimal scenario of the bimetric massive gravity theory. We find that the matter density perturbation and matter power spectrum are suppressed. We also examine the ghost and stability problems and show that the allowed deviation of this gravitational theory from the cosmological constant is constrained to be smaller than $\mathcal{O}(10^{-2})$ by the large scale structure observational data., Comment: 18 pages, 4 figures, revised version accepted by Annals of Physics

We investigate the matter density perturbation $\delta_m$ and power spectrum $P(k)$ in the running vacuum model (RVM) with the cosmological constant being a function of the Hubble parameter, given by $\Lambda = \Lambda_0 + 6 \sigma H H_0+ 3\nu H^2$, in which the linear and quadratic terms of $H$ would originate from the QCD vacuum condensation and cosmological renormalization group, respectively. Taking the dark energy perturbation into consideration, we derive the evolution equation for $\delta_m$ and find a specific scale $d_{cr}=2 \pi/k_{cr}$, which divides the evolution of the universe into the sub and super-interaction regimes, corresponding to $k \ll k_{cr}$ and $k \gg k_{cr}$, respectively. For the former, the evolution of $\delta_m$ has the same behavior as that in the $\Lambda$CDM model, while for the latter, the growth of $\delta_m$ is frozen (greatly enhanced) when $\nu + \sigma >(<)0$ due to the couplings between radiation, matter and dark energy. It is clear that the observational data rule out the cases with $\nu<0$ and $\nu + \sigma <0$, while the allowed window for the model parameters is extremely narrow with $\nu, |\sigma| \lesssim \mathcal{O}(10^{-7})$., Comment: 7 pages, 6 figures, revised version accepted for publication in MNRAS

We investigate the running cosmological constant model with dark energy linearly proportional to the Hubble parameter, $\Lambda = \sigma H + \Lambda_0$, in which the $\Lambda$CDM limit is recovered by taking $\sigma=0$. We derive the linear perturbation equations of gravity under the Friedmann-Lema\"itre-Robertson-Walker cosmology, and show the power spectra of the CMB temperature and matter density distribution. By using the Markov chain Monte Carlo method, we fit the model to the current observational data and find that $\sigma H_0/ \Lambda_0 \lesssim 2.63 \times 10^{-2}$ and $6.74 \times 10^{-2}$ for $\Lambda(t)$ coupled to matter and radiation-matter, respectively, along with constraints on other cosmological parameters., Comment: 12 pages, 5 figures, version accepted by PLB

In order to solve the fine-tuning problem of the cosmological constant, we propose a simple model with the vacuum energy non-minimally coupled to the inflaton field. In this model, the vacuum energy decays to the inflaton during pre-inflation and inflation eras, so that the cosmological constant effectively deflates from the Planck mass scale to a much smaller one after inflation and plays the role of dark energy in the late-time of the universe. We show that our deflationary scenario is applicable to arbitrary slow-roll inflation models. We also take two specific inflation potentials to illustrate our results., Comment: 12 pages, 5 figures, revised version accepted by JCAP

We investigate observational constraints on a specific one-parameter extension to the minimal quintessence model, where the quintessence field acquires a quadratic coupling to the scalar curvature through a coupling constant $\xi$. The value of $\xi$ is highly suppressed in typical tracker models if the late-time cosmic acceleration is driven at some field values near the Planck scale. We test $\xi$ in a second class of models in which the field value today becomes a free model parameter. We use the combined data from type-Ia supernovae, cosmic microwave background, baryon acoustic oscillations and matter power spectrum, to weak lensing measurements and find a best-fit value $\xi > 0.289$ where $\xi = 0$ is excluded outside the 95 per cent confidence region. The effective gravitational constant $G_{\rm eff}$ subject to the hint of a non-zero $\xi$ is constrained to $-0.003 < 1- G_{\rm eff}/G < 0.033$ at the same confidence level on cosmological scales, and can be narrowed down to $1- G_{\rm eff}/G < 2.2 \times 10^{-5}$ when combining with Solar System tests., Comment: Context extended, figures and references added, title changed to match with accepted version for publication

We investigate the observational constraints on the modified gravity, which combines the $R^{2-q}$ inflation with the power-law (exponential) type of the viable $f(R)$ dark energy models. We discuss the difference between the combined model and $R^{2-q}$ gravity in the inflationary epoch and obtain the constraints on the deviation power $q$ as well as the parameters in $f(R)$ by using the CosmoMC package. The allowed ranges of the spectral index and tensor-to-scalar ratio from the Planck data are highly restricted, resulting in $q < 2.66 \times 10^{-2}$ and $2.17 \times 10^{-2}$ for the power-law and exponential types of $f(R)$ gravity, respectively., Comment: 9 pages, 6 figures, revised version accepted for publication in Astrophysics and Space Science

We consider generic models of quintessence and we investigate the influence of massive neutrino matter with field-dependent masses on the matter power spectrum. In case of minimally coupled neutrino matter, we examine the effect in tracker models with inverse power-law and double exponential potentials. We present detailed investigations for the scaling field with a steep exponential potential, non-minimally coupled to massive neutrino matter, and we derive constraints on field-dependent neutrino masses from the observational data., Comment: 20 pages, 7 figures, revised version accepted by JCAP

We investigate the matter power spectra in the power law and exponential types of viable $f(R)$ theories along with massive neutrinos. The enhancement of the matter power spectrum is found to be a generic feature in these models. In particular, we show that in the former type, such as the Starobinsky model, the spectrum is magnified much larger than the latter one, such as the exponential model. A greater scale of the total neutrino mass, $\Sigma m_{\nu}$, is allowed in the viable $f(R)$ models than that in the $\Lambda$CDM one. We obtain the constraints on the neutrino masses by using the CosmoMC package with the modified MGCAMB. Explicitly, we get $\Sigma m_{\nu} < 0.451 \ (0.214)\ \mathrm{eV}$ at 95% C.L. in the Starobinsky (exponential) model, while the corresponding one for the $\Lambda$CDM model is $\Sigma m_{\nu} < 0.200\ \mathrm{eV}$. Furthermore, by treating the effective number of neutrino species $N_{\mathrm{eff}}$ as a free parameter along with $\Sigma m_{\nu}$, we find that $N_{\mathrm{eff}} = 3.78^{+0.64}_{-0.84} (3.47^{+0.74}_{-0.60})$ and $\Sigma m_{\nu} = 0.533^{+0.254}_{-0.411}$ ($< 0.386) \ \mathrm{eV}$ at 95% C.L. in the Starobinsky (exponential) model., Comment: 15 pages, 5 figures, updated version accepted by PLB

We investigate the viable exponential $f(R)$ gravity in the metric formalism with $f(R)=-\beta R_s (1-e^{-R/R_s})$. The latest sample of the Hubble parameter measurements with 23 data points is used to place bounds on this $f(R)$ model. A joint analysis is also performed with the luminosity distances of Type Ia supernovae and baryon acoustic oscillations in the clustering of galaxies, and the shift parameters from the cosmic microwave background measurements, which leads to $0.240<\Omega_m^0<0.296$ and $\beta>1.47$ at 1$\sigma$ confidence level. The evolutions of the deceleration parameter $q(z)$ and the effective equations of state $\omega_{de}^{eff}(z)$ and $\omega_{tot}^{eff}(z)$ are displayed. By taking the best-fit parameters as prior values, we work out the transition redshift (deceleration/acceleration) $z_T$ to be about 0.77. It turns out that the recent observations are still unable to distinguish the background dynamics in the $\Lambda$CDM and exponential $f(R)$ models., Comment: 19 pages, 4 figures, revised version accepted by PRD

We study future singularity in teleparallel dark energy models, particularly its behavior and its (non)occurrence in the observationally viable models. For the models with a general self-potential of the scalar field, we point out that both at early times and in the future near the singularity the behavior of dark energy can be described by the analytic solutions of the scalar field we obtained for the model with no self-potential. As to the (non)occurrence in the viable models, we consider a natural binding-type self-potential, the quadratic potential, when fitting observational data, and illustrate the constraining region up to the $3\sigma$ confidence level as well as the region where a singularity will occur. As a result, the singularity region is outside the $3\sigma$ constraint. Thus, although the future singularity problem potentially exists in teleparallel dark energy models, the observationally viable models may not suffer this problem., Comment: 12 pages, 6 figures, revised version accepted by PRD

We analyze the stability of the Einstein static closed and open universe in two types of exponential $f(T)$ gravity theories. We show that the stable solutions exist in these two models. In particular, we find that large regions of parameter space in equation of state $w=p/\rho$ for the stable universe are allowed in the $f(T)$ theories., Comment: 11 pages, 4 figures, published version with references updated

We study the cosmological effect of the simple scalar-torsion ($0^+$) mode in Poincar\'{e} gauge theory of gravity. We find that for the non-constant (affine) curvature case, the early evolution of the torsion density $\rho_T$ has a radiation-like asymptotic behavior of $a^{-4}$ with $a$ representing the scale factor, along with the stable point of the torsion pressure ($P_T$) and density ratio $P_T/\rho_T\rightarrow 1/3$ in the high redshift regime $(z \gg 0)$, which is different from the previous result in the literature. We use the Laurent expansion to resolve the solution. We also illustrate our result by the execution of numerical computations., Comment: 9 pages, 2 figures, accepted by PRD

We investigate the equation of state (EoS) of the scalar-torsion mode in Poincar\'{e} gauge theory of gravity. We concentrate on two cases with the constant curvature solution and positive kinetic energy, respectively. In the former, we find that the torsion EoS has different values in the various stages of the universe. In particular, it behaves like the radiation (matter) EoS of $w_r=1/3$ ($w_m=0$) in the radiation (matter) dominant epoch, while in the late time the torsion density is supportive for the accelerating universe. In the latter, our numerical analysis shows that in general the EoS has an asymptotic behavior in the high redshift regime, while it could cross the phantom divide line in the low redshift regime., Comment: 12 pages, 2 figures, title changed, revised version accepted for publication in JCAP

We propose the simplest model of teleparallel dark energy with purely a non-minimal coupling to gravity but no self-potential, a single model possessing various interesting features: simplicity, self-potential-free, the guaranteed late-time cosmic acceleration driven by the non-minimal coupling to gravity, tracker behavior of the dark energy equation of state at earlier times, a crossing of the phantom divide at a late time, and the existence of a finite-time future singularity. We find the analytic solutions of the dark-energy scalar field respectively in the radiation, matter, and dark energy dominated eras, thereby revealing the above features. We further illustrate possible cosmic evolution patterns and present the observational constraint of this model obtained by numerical analysis and data fitting., Comment: 12 pages, 3 figures, Title changed, Revised Version Accepted for publication in Phys. Lett. B

The curvature singularity in viable f(R) gravity models is examined when the background density is dense. This singularity could be eliminated by adding the $R^{2}$ term in the Lagrangian. Some of cosmological consequences, in particular the source for the scalar mode of gravitational waves, are discussed., Comment: 17 pages, 7 figures, version accepted by Progress of Theoretical Physics

We use data from Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO), and Cosmic Microwave Background (CMB) observations to constrain the recently proposed teleparallel dark energy scenario based on the teleparallel equivalent of General Relativity, in which one adds a canonical scalar field, allowing also for a nonminimal coupling with gravity. Using the power-law, the exponential and the inverse hyperbolic cosine potential ansatzes, we show that the scenario is compatible with observations. In particular, the data favor a nonminimal coupling, and although the scalar field is canonical the model can describe both the quintessence and phantom regimes., Comment: 19 pages, 6 figures, version accepted by JCAP

Using the "teleparallel" equivalent of General Relativity as the gravitational sector, which is based on torsion instead of curvature, we add a canonical scalar field, allowing for a nonminimal coupling with gravity. Although the minimal case is completely equivalent to standard quintessence, the nonminimal scenario has a richer structure, exhibiting quintessence-like or phantom-like behavior, or experiencing the phantom-divide crossing. The richer structure is manifested in the absence of a conformal transformation to an equivalent minimally-coupled model., Comment: 5 pages, 1 figure, Version published in PLB704 (2011) 384-387

We review the equation of state for dark energy in modified gravity theories. In particular, we summarize the generic feature of the phantom divide crossing in the past and future in viable $f(R)$ gravity models., Comment: 7 pages, 3 figures, talk presented at the 2nd International Workshop on Dark Matter, Dark Energy and Matter-Antimatter Asymmetry, Hsinchu, Taiwan, 5-6 Nov 2010