Type Ia Supernovae Data Research Articles

Testing dark energy beyond the cosmological constant barrier

Although well motivated from theoretical arguments, the cosmological constant barrier, i.e., the imposition that the equation-of-state parameter of dark energy $({\ensuremath{\omega}}_{x}\ensuremath{\equiv}{p}_{x}/{\ensuremath{\rho}}_{x})$ is $g~\ensuremath{-}1,$ seems to introduce bias in the parameter determination from statistical analyses of observational data. In this regard, phantom dark energy or superquintessence has been proposed in which the usual imposition $\ensuremath{\omega}g~\ensuremath{-}1$ is relaxed. Here, we study possible observational limits to the phantom behavior of the dark energy from recent distance estimates of galaxy clusters obtained from interferometric measurements of the Sunyaev-Zel'dovich effect and x-ray observations, type Ia supernova data, and cosmic microwave background measurements. We find that there is much acceptable parameter space beyond the $\ensuremath{\Lambda}$ barrier, which opens, from a purely observational point of view, the possibility of the existence of more exotic forms of energy in the Universe.

Particlelike description in quintessential cosmology

Assuming the equation of state for quintessential matter, $p=w(z)\ensuremath{\rho},$ we analyze the dynamical behavior of the scale factor in Friedmann-Robertson-Walker cosmologies. It is shown that its dynamics is formally equivalent to that of a classical particle under the action of a 1D potential $V(a).$ It is shown that the Hamiltonian method can be easily implemented to obtain a classification of all cosmological solutions in the phase space as well as in the configurational space. Examples taken from modern cosmology illustrate the effectiveness of the approach presented. The advantages of representing dynamics as a 1D Hamiltonian flow, in the analysis of acceleration and standard cosmological problems, are presented. The distant supernovae type Ia data are used to reconstruct the expansion scenario. The inverse problem of reconstructing the Hamiltonian dynamics (i.e., potential function) from the luminosity distance function ${d}_{L}(z)$ for supernovae is also considered.

Cosmic acceleration and extra dimensions: constraints on modifications of the Friedmann equation

An alternative to dark energy as an explanation for the present phase of accelerated expansion of the Universe is that the Friedmann equation is modified, e.g. by extra dimensional gravity, on large scales. We explore a natural parametrization of a general modified Friedmann equation, and find that the present supernova Type Ia and cosmic microwave background data prefer a correction of the form 1/H to the Friedmann equation over a cosmological constant.

BAYESIAN ANALYSIS OF THE CHAPLYGIN GAS AND COSMOLOGICAL CONSTANT MODELS USING THE SNe Ia DATA

The type Ia supernovae observational data are used to estimate the parameters of a cosmological model with cold dark matter and the Chaplygin gas. This exotic gas, which is characterized by a negative pressure varying with the inverse of density, represents in this model the dark energy responsible for the acceleration of the Universe. The Chaplygin gas model depends essentially on four parameters: the Hubble constant, the velocity of the sound of the Chaplygin gas, the curvature of the Universe and the fraction density of the Chaplygin gas and the cold dark matter. The Bayesian parameter estimation yields [Formula: see text] and [Formula: see text]. These and other results indicate that a Universe completely dominated by the Chaplygin gas is favoured, what reinforces the idea that the Chaplygin gas may unify the description for dark matter and dark energy, at least as the type Ia supernovae data are concerned. A closed and accelerating Universe is also favoured. The Bayesian statistics indicates that the Chaplygin gas model is more likely than the standard cosmological constant (ΛCDM) model at 55.3% confidence level when an integration on all free parameters is performed. Assuming the spatially flat curvature, this percentage mounts to 65.3%. On the other hand, if the density of dark matter is fixed at zero value, the Chaplygin gas model becomes more preferred than the ΛCDM model at 91.8% confidence level. Finally, the hypothesis of flat Universe and baryonic matter (Ωb0=0.04) implies a Chaplygin gas model preferred over the ΛCDM at a confidence level of 99.4%.

Confronting the IR fixed point cosmology with high-redshift observations

We use high-redshift type Ia supernova and compact radio source data in order to test the infrared (IR) fixed point model of the late Universe which was proposed recently. It describes a cosmology with a time dependent cosmological constant and Newton constant whose dynamics arises from an underlying renormalization group flow near an IR-attractive fixed point. Without any fine-tuning or quintessence field it yields ΩM = ΩΛ = 1/2. Its characteristic t4/3-dependence of the scale factor leads to a distance–redshift relation whose predictions are compared both to the supernova and to the radio source data. According to the χ2 test, the fixed point model reproduces the data at least as well as the best-fit (Friedmann–Robertson–Walker) standard cosmology. Furthermore, we extend the original fixed point model by assuming that the fixed point epoch is preceded by an era with constant G and Λ. By means of a Monte Carlo simulation we show that the data expected from the forthcoming SNAP satellite mission could detect the transition to the fixed point regime provided it took place at a redshift of less than about 0.5.

Constraints on a Cardassian Model from Type Ia Supernova Data, Revisited

We discuss some observational constraints, resulting from Type Ia supernova (SN Ia) observations, imposed on the behavior of the original flat Cardassian model and on its extension with the curvature term included. We test the models using the Perlmutter SN Ia data, as well as the new Knop and Tonry samples. We estimate the Cardassian model parameters using the best-fit procedure and the likelihood method. In the fitting procedure we use density variables for matter, Cardassian fluid, and curvature and include the errors in redshift measurement. For the Perlmutter sample in the nonflat Cardassian model we obtain a high-density or normal (Ωm,0 ≈ 0.3) universe, while for the flat Cardassian model we have a high-density universe. For sample A in the high-density universe, we find negative values of estimates of n, which can be interpreted as a phantom fluid effect. For the likelihood method we find that a nearly flat universe is preferred. We show that if we assume that matter density is 0.3, then n ≈ 0 in the flat Cardassian model, which corresponds to the Perlmutter model with a cosmological constant. Tests with the Knop and Tonry SN Ia samples show no significant differences in results.

Future Type Ia Supernova Data as Tests of Dark Energy from Modified Friedmann Equations

In the Cardassian model, dark energy density arises from modifications to the Friedmann equation, which becomes $H^2 = g(\rhom)$, where $g(\rhom)$ is a new function of the energy density. The universe is flat, matter dominated, and accelerating. The distance redshift relation predictions of generalized Cardassian models can be very different from generic quintessence models, and can be differentiated with data from upcoming pencil beam surveys of Type Ia Supernovae such as SNAP. We have found the interesting result that, once $\Omega_m$ is known to 10% accuracy, SNAP will be able to determine the sign of the time dependence of the dark energy density. Knowledge of this sign (which is related to the weak energy condition) will provide a first discrimination between various cosmological models that fit the current observational data (cosmological constant, quintessence, Cardassian expansion). Further, we have performed Monte Carlo simulations to illustrate how well one can reproduce the form of the dark energy density with SNAP. To be concrete we study a class of two parameter ($n$,$q$) generalized Cardassian models that includes the original Cardassian model (parametrized by $n$ only) as a special case. Examples are given of MP Cardassian models that fit current supernovae and CMB data, and prospects for differentiating between MP Cardassian and other models in future data are discussed. We also note that some Cardassian models can satisfy the weak energy condition $w>-1$ even with a dark energy component that has an effective equation of state $w_X < -1$.

A Check on the Cardassian Expansion Model with Type-Ia Supernovae Data

We use the magnitude-redshift relation for the type Ia supernova data compiled by Riess et al. to analyze the Cardassian expansion scenario. This scenario assumes the universe to be flat, matter dominated, and accelerating, but contains no vacuum contribution. The best fitting model parameters are H0 = 65.3 ksm-1 Mpc-1, n = 0.35 and Ωm = 0.05. When the highest redshift supernova, SN 1997ck, is excluded, H0 remains the same, but n becomes 0.20 and Ωm, 0.15, and the matter density remains unreasonably low. Our result shows that this particular scenario is strongly disfavoured by the SNeIa data.

Observational constraints on general relativistic energy conditions, cosmic matter density and dark energy from X-ray clusters of galaxies and type-Ia supernovae

New observational constraints on the cosmic matter density Ωm and an effectively redshift-independent equation of state parameter wx of the dark energy are obtained while simultaneously testing the strong and null energy conditions of general relativity on macroscopic scales. The combination of REFLEX X-ray cluster and type-Ia supernova data shows that for a flat Universe the strong energy condition might presently be violated whereas the null energy condition seems to be fulfilled. This provides another observational argument for the present accelerated cosmic expansion and the absence of exotic physical phenomena related to a broken null energy condition. The marginalization of the likelihood distributions is performed in a manner to include a large fraction of the recently discussed possible systematic errors involved in the application of X-ray clusters as cosmological probes. This yields for a flat Universe, Ωm = 0.29 +0.08 −0.12 and wx = −0.95 +0.30 −0.35 (1σ errors without cosmic variance). The scatter in the different analyses indicates a quite robust result around wx = −1, leaving little room for the introduction of new energy components described by quintessence-like models or phantom energy. The most natural interpretation of the data is a positive cosmological constant with wx = −1 or something like it.

Cosmology with tachyon field as dark energy

We present a detailed study of cosmological effects of homogeneous tachyon matter coexisting with nonrelativistic matter and radiation, concentrating on the inverse square potential and the exponential potential for the tachyonic scalar field. A distinguishing feature of these models (compared to other cosmological models) is that the matter density parameter and the density parameter for tachyons remain comparable even in the matter dominated phase. For the exponential potential, the solutions have an accelerating phase, followed by a phase with $a(t)\ensuremath{\propto}{t}^{2/3}$ as $\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{\infty}.$ This eliminates the future event horizon present in cold dark matter models with a cosmological constant $(\ensuremath{\Lambda}\mathrm{CDM})$ and is an attractive feature from the string theory perspective. A comparison with supernova type Ia data shows that for both the potentials there exists a range of models in which the universe undergoes an accelerated expansion at low redshifts which are also consistent with the requirements of structure formation. They do require fine-tuning of parameters but not any more than in the case of $\ensuremath{\Lambda}\mathrm{CDM}$ models or quintessence models.

Constraints on Cardassian Expansion from Distant Type Ia Supernovae

The distant Type Ia supernovae data compiled by Perlmutter et al. are used to analyze the Cardassian expansion scenario, which was recently proposed by Freese & Lewis as an alternative to a cosmological constant (or more generally a dark energy component) in explaining the currently accelerating universe. We show that the allowed intervals for n and zeq, the two parameters of the Cardassian model, will give rise to a universe with a very low matter density, which can hardly be reconciled with the current value derived from the measurements of the cosmic microwave background anisotropy and galaxy clusters (cluster baryon fraction). As a result, this Cardassian expansion proposal does not seem to survive the magnitude-redshift test for the present Type Ia supernovae data, unless the universe contains primarily baryonic matter.

Cosmological Acceleration through Transition to Constant Scalar Curvature

As shown by Parker and Raval, quantum field theory in curved spacetime gives a possible mechanism for explaining the observed recent acceleration of the universe. This mechanism, which differs in its dynamics from quintessence models, causes the universe to make a transition to an accelerating expansion in which the scalar curvature, R, of spacetime remains constant. This transition occurs despite the fact that we set the renormalized cosmological constant to zero. We show that this model agrees very well with the current observed typeIa supernova (SNe-Ia) data. There are no free parameters in this fit, as the relevant observables are determined independently by means of the current cosmic microwave background radiation (CMBR) data. We also give the predicted curves for number count tests and for the ratio, w(z), of the dark energy pressure to its density, as well as for dw(z)/dz versus w(z). These curves differ significantly from those obtained from a cosmological constant, and will be tested by planned future observations.

Erratum: Vacuum effects of an ultralow mass particle account for the recent acceleration of the universe [Phys. Rev. D60, 123502 (1999)

In recent work, we showed that non-perturbative vacuum effects of a very low mass particle could induce, at a redshift of order 1, a transition from a matter-dominated to an accelerating universe. In that work, we used the simplification of a sudden transition out of the matter-dominated stage and were able to fit the Type Ia supernovae (SNe-Ia) data points with a spatially-open universe. In the present work, we find a more accurate, smooth {\it spatially-flat} analytic solution to the quantum-corrected Einstein equations. This solution gives a good fit to the SNe-Ia data with a particle mass parameter $m_h$ in the range $6.40 \times 10^{-33}$ eV to $7.25 \times 10^{-33}$ eV. It follows that the ratio of total matter density (including dark matter) to critical density, $\O_0$, is in the range 0.58 to 0.15, and the age $t_0$ of the universe is in the range $8.10 h^{-1}$ Gyr to $12.2 h^{-1}$ Gyr, where $h$ is the present value of the Hubble constant, measured as a fraction of the value 100 km/(s Mpc). This spatially-flat model agrees with estimates of the position of the first acoustic peak in the small angular scale fluctuations of the cosmic background radiation, and with light-element abundances of standard big-bang nucleosynthesis. Our model has only a single free parameter, $m_h$, and does not require that we live at a special time in the evolution of the universe.

Erratum: New quantum aspects of a vacuum-dominated universe [Phys. Rev. D62, 083503 (2000)

In a new model that we proposed, nonperturbative vacuum contributions to the effective action of a free quantized massive scalar field lead to a cosmological solution in which the scalar curvature becomes constant after a time $t_j$ (when the redshift $z \sim 1$) that depends on the mass of the scalar field and its curvature coupling. This spatially-flat solution implies an accelerating universe at the present time and gives a good one-parameter fit to high-redshift Type Ia supernovae (SNe-Ia) data, and the present age and energy density of the universe. Here we show that the imaginary part of the nonperturbative curvature term that causes the cosmological acceleration, implies a particle production rate that agrees with predictions of other methods and extends them to non-zero mass fields. The particle production rate is very small after the transition and is not expected to alter the nature of the cosmological solution. We also show that the equation of state of our model undergoes a transition at $t_j$ from an equation of state dominated by non-relativistic pressureless matter (without a cosmological constant) to an effective equation of state of mixed radiation and cosmological constant, and we derive the equation of state of the vacuum. Finally, we explain why nonperturbative vacuum effects of this ultralow-mass particle do not significantly change standard early universe cosmology.

Classical stochastic approach to cosmology revisited

The classical stochastic model of cosmology recently developed by us is reconsidered. In that approach the parameterw defined by the equation of statep = wp was taken to be fluctuating with mean zero and we compared the theoretical probability distribution function (PDF) for the Hubble parameter with observational data corresponding to a universe with matter and vacuum energy. Even though qualitative agreement between the two was obtained, an attempt is herein made to introduce a more realistic assumption for the mean ofw and use it for the calculations. In the present theory the mean values of bothp andw are taken to be nonzero. The theoretical and observational PDFs are compared for different epochs and values of the Hubble parameter. The corresponding values of the diffusion constantD obtained are approximately constant. We use the scatter in the observed redshift-magnitude data of Type Ia supernova to place limits on the stochastic variation in expansion rate and consequently, on the stochastic variation of the equation of state.

Probing the dark side: Constraints on the dark energy equation of state from CMB, large scale structure, and type Ia supernovae

We have reanalyzed constraints on the equation of state parameter, ${w}_{Q}\ensuremath{\equiv}P/\ensuremath{\rho},$ of the dark energy, using several cosmological data sets and relaxing the usual constraint ${w}_{Q}&gt;~\ensuremath{-}1.$ We find that combining cosmic microwave background, large scale structure, and type Ia supernova data yields a nontrivial lower bound on ${w}_{Q}.$ At 95.4% confidence we find, assuming a flat geometry of the universe, a bound of $\ensuremath{-}2.68&lt;{w}_{Q}&lt;\ensuremath{-}0.78$ if ${w}_{Q}$ is taken to be a completely free parameter. Reassuringly we also find that the constraint ${w}_{Q}&gt;~\ensuremath{-}1$ does not significantly bias the overall allowed region for ${w}_{Q}.$ When this constraint is imposed the 95.4% confidence bound is $\ensuremath{-}1&lt;~{w}_{Q}&lt;\ensuremath{-}0.71.$ Also, a pure cosmological constant $(w=\ensuremath{-}1)$ is an excellent fit to all available data. Based on simulations of future data from the Planck CMB experiment and the SNAP and SNfactory supernova experiments we estimate that it will be possible to constrain ${w}_{Q}$ at the 5% level in the future.

CMB constraints on spatial variations of the vacuum energy density

In a recent article, a simple `spherical bubble' toy model for a spatially varying vacuum energy density was introduced, and type Ia supernovae data was used to constrain it. Here we generalize the model to allow for the fact that we may not necessarily be at the center of a region with a given set of cosmological parameters, and discuss the constraints on these models coming from cosmic microwave background radiation data. We find tight constraints on possible spatial variations of the vacuum energy density for any significant deviations from the center of the bubble and we comment on the relevance of our results.

Supernova type Ia data and the cosmic microwave background of modified curvature at short and large distances

Supernova type Ia data and the cosmic microwave background of modified curvature at short and large distances

Constraining neutrino physics with big bang nucleosynthesis and cosmic microwave background radiation

We perform a likelihood analysis of the recent results on the anisotropy of cosmic microwave background radiation from the BOOMERanG and DASI experiments to show that they single out an effective number of neutrinos in good agreement with standard big bang nucleosynthesis. We also consider degenerate big bang nucleosynthesis to provide new bounds on effective relativistic degrees of freedom ${N}_{\ensuremath{\nu}}$ and, in particular, on the neutrino chemical potential ${\ensuremath{\xi}}_{\ensuremath{\alpha}}.$ When including supernova type Ia data we find, at $2\ensuremath{\sigma},$ ${N}_{\ensuremath{\nu}}&lt;~7$ and $\ensuremath{-}0.01&lt;~{\ensuremath{\xi}}_{e}&lt;~0.22,$ $|{\ensuremath{\xi}}_{\ensuremath{\mu},\ensuremath{\tau}}|&lt;~2.6.$

Supernova type Ia data and the cosmic microwave background of modified curvature at short and large distances

The SNIa data, although inconclusive, when combined with other observations makes a strong case that our universe is presently dominated by dark energy. We investigate the possibility that large distance modifications of the curvature of the universe would perhaps offer an alternative explanation of the observation. Our calculations indicate that a universe made up of no dark energy but instead, with a modified curvature at large scales, is not scale invariant; therefore quite likely it is ruled out by the CMB observations. The sensitivity of the CMB spectrum is checked for the whole range of mode modifications of large or short distance physics. The spectrum is robust against modifications of short-distance physics and the UV cutoff when the initial state is the adiabatic vacuum, and the inflationary background space is de Sitter space.